In this study, we obtained results for the computation of eigen-pairs, singular value decomposition, pseudo-inverse, and the least square problem for elliptic quaternion matrices. Moreover, we established algorithms based on these results and provided illustrative numerical experiments to substantiate the accuracy of our conclusions. In the experiments, it was observed that the p-value in the algebra of elliptic quaternions and elliptic numbers directly affects the performance of the problem under consideration. Selecting the optimal p-value for problem-solving and the elliptic behavior of many physical systems make this number system advantageous in applied sciences.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

In photolithography process, nanometer level precise, wavefront aberration models enable the machine to be able to meet the overlay (OVL) drift and critical dimension (CD) specifications. Software control algorithms take as input these models and correct any expected wavefront imperfections before reaching the wafer. In such way a near optimal image is exposed on the wafer surface. Optimizing the parameters of these models though, involves several time costly sensor measurements which reduce the throughput performance, in terms of exposed wafers per hour, of the machine. In that case, photolithography machines come across the trade-off between throughput and quality. Therefore one of the most common Optimal Experimental Design (OED) problems in photolithography machines (and not only) is how to choose the minimum amount of sensor measurements that will provide the maximum amount of information. Additionally, each sensor measurement corresponds to a point on the wafer surface and therefore we must measure uniformly around the wafer surface as well. In order to solve this problem, we propose a Sensor Marks Selection Algorithm which exploits Genetic Algorithms. The proposed solution first selects a pool of points that qualify as candidates to be selected in order to meet the uniformity constraint. Then, the point that provides the maximum amount of information, quantified by the Fisher based criteria of G, D and A-Optimality, is selected and added to the measurement scheme. This process though is considered "greedy", and for this reason Genetic Algorithms (GA) are exploited to further improve the solution. By repeating in parallel the "greedy" part several times we get an initial population that will be the input to our GA. This meta-heuristic approach outperforms the "greedy" approach significantly. The proposed solution is applied in a real life semiconductors industry use case and achieves interesting industry and academical results as well.

For order-of-addition experiments, the response is affected by the addition order of the experimental materials. Consequently, the main interest focuses on creating a predictive model and an optimal design for optimizing the response. Van Nostrand (1995) proposed the pairwise-order (PWO) model for detecting PWO effects. Under the PWO model, the full PWO design is optimal under various criteria but is often unaffordable because of the large run size. In this paper, we consider the D-, A- and M.S.-optimal fractional PWO designs. We first present some results on information matrices. Then, a flexible and efficient algorithm is given for generating these optimal PWO designs. Numerical simulation shows that the generated design has an appealing efficiency in comparison with the full PWO design, though with only a small fraction of runs. Several comparisons with existing designs illustrate that the generated designs achieve better efficiencies, and the best PWO designs and some selected 100% efficient PWO designs generated by the new algorithm are reported.

In some applications of microgrid and distributed generation, it is required to feed islanded or stand-alone loads with high-quality voltage to provide low total harmonic distortion (THD). To fulfil these demands, an LC filter is connected to the output terminals of power electronics converters. A cascaded voltage and current control loop with pulse-width modulation schemes are used to regulate the voltage and current in these systems. However, these strategies have some drawbacks, particularly when multiple-input multiple-output plants (MIMO) are controlled using single-input single-output (SISO) design methods. This methodology usually produces a sluggish transient response and cross-coupling between different control loops. In this paper, a model predictive control (MPC) strategy based on the concept of optimal switching sequences (OSS) is designed to control voltage and current in an LC filter connected to a three-level neutral-point clamped converter. The strategy solves two well-formulated optimisation problems to achieve control of the LC filter variables and the voltages of the DC-link capacitors. Hardware-in-the-Loop (HIL) results are obtained to validate the feasibility of the proposed strategy, using a PLECS-RT HIL platform and a DSP Microlab Box controller. In addition to the good dynamic performance of the proposed OSS-MPC, it is demonstrated by the HIL results that the control algorithm is capable of obtaining low total harmonic distortion (THD) in the output voltage for different conditions.

Autonomous navigation of spacecraft necessitates innovative technologies, methods, and algorithms, particularly when orbiting in proximity of other space objects. Optimization methods are useful for autonomous spacecraft navigation, guidance, and control, but their performance is hampered by noisy multi-sensor technologies and poorly modeled system equations, and real-time on-board utilization is generally computationally burdensome. Some proposed methods use noisy sensor data to learn the optimal guidance and control solutions real-time (online), where non-iterative instantiations are preferred to reduce computational burdens. This study aims to highlight efficacy and limitations of several common methods for optimizing guidance and control while proposing a few more, where all methods are applied to the full, nonlinear, coupled equations of motion including cross-products of motion from the transport theorem. Five disparate types of optimum guidance and control algorithms are presented and compared to a classical benchmark. Comparative analysis is based on tracking errors (both states and rates), fuel usage, and computational burden. Real-time optimalization with singular switching plus nonlinear transport theorem decoupling proves superior by matching open-loop solutions to the constrained optimization problem (in terms of state and rate errors and fuel usage), while robustness is validated in the utilization of mixed, noisy state and rate sensors and uniformly varying mass and mass moments of inertia. State tracking errors are reduced one-hundred ten percent. Rate tracking errors are reduced one-hundred thirteen percent. Control utilization (e.g., fuel) is reduced eighty four percent, while computational burden in reduced ten percent simultaneously.

This research proposes a methodology for minimizing losses in transmission lines (LT), considering the reconfiguration of the architecture of the electrical power system (SEP). The implementation of this methodology redirects the power flow with optimal switching through its LTs to guarantee the stability of the voltage, angle, frequency, and power balance to minimize losses that affect the reliability and quality of the system. Optimal transmission switching (OTS) allows various types of analysis to be carried out, where the loadability of the lines, response times, and operating costs, among others, can be improved. This article proposes to minimize the losses in the transmission lines with the OTS by using AC power flows as a mixed integer nonlinear problem (MINLP). Several test scenarios evaluate the method’s effectiveness, determining the optimal topology for corrective control that optimizes power flows in different situations. It has been proven that this approach reduces losses compared to a base case by 99%, even in the face of N-1 or random contingencies, without losing load, maintaining the same active power dispatch, and finally verifying a strategic increase in dispatch of reactive power to maintain operating parameters within stable limits.

In this paper we analyze and propose new method and algorithm of selecting the optimal labor time as a function of skills following our main references Mirrlees (1971), Saez (2001) and Stancheva (2014). The optimal labor time is a situation when the utility function of individual reaches a maximum. One of the main differences with Saez (2001) is our algorithm for creation the skill distribution.

We consider a constrained optimal control problem and an extension of it, in which the set of strict-sense trajectories is enlarged. Extension is a common procedure in optimal control, used to derive necessary and sufficient optimality conditions for the original problem from the extended one, which usually admits a minimizer and has a more regular structure. However, this procedure fails if the two problems have different infima. It is therefore relevant to identify such situations. Following on from earlier work by Warga but adopting perturbation techniques developed in non-smooth analysis, we investigate the relation between the occurrence of an infimum gap and abnormality of necessary conditions. For a notion of local minimizer based on control distance and an extension including the impulsive one, we prove that (i) a local extended minimizer which is not a local minimizer of the original problem and (ii) a local strict-sense minimizer which is not a local minimizer of the extended problem, both satisfy the extended maximum principle in abnormal form. The main novelty is result (ii), as until now it had only been shown that a strict-sense minimizer which is not an extended minimizer is abnormal for an `averaged version’ of the maximum principle.

The radial distribution networks are designed for unidirectional power flows and are passive in nature. However, with the penetration of Distributed Generation (DG), the power flow becomes bidirectional and the network becomes active. The integration of DGs into distribution network creates many issues with: system stability, protection coordination, power quality, islanding, proper placement and sizing etc. Among these issues, the two most significant are optimal sizing and placement of DGs and their protection coordination in utility network. The proper coordination of relays with high penetration of DGs placed at optimal location increases the availability and reliability of the network during abnormal operating conditions.This research addresses most of the available methods for efficient sizing and placement of DGs in distribution system (numerical, analytical and heuristic) as well as the developed protection coordination techniques for utility networks in the presence of DGs (Artificial Intelligence (AI), adaptive and non-adaptive, multi-agent, hybrid). This paper indicates the possible research gaps and highlights the applications possibilities and methods’ limitations in the area of DGs.

In this paper, modelling designing and simulation of a simple voltage amplidyne system is done using robust control theory. In order to increase the performance of the voltage amplidyne system with H ∞ optimal control synthesis and H ∞ optimal control synthesis via ∞-iteration controllers are used. The open loop response of the voltage amplidyne system shows that the system can amplify the input 7 times. Comparison of the voltage amplidyne system with H ∞ optimal control synthesis and H ∞ optimal control synthesis via ∞-iteration controllers to track a desired step input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed voltage amplidyne system with H ∞ optimal control synthesis controller in improving the percentage overshoot and the settling time.

The Combined Inversion of Surface and AeRosols (CISAR) algorithm for the joint retrieval of surface and aerosol single scattering properties has been further developed in order to extend the retrieval to clouds and overcome the need for an external cloud mask. Pixels located in the transition zone between pure cloud and pure aerosol are often discarded by both aerosol and cloud algorithms, despite being essential for studying aerosol-cloud interactions, which still represent the largest source of uncertainty in climate predictions. The proposed approach aims at filling this gap and deepening the understanding of aerosol properties in cloudy environments. The new CISAR version is applied to Sentinel-3A/SLSTR observations and evaluated against different satellite products and ground measurements. The spatial coverage is greatly improved with respect to algorithms processing only pixels flagged as clear sky by the SLSTR cloud mask. The continuous retrieval of aerosol properties without any safety zone around clouds opens new possibilities for studying aerosol properties in cloudy environments.

This brief report presents a comparative analysis to examine differences in the mean dose of nitrate supplementation between studies with positive and negative results on exercise performance. Protocols of at least six days that had positive results used lower nitrate doses (~7.7 mmol), whereas those with negative results used higher doses (~10.2 mmol), showing a statistically significant difference (p < 0.05). These findings suggest long-term supplementation with higher doses (~10.2 mmol) may not improve exercise performance. Further research is essential to understand the underlying mechanisms.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

The paper deals with two new properties of the linear time-optimal control problems with real non-positive eigenvalues of the system. They are the foundation of a new method of synthesizing the time-optimal control without the need to describe the switching hyper-surfaces. The so called “axes initialization” and the synthesis technique are illustrated on the already classical example of the time-optimal control of a double integrator.

The paper deals with one new property of the linear time-optimal control problems with real eigenvalues of the system, no matter of the number of eigenvalue multiplicity. This property unveils a prospective of synthesizing the time-optimal control without the need of describing the switching hyper-surfaces. The already chrestomathy example of the time-optimal control of a double integrator is resolved by the new technique and compared with the classical synthesis.

In this study, we investigate different control scenarios through theoretical analysis and numerical simulations. To account for two important types of control for an early ascending stage of an outbreak, social distancing and treatment with antiviral medications, a compartmental model is considered with one control, $u_1(t)$, aimed to lower the disease transmission rate and the other control, $u_2(t)$, aimed to lower the period of infectiousness. In all experiments, the implementation of control strategies reduces the daily cumulative number of cases and successfully "flattens the curve". The reduction in the cumulative cases is achieved by eliminating or delaying new cases. This delay is incredibly valuable as it provides public health organizations with more time to advance antiviral treatments and devise alternative preventive measures. The main theoretical result of the paper, Theorem 3.1, concludes that the optimal control functions, $u_i(t)$, $i=1,2,$ may be increasing until some moment $\tau \in [0, T)$. However, for all $t \in [\tau, T]$, both controls, $u_i(t)$, decline as $t$ approaches $T$ (possibly causing the number of newly infected people to grow). Numerical simulations presented in Section 4 confirm theoretical findings, which indicates that, ideally, around the time $t=\tau$, the control strategy has to be upgraded and a vaccination campaign needs to start to ensure the epidemic wave does not rebound.

Using metaheuristics, such as the Evolutionary Algorithm (EA), within control structures is a realistic approach for certain optimal control problems. Their role is often predicting the optimal control values over a prediction horizon using a process model (PM). The big computational effort sometimes causes problems. Our work addresses a new issue: whether a machine learning (ML) algorithm could “learn” the optimal behaviour of the couple (EA, PM). A positive answer is given by proposing datasets apprehending this couple's optimal behaviour and appropriate ML models. Following a design procedure, a number of closed-loop simulations will provide the sequences of optimal control and state values, which are collected and aggregated in a data structure. For each sampling period, datasets are extracted from the aggregated data. The ML algorithm experiencing these datasets will produce a set of regression functions. Replacing the EA predictor with the ML model, new simulations are carried out, proving that the state evolution is almost identical. The execution time decreases drastically because the PM’s numerical integrations are totally avoided. The performance index equals the best-known value. In different case studies, the ML models succeeded in capturing the optimal behaviour of the couple (EA, PM) and yielded efficient controllers.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

This paper addresses a wildlife monitoring problem using a team of UAVs for efficient monitoring of wildlife. The state-of-the-art technology using UAVs has been an increasingly popular tool to monitor wildlife compared to the traditional methods such as satellite imagery-based sensing or GPS trackers. However, there still exist unsolved problems as to how the UAVs need to cover a spacious domain to detect animals as many as possible. In this paper, we propose the optimal transport-based wildlife monitoring strategy for a multi-UAV system, to prioritize monitoring areas while incorporating complementary information such as GPS trackers and satellite-based sensing. Through the proposed scheme, the UAVs can explore the large-size domain effectively and collaboratively with a given priority. The time-varying nature of wildlife due to their movements is modeled as a stochastic process, which is included in the proposed work to reflect the spatio-temporal evolution of their position estimation. In this way, the proposed monitoring plan can lead to efficient wildlife monitoring with a high detection rate. Various simulation results including statistical data are provided to validate the proposed work.

In this paper, a horizontally moving suspended mass pendulum base is designed and controlled using robust control theory. H infinity optimal loop shaping with first and second order desired loop shaping function controllers are used to improve the performance of the system using Matlab/Simulink Toolbox. Comparison of the H infinity optimal loop shaping with first and second order desired loop shaping function controllers for the proposed system have been done to track the desired angular position of the pendulum using step and sine wave input signals and a promising result has been obtained succesfully.

A vehicle boom barrier gate system is one of the recently developed technologies operating at the entrances to the restricted areas. This paper aims to design and control of vehicle’s boom barrier gate system using robust augmentation technique. H 2 optimal and H infinity synthesis controllers are used to improve the performance of the system. The open loop response analysis of the vehicle boom barrier gate system shows that the input of the system need to be improved. Comparison of the vehicle boom barrier gate system with H2 optimal and H infinity synthesis controllers have been done to track a set point desired angular position using a step and operational open and close input signals and a promising results have been observed.

This paper mainly analyzes the design and control of the rotational inverted pendulum, and presents a state space expression. Since the system is highly unstable a feedback control system is used. Augmentations with weighting functions based mixed sensetivity and H2 optimal control methods are used to make the system stable for uprise position. The rotational inverted pendulum have been simulated and compared with the proposed controllers and a promising results have been analyzed sussesfuly.

In this paper, the design and control of a hydraulic system based tire changer machine have been analyzed and simulated using Matlab/Simulink Toolbox successfully. The machine have a displacement input which is a leg pedal displacement in order to push the piston of the pump to fed the motor with a pressured hydraulic fluid to rotate the tire with an angular speed to mount and dismount it. Augmentation based H_∞ and H₂ optimal synthesis controllers have been used to improve the performance of the machine. Comparison of the proposed controllers for tracking a reference input speed have been done using two reference inputs (step and random) signals. Finally the comparative simulation results proved the effectiveness of the proposed tire changer with H synthesis controller in improving the settling time and percentage overshoot.

Optimal conditions for maximum efficacy of photoinitiated polymerization are theoretically presented. Analytic formulas are shown for the crosslink time, crosslink depth and efficacy function. The roles of photoinitiator (PI) concentration, diffusion depth and light intensity on the polymerization spatial and temporal profiles, for both uniform and non-uniform cases, are presented. For optimal efficacy, a strategy via controlled PI concentration is proposed, where re-supply of PI in high light intensity may achieve a combined-efficacy similar to low light intensity, but has a much faster procedure. A new criterion of efficacy based on the polymerization (crosslink) [strength] and [depth] is introduced. Experimental data are analyzed for the role of PI concentration and light intensity on the gelation time and efficacy.

In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analysis was carried out using varieties of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs ketogenic diet and cancer emission when anti-cancer drugs, immune-booster, ketogenic diet are included were established. Furthermore, optimal control theory is applied to find out the optimal drug adjustment as an input control of the system therapies to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin’s Maximum Principle. Numerical simulations were presented to validate our theoretical results.

Bipedal locomotion remains one of the major open challenges of humanoid robotics. The common approaches are based on simple reduced model dynamics to generate walking trajectories, often neglecting the whole-body dynamics of the robots. As motions in nature are often considered as optimal with respect to certain criteria, in this work we present an optimal control based approach that allows us to generate optimized walking motions using a precise whole-body dynamic model of the robot, in contrast with the common approaches. The optimal control problem is formulated to minimize a set of desired objective functions with respect to physical constraints of the robot and contact constraints of the walking phases. We apply the method with combinations of different objective criteria to the model of a reduced version of the iCub humanoid robot of 15 internal DOF. The obtained trajectories are executed on the real robot and we carry out a discussion on the differences between the outcomes of this approach with the classic approaches.

In this paper, modelling designing and simulation of a Ward Leonard layout system is done using robust control theory. In order to increase the performance of the Ward Leonard layout system with H infinity optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers are used. The open loop response of the Ward Leonard layout system shows that the system needs to be improved. Comparison of the Ward Leonard layout system with H∞ optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers to track a desired step speed input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed Ward Leonard layout system with H infinity optimal control synthesis controller in improving the percentage overshoot and the settling time.

In recent decades, the cultivation of avocados has expanded throughout the Iberian Peninsula, with most of the production occurring on the southern Atlantic and Mediterranean coast, as well as in the Canary Islands and the north. This expansion is due to high demand and high prices, which have made the crop very attractive. However, climatic suitability criteria have not always been followed, putting sustainability at risk. Avocados originate from tropical and subtropical areas and have very specific climatic requirements that must be met to ensure good production. This study analyzed key climatic variables, including winter cold damage, pollen viability, and flowering and fruit set temperatures. Using daily climate data from 1975 to 2022, advanced spatial analysis techniques were applied to produce suitability maps. The results indicate that the ex-pansion of the crop is possible in certain areas of southern Andalusia, but not in the rest of the peninsula. Minimum winter and March temperatures are the main limiting factors. This work provides valuable insights into the potential for sustainable agricultural intensification, the sus-tainability of agricultural decision-making, and resilience to climate change.

Some optimal control problems need metaheuristics in searching for the optimal solution, especially when the process has certain characteristics like the Photobioreactor for Algae Growth (distributed parameter, nonlinearities, etc.). Particle Swarm Optimization (PSO) algorithms within control structures are a realistic approach; their task is often to predict the optimal control values working with a process model (PM). Owing to numerous numerical integrations, there is a big computational effort that is reflected in a large controller execution time. The authors propose to replace the PSO predictor with a machine learning model that has “learned” the quasi-optimal behavior of the couple (PSO, PM); the training data is obtained through closed-loop simulations over the control horizon. The new controller should preserve the process’s quasi-optimal control. In identical conditions, the process evolutions must also be quasi-optimal. The multiple Linear Regression and the Regression Neural Networks were considered as predicting models. The paper first proposes algorithms for collecting and aggregating data sets for the learning process. Algorithms for constructing the machine learning models, implementing the controllers, and closed-loop simulations are also proposed. The simulations prove that the two machine learning predictors have learned the PSO predictor’s behavior such that the process evolves almost identically. The resulting controllers’ execution time drastically decreased while keeping their optimality.

To assure the opacity, an optimal problem is to retain the occurring events sequences as many as possible. Contrary to such problem, the other optimal problem is to preserve the minimal occurring events sequences. In the paper, based on the choosing cost, an optimal opacity-enforcing model is presented to minimize the sum of discount choosing cost, which is not only to preserve the opacity, but also to retain the secret to the maximum. To solve the model, two scenarios on opacity are considered. For the two scenarios, some algorithms are presented to achieve the optimal solution for the model by using the method of dynamic programming. And then, the solutions produced by the algorithms are proved correctly by theoretical proof. Finally, some illustrations for the algorithms are given.

In this paper we study a bilinear optimal control problem related to a 2D parabolic-elliptic chemo-repulsion system consider a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a result on the existence of Lagrange multipliers in Banach spaces, we derive an optimality system for a local optimal solution.

A study to produce cellulose nanofibrils (CNF) from Kraft cellulose pulp, an optimal enzyme mixture, was defined using a centroid simplex mixture design. The enzyme blend contains 69% endoglucanase and 31% exoglucanase. The central composite rotational design (CCRD) optimized the CNF production process by achieving a higher crystallinity index. It thus corresponded to a solid loading of 15 g/L and an enzyme loading of 0.974. Using the Segal formula, the crystallinity index (CrI) of CNF was determined by X-ray diffraction to be 80.87%. The average diameter of nanocellulose fibers measured by scanning electron microscopy between 550 - 600 nm for the CNF prepared by enzymatic hydrolysis and between 250 - 300 nm for the CNF produced by enzymatic hydrolysis with the optimal enzyme mixture followed by ultrasonic dispersion. Finally, synergistic interactions between the enzymes involved in nanocellulose production were demonstrated, with Colby factor values greater than one.

In this paper we present AWEbox, a Python toolbox for modeling and optimal control of multi-aircraft systems for airborne wind energy (AWE). AWEbox provides an implementation of optimization-friendly multi-aircraft AWE dynamics for a wide range of system architectures and modeling options. It automatically formulates typical AWE optimal control problems based on these models, and finds a numerical solution in a reliable and efficient fashion. To obtain a high level of reliability and efficiency, the toolbox implements different homotopy methods for initial guess refinement. The first type of methods produces a feasible initial guess from an analytic initial guess based on user-provided parameters. The second type implements a warmstart procedure for parametric sweeps. We investigate the software performance in two different case studies. In the first case study we solve a single-aircraft reference problem for a large number of different initial guesses. The homotopy methods reduce the expected computation time by a factor of 1.7 and and the peak computation time by a factor of 8, compared to when no homotopy is applied. Overall, the CPU timings are competitive to timings reported in the literature. When the user initialization draws on expert a priori knowledge, homotopies do not increase expected performance, but the peak CPU time is still reduced by a factor of 5.5. In the second case study, a power curve for a dual-aircraft lift-mode AWE system is computed using the two different homotopy types for initial guess refinement. On average, the second homotopy type, which is tailored for parametric sweeps, outperforms the first type in terms of CPU time by a factor of 3. In conclusion, AWEbox provides an open-source implementation of efficient and reliable optimal control methods that both control experts and non-expert AWE developers can benefit from.

A proxy war, between a coalition of countries, BLUE and a country, RED, is considered. RED wants to increase the size of the RED territory. BLUE wants to involve more regions in trade and other types of cooperation. GREEN is a small and independent nation that wants to become a member of BLUE. RED attacks GREEN and tries to invade. BLUE decides to give optimal arms support to GREEN. This support can help GREEN in the war against RED and simultaneously reduce the military power of RED, which is valuable to BLUE, also outside this proxy war, since RED may confront BLUE also in other regions. The optimal control problem of dynamic arms support, from the BLUE perspective, is defined in general form. The objective function is a weighted sum of the present value of the free GREEN territory and the present value to BLUE of the net loss of military resources in the RED army. The net loss of RED at a particular point in time is a function of the location of the front line and the size of the mobile GREEN forces behind the RED line. First, it is assumed that the expected net loss is proportional to the force ratio behind the red front line. It is proved that the net loss function is a strictly concave quadratic function of x, the location of the front line. It is also proved that the unique maximum of the net loss function occurs at the same front location, also if the net loss function is proportional to the strength ratio behind the RED lines, raised to any strictly positive exponent. From the BLUE perspective, there is an optimal position of the front. This position is a function of the weights in the objective function and all other parameters. Optimal control theory is used to determine the optimal dynamic BLUE strategy, conditional on a RED strategy, which is observed by BLUE military intelligence. The optimal arms support strategy for BLUE is to initially send a large volume of arms support to GREEN, to rapidly move the front to the optimal position. Then, the support should be almost constant during most of the war, keeping the war front location stationary. In the final part of the conflict, when RED will have almost no military resources left and tries to retire from the GREEN territory, BLUE should strongly increase the arms support and make sure that GREEN rapidly can regain the complete territory and end the war

: Solar sails use radiation from the sun to generate thrust without any fuel or propellant. Since this is a form of propulsion that has theoretically infinite use, we would like to test its capability on long-term missions by simulating a spacecraft equipped with solar sails to the Sun-Earth L5 Lagrange point. To control the sail angle, which is the main form of control we have over the sail’s performance, we will devise a form of optimal control based on Pontryagin’s Minimum Principle. Simulating the dynamics in MATLAB SIMULINK, we find that such a control method relies on iterating over initial conditions for the co-states to find the necessary parameters for the trajectory to reach the desired point. Therefore, an autonomous control scheme that uses this form of optimal control will need a way to numerically find said initial conditions in order to find the control angle needed at any point in time, which may be computationally intensive.

The increasing penetration of renewable energy sources in power grids highlights the role of battery energy stor- age systems (BESSs) in enhancing the stability and reliability of electricity. A key challenge with the renewables’, specially the BESSs, integration into the power system is the lack of proper dynamic model for stability analysis. Moreover, a proper control design for the power system is a complicated issue due to its complexity and inter-connectivity. Thus, the application of decentralized control to improve the stability of a large- scale power system is inevitable, especially in distributed energy sources (DERs). This paper presents an optimal distributed hybrid control design for the interconnected systems to suppress the effects of small disturbances in the power system employing utility-scale batteries based on existing battery models. The results show that i) the smart scheduling of the batteries’ output reduces the inter-area oscillations and improves the stability of the power systems; ii) the hybrid model of the battery is more user-friendly compared to the Western electricity coordinating council (WECC) model in power system analysis.

In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+ T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.

The main ideas of F-transform came from representing expert rules. It would be therefore re reasonable to expect that the more accurately the membership functions describe human reasoning, the more efficient will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions -- however, somewhat surprisingly, most efficient applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon which are based on local behavior of the signal. In this paper, we supplement this local explanation by a global one: namely, we prove that triangular membership functions are the only one that provide the accurate description of appropriate global characteristics of the signal.

The diffusion of electric vehicles (EVs) can be sustained by the presence of integrated solutions offering parking and clean power supply. The recourse to DC systems allows to better integrate EV bidirectional energy exchange, photovoltaic panels and energy storage. In this paper, a methodology for optimal techno-economic sizing of a DC-microgrid for covering EV mobility needs is carried out. It is based on the definition of different scenarios of operation, according to typical EV usage outlooks and environmental conditions. In each scenario, optimal operation is carried out by means of a specific approach for EV commitment on different stations. The sizing procedure is able to handle the modular structure of microgrid devices. The proposed approach is applied to a case study of envisaged EV service fleet for Bari port authority.

Malaria and Pneumonia are leading causes of serious illness in children and adults worldwide with their death rate and prevalence on the rise. Such alarming statistics may retard the milestones so far achieved in meeting the Millennium Development Goals 4 and 6 whose targets are to improve child survival and reverse the high prevalence of diseases such as pneumonia and malaria respectively. Two sub-models of malaria-pneumonia co-infection namely malaria model and pneumonia model were considered first and then followed by the full malaria-pneumonia co-infection model. The malaria model, pneumonia model and co-infection model basic reproduction numbers denoted by R_m, R_p and R_mp respectively was obtained using the Next Generation Matrix method. The model disease free equilibrium’s local and global stability was analysed using Descartes’ Rule of signs and Comparison method. The bifurcation analysis for the malaria, pneumonia and co-infection models was studied using the Centre Manifold Theory. The sensitivity indices of the model basic reproduction numbers R_m, R_p and R_mp to the parameters in the models were calculated. Optimal control theory was applied using the Pontryagins’ Maximum Principle to investigate optimal strategies for controlling the spread of malaria, pneumonia and co-infection models using insecticide treated bed nets (u₁(t)) spraying of mosquitoes insecticides (u₂(t)), sanitation (u₃(t)), vaccination (u₄(t)), anti-malaria drugs (u₅(t)), anti-pneumonia drugs (u₆(t)), both anti-malaria drugs and anti-pneumonia drugs (u₇(t)) as the system time control variables. Numerical simulations using a set of parameter values were provided to validate the analytical results.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

The integration of diverse distributed generation (DG) units, encompassing both Renewable Energy Sources (RES) and non-RES technologies delves into voltage levels, current distributions, and power flows, aiming to optimize and effectively manage the distribution network. An RES-based DGs such as photovoltaic systems and wind turbines, alongside non-RES units like fuel cells and micro turbines. This study proposes a hybrid approach the Multi-Objective Genetic Algorithm - Grey Wolf Optimizer (MOGA-GWO). By merging the strengths of multi-objective genetic algorithms with the efficiency of the Grey Wolf Optimizer, this advanced algorithm seeks semi-optimal solutions for multi-objective optimization problems. The algorithm aims to improve convergence speed without compromising solution quality, offering a promising solution for optimizing the characteristics of DG and RES integration in distribution networks compared to Cuckoo Search and Simulation Annealing Techniques. Key algorithmic operations include individual representation, initialization, fitness function computation, selection, crossover, mutation, and ending conditions. The DG optimal power flow problem is explored with a focus on minimizing generation costs, improving voltage profiles, minimizing losses, enhancing reliability, integrating renewable energy, reducing environmental impact, managing congestion, and ensuring compliance with operational constraints. Beyond traditional considerations, the study emphasizes neglected objectives and constraints, such as cyber-security concerns, real-time operation, regulatory frameworks, social acceptance, lifecycle environmental impact, grid resilience, data privacy, aging infrastructure compatibility, and economic viability.

This paper concentrates on computing the efficiency of heliostat field systems. By conducting a comprehensive analysis of the mathematical model for optical efficiency, we have effectively simplified the complex three-dimensional illumination problem of heliostat fields into a two-dimensional issue. Our work primarily investigates the calculation methods for the average optical efficiency and output power of heliostat. Traditionally, calculating shadow and blocking efficiency, key factors affecting the optical performance of mirror fields, has posed a significant technical challenge. Through innovative improvements to the Monte Carlo simulation technique, this study has successfully reduced the spatial dimensionality of the problem. We employed a series of novel coordinate transformations to simulate light tracing on a two-dimensional plane, thereby efficiently calculating the efficiency of shadows and obstructions. Not only have we solved the computational challenges of shadow and obstruction efficiency, but our unique algorithm design also allows us to precisely obtain the overall average optical efficiency of the heliostat field while enhancing computational efficiency.

Dynamic systems which underly controlled systems are expected to increase in complexity as robots, devices, and connected networks become more intelligent. While classical stable systems converge to a stable point (a sink), another type of stability is to consider a stable path rather than a single point. Such stable paths can be made of saddles which draw in trajectories from certain regions, and then push the trajectory toward the next saddle point. These are chains of saddles are called stable heteroclinic channels (SHCs), and can be used in robotic control to represent time sequences. While we have previously shown that each saddle is visualizable as a trajectory waypoint in phase space, how to increase the fidelity of the trajectory was unclear. In this paper, we hypothesized that the waypoints can be individually modified to locally vary fidelity. Specifically, we expected that increasing the saddle value (ratio of saddle eigenvalues) causes the trajectory to slow to more closely approach a particular saddle. Combined with other parameters that control speed and magnitude, a system expressed with an SHC can be modified locally, point by point, without disrupting the rest of the path, supporting their use in motion primitives. However, even more complex trajectory shape modifications are possible. While some combinations can enable a trajectory to better reach into corners, other combinations can rotate, distort and round the trajectory in the region of a corner. In our example, modifying select saddle values produced a 32% decrease in the trajectory error of a complex trajectory produced using this system. This is an effect not visible in previous 1D studies, that can lead to different learnable and tunable representations of dynamic systems.

Water plays a vital role in the healthy growth of pears. Early detection of water stress can play a significant role in the timely management of water deficiency for pear yield. Most current methods are labour-intensive, time-consuming, only provide point measurements, and could be destructive. In this research, a real-time non-destructive method using a push-broom hyperspectral system (400-1000nm) was used to collect hyperspectral image data and detect the water stress of the pear seedling leaves. To build a reliable prediction model, machine learning techniques were used. The Successive Projections Algorithm (SPA) was applied for optimal wavelength selection. In particular, CNN was applied to obtain the features of key wavelengths. Both the CNN features and key wavelengths were put into RR-MLR, BLR and ENN for analysis. The training accuracy of the three modellings all reach the accuracy above 70% after about 100 epochs, while combination of CNN features outperformed the mere main spectra analysis. This research demonstrated that hyperspectral imaging coupled with machine learning techniques could be applied to predict the water content of pear leaves predict non-destructively.

The spread of high-performance personal computers, frequently equipped with powerful Graphic Processing Units (GPU), raised the interest on a set of techniques able to extract models of electromagnetic phenomena (and devices) directly from available examples of the desired behavior. Such approaches are collectively referred to as Machine Learning (ML). A typical representative ML approach is the so called “Neural Network” (NN). Using such data-driven models allows evaluating the output in a much shorter time when a theoretical model is available, or allows predicting the behavior of the systems and devices when no theoretical model is available. With reference to a simple yet representative benchmark electromagnetic problem, some of the possibilities and the pitfalls of the use of NN for the interpretation of measurements (inverse problem) or to obtain the required measurements (optimal design problem) are discussed. The investigated aspects include the choice of the NN model; the generation of the dataset(s); the selection of hyperparameters (hidden layers, training paradigm). Finally, the capabilities in the handling of ill-posed problems are critically revised.

This paper is primarily focused on the robust control of an inverted pendulum system based on the policy iteration in reinforcement learning. First, a mathematical model of the single inverted pendulum system is established through a force analysis of the pendulum and trolley. Second, based on the theory of robust optimal control, the robust control of the uncertain linear inverted pendulum system is transformed into an optimal control problem with an appropriate performance index. Moreover, for the uncertain linear and nonlinear systems, two reinforcement-learning control algorithms are proposed using the policy iteration method. Finally, two numerical examples are provided to validate the reinforcement learning algorithms for the robust control of the inverted pendulum systems.

Recent technological advances have significantly increased the data volume obtained from deep space exploration missions, making the downlink rate a primary limiting factor. Particularly, JAXA’s Martian Moons eXploration (MMX) mission encounters this problem when identifying safe and scientifically valuable landing sites on Phobos using high-resolution images. A strategic approach in which we effectively reduce image data volumes without compromising essential scientific information is thus required. In this work, we investigate the influence of image data compression, especially as it concerns the accuracy of generating the local Digital Terrain Models (DTMs) that will be used to determine MMX’s landing sites. We obtain simulated images of Phobos that are compressed using the CCSDS-120 with integer/float-point discrete wavelet transform (DWT), candidate algorithms for the MMX mission. Accordingly, we show that, if the compression ratio is 70% or lower, the effect of image compression remains constrained, and local DTMs can be generated within altitude errors of 40 cm on the surface of Phobos, which is ideal for selecting safe landing spots. We conclude that the compression ratio can be increased as high as 70%, and such compression enables us to facilitate critical phases in the MMX mission even with the limited downlink rate.

In this paper we derive a unified perspective for Optimal Transport (OT) theory and Mean Field Control (MFC) theory to analyse the learning process for Neural Networks algorithms in a high-dimensional framework. We consider Mean Field Neural Networks in the context of MFC theory, specifically the mean field formulation of OT theory that allows the development of highly efficient algorithms while providing a powerful tool in the context of explainable Artificial Intelligence.

The perception in pair trading is to recognize two stocks that move together, and their prices will converge to a mean value in future. However, finding the mean-reverted point at which the value of the pair will converge, and optimal boundaries of the trade is not easy. As uncertainty and model misspecifications may lead to losses. To cater for the problems, this study employs the novel entropic approach that utilizes entropy as penalty function for the misspecification of the model. The use of entropy as a measure of risk in pair trading is a nascent idea and this study utilizes daily data for 64 companies listed on PSX for the years 2017, 2018, and 2019, respectively to compute the returns based on the entropic approach. These companies cover the major sectors including Cement, Chemical, Automobile Assembler, Food and Personal Care Products, Oil and Gas Marketing Companies, Oil and Gas Exploration Companies Ltd, Power Generation and Distribution, Refinery and Pharmaceuticals. The returns to these stocks are then evaluated and compared with the Buy and Hold strategy. The results show positive and significant returns from pair trading using an entropic approach.

The sudden onset of the Covid-19 pandemic disrupted the modern multi-national interconnected society and led the countries and societies to enforce unprecedented restrictions on movement. Among myriad containment measures, the policy of trace and quarantine found universal adoption among countries; the swift adoption of the policy was soon met with widespread criticism and opposition activists who questioned the utility and the risk associated with such a large scale collection of data and infringement on the movement of individuals. Consequently, one often tends to be either pro- or anti-trace and quarantine; the ensuing polarizing and politicized left little room for nuance. In this work, we undertake a methodology study to understand the nuances of the impact of different implementations of trace and quarantine. To this end, we design a user-friendly and intuitive tool that can be employed by experts to model the disease dynamics and societal structure. We focus on the study of the cost of policy with respect to quarantine degree, which captures the distance between the person required to quarantine after a person is detected to be infected. Our study results in a surprising conclusion: the cost is not necessarily monotone with respect to the degree of quarantine. Our analysis indicates that governments must curb the urge to adopt simplistic policy and the optimal policy of trace and quarantine for a country strongly depends on its societal structure and disease dynamics.

The use of crime mapping has been used by the police to inform deployment of resources for many decades. Such approaches are commonly used to underpin crime control strategies designed to prevent or reduce acquisitive crimes such as domestic burglary. In recent decades there has been a shift away from simple hot spot identification to more complex geospatial mapping methodologies, such as near repeat analysis which was developed through research regarding burglary victimisation. One of these newly emerging methodologies is built upon the ecological, optimal forager theory (OFT). Research using this theory to examine domestic burglary offending intimated potential for positive results in predicting areas at risk of future crime. This led to a number of police services using crime analysis methodologies built upon OFT to underpin their deployment of resources in an effort to prevent or reduce domestic burglary through increased capable guardianship. However, to date, there has been no detailed examination of how the police services implemented such approaches. As such, this study seeks to fill this gap by examining OFT strategies implemented within 5 police services. By interviewing participants directly involved in the programs the study gathers views and perspectives of its relative success. As a result, we identify that participants felt the strategies produced limited impact on recorded burglary crime. We discuss how despite some positive by-products of the strategies, failure to comprehensively apply the theoretical foundations of OFT, and a variety of implementation failures have undermined the various programs, ultimately impacting their effectiveness.

With the depletion of shallow surface resources, the future mining work will develop towards the deep surface, and the objective conditions such as the mining environment will be more complex and dangerous than now, and the requirements for personnel and equipment will be higher and higher. The efficient exploitation of deep space cannot be separated from such mobile and flexible production and transportation equipment as scraper. In the new era, intelligence is the development trend of the LHD, and path tracking control technology is the key to the intelligent LHD, and it is also an urgent problem to be solved for its unmanned driving. This paper describes the realization of the automatic operation function of articulated LHD from two aspects of mathematical model and trajectory tracking control method, and focuses on the research of the path tracking control scheme in the field of unmanned driving, that is, LQR controller. On this basis, the parameters of the LQR controller are optimized by combining different intelligent cluster algorithms to find the optimal solution of the LQR controller.

The present work studies a swelling porous-elastic system with viscoelastic damping. We establish a general and optimal decay estimate which generalizes some recent results in the literature. Our result is established without imposing the usual equal-wave-speed condition associated with similar problems in literature.

In this paper, an electromechanical mass lifter system is designed, analyzed and compare using optimal and robust control theories. LQR and μ -synthesis controllers are used to improve the lift displacement by comparison method for tracking the desired step and sinusoidal wave signals input. Finally, the comparison simulation result prove the effectiveness of the electromechanical mass lifter system with μ -synthesis controller for improving the rise time, percentage overshoot, settling time and peak value of tracking the desired step displacement signal and improving the peak value for tracking the desired sinusoidal displacement signal with a good performance.

The prevention, mitigation and treatment of movement impairments, ideally, requires early diagnosis or identification. As the human movement system has physiological and functional redundancy, movement limitations do not promptly arise at the onset of physical decline. A such, prediction of movement limitations is complex: it is unclear how much decline can be tolerated before movement limitations start. Currently, the term ‘homeostatic reserve’ or ‘physiological reserve’ is used to refer to the redundancy of the human biological system, but these terms do not describe the redundancy in the muscle architecture of the human body. The result of functional redundancy is compensation. Although compensation is an early predictor of movement limitations, clear definitions are lacking and the topic is underexposed in literature. The aim of this article is to provide a definition of compensation and emphasize its importance. Compensation is defined as an alteration in the movement trajectory and/or altering muscle recruitment to complete a movement task. Compensation for capacity is the result of a lack in neuromusculoskeletal reserve, where reserve is defined as the difference between the capacity (physiological abilities of the neuromusculoskeletal system) and the task demand. Compensation for movement objectives is a result of a shift in weighting of movement objectives, reflecting changing priorities. Studying compensation in biomechanics requires altered protocols in experimental set-ups, musculoskeletal models that are not reliant on prescribed movement, and inclusion of alternative movement objectives in optimal control theory.

In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(p^r, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p} (q=p^n)$ by Theorem 1. We determine all optimal normal bases for Galois ring extension.

Little in the scholarly economics literature is directed specifically to the performance of sta­ble value funds, although they occupy a leading place among retirement investment vehicles. They are currently offered in more than one-third of all defined contribution plans in the USA, with more than $800 billion of assets under management. This paper rigorously ex­amines their performance throughout the entire period since their inception in 1973. We produce a composite index of stable value returns. We next conduct mean-variance analysis, Sharpe and Sortino ratio analysis, stochastic dominance analysis, and optimal multi-period portfolio composition analysis. Our evidence suggests that stable value funds dominate (on average) two major asset classes based on a historical analysis, and that they often occupy a significant position in optimized portfolios across a broad range of risk aversion levels. We discuss factors that contributed to stable value funds’ past performance and whether they can continue to perform well into the future. We also discuss considerations regarding whether or not to include stable value as an element in target date funds within defined con­tribution pension plans.

Fractional differential systems have received much attention in recent decades likely due to its powerful ability in modeling memory processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. Obviously, bang-bang property is of a significant importance in optimal control theory. In this paper a Bang-Bang property and time-optimal control problem for time-Fractional Differential System (FDS) is under consideration. First we formulate our problem and we prove the existence theorem. We state and prove the bang-bang theorem. Finally we give the optimality conditions that characterized the optimal control. Some illustrate applications are given to clarify our results.

Ensuring the quality of printed circuit boards (PCBs) in gas meters is essential to the reliable operation and safety of these devices. Traditional methods for detecting welding defects on PCBs, such as machine vision and deep learning, present significant limitations. Machine vision-based approaches lack the precision required in complex environments, while deep learning methods demand large, labeled datasets that are costly and impractical in industrial contexts. This paper introduces a novel melding defect detection method based on discrete optimal transport (DOT) theory, focused on identifying discrepancies in welding areas between sample and reference images. By limiting analysis to the welding regions, the proposed approach reduces computational costs associated with high-resolution image processing while maintaining detection precision and independence from large datasets. The DOT model calculates the optimal mass flow between images, pinpointing specific defects and providing actionable insights for defect tracing and repair, thereby overcoming the limitations of existing methods. Experimental results demonstrate that this approach is both effective and efficient, offering a robust solution for quality assurance in PCB manufacturing for gas meters.

Key findings include the modelling of the material behavior when ZnAl15% wires were subjected to the tensile test at different speeds, with strain rate sensitivity coefficient m = 0.0128, demonstrating that this type of alloy is especially sensitive to the strain rate. Besides, the optimal friction coefficient (µ) for the drawing process of this material was experimentally identified as µ = 0.28, the ideal drawing die angle was determined to be 2α = 10°, and the alloy's deformability limit has been established by a reduction ratio r ≤ 22.5%, that indicates good plastic deformation capacity. The experimental results confirmed that the proposed models are feasible for the design and optimization of industrial processes to improve the efficiency and quality of ZnAl15% alloy wire production.

Vibration problems have become one of the most important factors affecting robot performance. To this end, a terminal residual vibration suppression method based on joint trajectory optimization is proposed to improve the accuracy and stability of robot motion. Firstly, based on the characteristics of the friction nonlinearity due to joint coupling and physical feasibility of dynamic parameters, a semidefinite programming method is used to identify dynamic parameters with actual physical meaning, thereby obtaining an accurate dynamic model. Then, based on the result of the residual vibration time domain analysis, a joint trajectory optimization model with the goal of minimizing joint tracking error is established. The Chebyshev collocation method is used to discretize the optimization model. The dynamic model is used as the optimization constraint, and barycentric interpolation is used to obtain the optimized joint motion trajectory. Finally, industrial robot experiments prove that the vibration suppression method proposed in this article can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed in this paper can reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory.

The dynamic evolution and variation of electrical loads is now a priority for optimum management and, above all, forecasting. Indeed, these dynamic load variations require computer tools able to implement optimal load forecasting models. Scientific research into automated models for forecasting electrical loads therefore represents a challenge for scientific researchers. Several research studies have therefore been carried out. These include machine learning approaches such as: LSTM (Long Short-Term Memory), Support Vector Machine (SVM) and others. This article proposes a comparison study between a hybrid model based on the wavelet transform coupled with the adaboost method, and LSTM, for forecasting electricity consumption loads. Python 3.10 was used for the studies. The first results obtained consisted in the study of electricity load forecasts over four (04) data sets of the year (January, April, August and December). These results are very satisfactory, showing a good correlation between the real results of the electrical load consumption data, and the results of the implemented model. The electrical load consumption data are collected from a renewable energy production source: photovoltaic solar energy. The model test results (R2) obtained range from 0.919 to 0.958. These results are representative of real data and reflect the model's performance. The second set of results concerns a comparative study between the methods used by Y. Xie et al (CNN, MLP, LSTM-AM and LSTM-AM-MLP), and our approach. The prediction results obtained between the approaches show a prediction gap ranging from 0.15 to 0.78 for RMSE and 0.83 for MAPE. These results show significant differences between the methods. The minimization of errors by our model, therefore, reflects the model's performance in terms of accuracy, which is necessary for the optimal management of consumer electricity load forecasts in order to ensure balance between supply and demand.

Optimal control is a critical tool for mechanical robotic systems, facilitating precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin's Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.

Typhoid fever is an infectious disease that affects humanity worldwide particularly in the lower socio-economic communities where many individuals are exposed to a dirty environment and unclean food. A mathematical model is formulated to analyze the impact of control measures such as vaccination of susceptible humans, treatment of infected humans and sanitation in the different socio-economic communities. The model assumed that the population comprises of two socio-economic classes. The essential dynamical system analysis of our model was appropriately carried out. The impact of the control measures was analyzed, and the optimal control theory was applied on the control model to explore the impact of the different control measures. Numerical simulation of the models and the optimal controls were carried out and results obtained indicates that the overall combination of the control measures eradicates Typhoid fever in the population but the controls are more optimal in the higher socio-economic communities.

This paper studies the pilot control strategy and workload of tilt-rotor aircraft dynamic conversion procedure between helicopter mode and fixed-wing mode. A nonlinear flight dynamics model of tilt-rotor aircraft with full flight modes is established. On this basis, a nonlinear optimal control model of dynamic conversion is constructed, considering factors such as conversion corridor limitations, pilot control, flight attitude, engine rated power, and wing stall effects. To assess pilot workload, an analytical method based on wavelet transform is proposed, which examines the mapping relationship between pilot control input's amplitude, constituent frequencies, and control tasks. By integrating the nonlinear optimal control model and the pilot workload evaluation method, the analysis of pilot control strategy and workload during the conversion procedure is conducted, leading to the identification of strategies to reduce pilot workload. The results indicate that incorporating the item of pilot workload in the performance index results in a notable reduction in the magnitude of collective stick inputs and longitudinal stick inputs. Moreover, it facilitates smoother adjustments in altitude and pitch attitude. Additionally, the conversion of the engine nacelle can be achieved at a lower and constant angular velocity. In summary, the conversion and reconversion procedures are estimated to have a low workload (Level 1 ~ Level 2), with relatively simple and easy manipulation for the pilot.

The dynamics of the main photosynthetic structures is studied by mathematical modeling methods in this article. Chlorophyll portion variability in phytoplankton and the formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are presented that simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models were tested for biological adequacy and their effectiveness was compared. For the model selected as a result of the comparison, the optimal control problem has been formulated and solved. It is shown that in this way it is possible to reduce the space of the initial components of the model system.

How to optimally allocate COVID-19 vaccines and scarce public goods is a crucial and sensitive question to scholars, policy-makers, and practitioners. The ethical dimensions and principles of vaccine allocation between groups are widely agreed upon, whereas the ethical dimensions and principles of vaccine distribution between countries at the peak of the COVID-19 pandemic are highly controversial. This article aims to investigate how vaccines were globally allocated across countries and propose an optimal allocation mechanism for vaccines and scarce public goods. The results show that, to a certain extent, the global allocation of COVID-19 vaccines was fair and effective. Countries with more cases and deaths obtained more vaccines and vaccinations. Wealthier countries might receive more vaccinations but also suffer more severe consequences of COVID-19. Though COVAX could miss its initial vaccine delivery targets, the facility should be considered successful in its core goals and plays a critical role in controlling the pandemic. The study proposes a fair and effective mechanism of vaccine allocation that combines the roles of markets and interventions of international organizations and national governments with three degrees: emergency, priority, and market.

The challenge of achieving ultrafast switching of electric polarization in ferroelectric materials remains unsolved, as there is no experimental evidence of such switching to date. In this study, we have developed an enhanced model that describes switching within a two-dimensional space of generalized coordinates. Our findings indicate that stable switching in barium titanate cannot be achieved through a single linearly polarized pulse. When the intensity of the linearly polarized pulse reaches a certain threshold, the sample experiences depolarization, but not stable switching. Our study also reveals that phonon friction plays a minor role in the switching dynamics and provides an estimate of the optimal parameters of the perturbing pulse with the lowest intensity that results in depolarization of an initially depolarized sample.

: This study investigates the use of various thunderstorm indices in predicting severe thunderstorms events during the monsoon season in four different regions in India. The research evaluates the performance of the prediction model using a model skill score and utilizes the Weather Research and Forecasting (WRF) model with the double moment microphysics scheme to simulate model cases. It also compares fifteen thunderstorm indices derived from the ERA5 dataset to identify the most effective index for predicting severe thunderstorms events. The results of this study show that in-corporating thunderstorm indices with model skill scores improves severe thunderstorms fore-casting in the monsoon season in India. The result revealed that determining the optimal threshold for each index is crucial in achieving accurate predictions. The study also highlights the importance of considering multiple indices rather than relying on a single index to predict severe thunderstorms events. The advance indices such as Energy Helicity Index (EHI), Supercell Composite Parameter (SCP), mainly works well with extreme severe thunderstorms. The simplistic indices can predict the weak or severe thunderstorm easily. The use of multiple thunderstorm indices can also help mete-orologists to make more accurate predictions, which can further enhance public safety. In conclu-sion, this study demonstrates the potential of incorporating thunderstorm indices with model skill scores like HSS and TSS and combinations of different skill scores in severe thunderstorms fore-casting during the monsoon season in India. Future research can build upon the findings of this study to develop more accurate and reliable severe weather forecasting models.

We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. The estimate is global in the sense that no a priori knowledge is required on the parameters to be determined. Different neural network algorithms are tested on a series of data sets. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.

Trajectory Optimization (TO) is the sequence of processes that are considered in order to produce the best path that mends the overall performance or reduces the consumption of the resources where the restriction system remains maintained. In this survey, an inclusive review of the latest advancements in modeling and optimization of trajectory generation in robotic applications will be discussed broadly. In recent times, numerous studies have employed optimal control techniques involving direct and indirect methods in order to convert the authentic Trajectory Optimization problem into a constrained parameter optimization problem. Moreover, a huge variety of optimization algorithms such as Genetic Algorithms (GA), Simulated Annealing (SA), Sequential Quadratic Programming (SQP), and Particle Swarm Optimization (PSO) are used aiming to find the optimal solutions for trajectory planning. It is observable that, minimizing the jerk, energy consumption, and execution time among the most widely used design objectives, on the other hand, the robot’s joints configurations and the motor torques are the most used design variables. This paper aims to review the fundamental techniques and their coincident robotic applications in the field of trajectory optimization aiming to afford some steering for related researchers.

Studies have shown that in many practical applications, data interpolation by splines leads to better approximation and higher computational efficiency as compared to data interpolation by a single polynomial. Data interpolation by splines can be significantly improved if knots are allowed to be free rather than at a priori fixed locations such as data points. In practical applications, the smallest possible curvature is often desired. Therefore, optimal splines are determined by minimizing a derivative of continuously differentiable functions comprising the spline of the required order. The problem of obtaining an optimal spline is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished analytically, interpolation by splines of higher orders or in higher dimensions is challenging. In this paper, to overcome difficulties associated with the complexity of the interpolation problem, the interval over which data points are defined, is discretized and continuous derivatives are substituted by their discrete counterparts. It is shown that as the mesh of the discretization approaches zero, a resulting near-optimal spline approaches an optimal spline. Splines with the desired accuracy can be obtained by choosing an appropriate mesh of the discretization. By using cubic splines as an example, numerical results demonstrate that the linear programming (LP) formulation, resulting from the discretization of the interpolation problem, can be solved by linear solvers with high computational efficiency and resulting splines provide a good approximation to the optimal splines.

Model predictive control (MPC) is a multi-objective control technique that can handle 2 system constraints. However, the performance of an MPC controller highly relies on a proper 3 prioritization weight for each objective, which highlights the need for a precise weight tuning 4 technique. In this paper, we propose an analytical tuning technique by matching the MPC 5 controller performance with the performance of a linear quadratic regulator (LQR) controller. The 6 proposedmethodology derives the transformation of LQRweightingmatrixwith a fixedweighting 7 factor using discrete algebraic Riccati equation (DARE) and designs MPC controller using the 8 idea of discrete time linear quadratic tracking problem (LQT) in the presence of constraints. 9 The proposed methodology ensures the optimal performance between unconstrained MPC and 10 LQR controller and provides a sub-optimal solution while the constraints are active during 11 transient operations. The resultingMPC behaves as the discrete time LQR by selecting appropriate 12 weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. 13 In this paper, the effectiveness of the proposed technique is investigated in the application of 14 a novel vehicle collision avoidance system which is designed in the form of linear inequality 15 constraints within MPC. The simulation results confirm the potency of the proposed MPC control 16 technique in performing a safe, feasible and collision free path while respecting the inputs, states 17 and collision avoidance constraints.

Noise reduction is the major issue in the loudspeaker for the application of the musical instruments and related areas. In this paper, a noise disturbance control of a loudspeaker with optimal and robust controllers has been done successfully. The noise of the loudspeaker has been analyzed by simply track a reference cone displacement with the actual cone displacement. Static output feedback and H infinity optimal loop shaping controllers have been used to compare the actual and reference cone displacements by using a sine wave and random cone displacement signals and a promising results have been analyzed.

With the rapid spread of carbon trading in the global economy, the interactions of prices between carbon (or clean/renewable energy) and traditional fossil energies such as coal and oil have raised growing attention, but little research have discussed their dynamic volatility spillover and time-varying correlation. The purpose of this study is to investigate these issues, for the weekly data of EUA futures, Biofuel and Brent oil prices from 25 October 2009 to 5 July 2020. We employ the VAR-GARCH model with the BEKK specification. Our results are summarized as follows. At first, we identified the sudden changes and the volatility persistence in the three markets, and also confirmed that the volatility of the markets has changed significantly over time. Secondly, we find that there are a weak volatility spillover effect among the three markets, while a strong spillover effect between the EUA and Brent oil markets. Lastly, in financial markets, the EUA can be used as a hedging portfolio for the Biofuel and Brent oil markets. These results can help investors to well compose their portfolios and manage their investment risks, and help potential pollutant emission sources to join in carbon market in a cost-effective way.

The energy efficient problem of parallel-connected pumps in heating, ventilation, and air-conditioning (HVAC) systems has received an increasing attention in recent years. While many pump optimization methods are proposed and show great performance, pumps are not always energy efficient and lack flexibility. In this paper, we propose a distributed control algorithm for parallel pumps in HVAC system in a peer-to-peer setting. Based on a spanning tree of the network of the intelligent nodes and a population of potential solutions randomly sampled, the algorithm makes optimal control decision for pumps to minimize energy consumption and meet the system demand. The theoretical analysis on convergence of the algorithm is established. Unlike traditional control structure, the whole system is fully distributed and each pump is controlled by an intelligent node that runs identical control code and coordinates with other nodes through direct data exchange. Simulation experiments on 6 parallel-connected pumps are provided for different working cases to demonstrate the effectiveness of the proposed algorithm and compare with other four methods. The results show that our method strictly satisfies the demand constraint and presents a good energy saving potential, the convergence guarantee, the flexibility. The maximum energy saving can be up to 29.92%. Besides, the hardware test clearly presents that our method can perform on low-cost Raspberry Pi3 and reduce system cost.

Background: Outbreak of the Covid-19 is now an ongoing global health emergency. At the end of December 2019, the first infection was reported in Wuhan and the world did not pay attention to this extremely contaminated disease and plucked to react rapidly. The World is in an vulnerable state in disease spreading, facing a great loss of lives and socio-economic aspects also. That is why we have proposed a potential mathematical model with data analysis to predict and control the outcome of this pandemic. Methods: The model presented the epidemic dynamics of multiple compartments. We collected available online data of Spain. In primary step, we estimated the parameters using either the data analysis or reference papers. Then we did the data fitting analysis in comparison with the outcome of our mathematical results. The results of the system depended not only the parameters also on social consciousness. Results: It is found that disease progression in this model is determined by the basic reproductive ratio, $R_0$, the actual epidemic of $R_0$ and effective $R(t)$ of each day. If $R_0>1$, the number of latently infected individuals grows exponentially; endemic solution is stable while infection rate decays if $R_0<1$. The optimal control theory stated that vaccination and treatment strategies are highly effective for reducing both susceptible and infected population and to increase the recover rate high. In Spain, after state of alarm (quarantine) on 14 March 2020, reported cases increasing for 13 days only and from the 14th day, daily reported cases started to decline albeit with small fluctuation. Our proposed model approximates that the disease in Spain could be fully under control by after July 2020. Conclusion: Outbreak will be in control of health care system, reduce the death rate and will ensure social-economic stability.

Demand responsive transport (DRT) is operated according to flexible routes, dispatch intervals, and dynamic demand, is attracting a lot of attention. The biggest characteristic of DRT service is that the vehicle routes and schedules are operated optimally based on real-time travel requests of using passengers without fixed operating schedules. Today, the smart-city era has arrived, particularly because of progress in the wireless communications technology and technology related to location information service and real-time passenger demands and requests, and services that change the vehicles’ operating schedules in real-time according to dynamic demand have attracted more attention. In this study, we analyze the effects of the DRT system to solve the first mile/last mile problem based on a proposed DRT routing algorithm considering real-time travel behavior. The algorithm is modified from the dynamic vehicle routing problem (DVRP), in which a DRT-based routing algorithm tends to minimize users’ cost and providers’ operation cost. So far, the DVRP has only been able to serve a single request per vehicle at a time. However, this needs to be extended for the purpose of DRT, wherein several passengers board a vehicle at the same time. The routing algorithm can serve multiple requests at a time and schedule picks ups, drop offs, and rides according to the requests and as calculated by the dispatch algorithm. The basic principle of routing is as follows. The DRT vehicle moves on an attractive path and picks up a passenger if boarding is requested, but it does not simply hang around as a DVRP would. In this step, if another DRT vehicle is present near another passenger, the vehicle that would minimize that passenger’s total travel time picks up the passenger. The optimal routing algorithm developed in this study is applied to the activity-based model; that is, a microscopic traffic demand estimation method is implemented through an activity-based model by using an open-source, activity-based model package called Multi-Agent Transport Simulation (MATSim). MATSim is used for the simulation, because it combines a multi-modal traffic flow simulation with a scoring model for agents, and it provides co-evolutionary algorithms that can alter agents’ daily routines. This process is applied to a type of mode choice and route choice repeatedly over several iterations until some form of user equilibrium has been reached. This study analyzed the feasibility of implementing the DRT service by analyzing the benefits for the users and cost of the operator from the effects of increasing public transportation use and providing personalized mobility service based on DRT implementation by the introduction of DRT will be analyzed according to the scale of DRT supply. Through the simulation, the DRT is expected to provide convenient, fast, and cost-effective mobility services to customers; provide an optimal vehicle scale to providers; and, ultimately, achieve a safe and efficient transportation system.

An SIRS (Susceptible–Infected–Removed-Susceptible) mathematical model for the transmission dynamics of the Transfusion–Transmitted Malaria (TTM) model with optimal control pair u₁(t) and u₂(t) was developed and studied in this research work. The model Transfusion–Transmitted Malaria disease–free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It is shown that the disease–free equilibrium was locally asymptotically stable if the associated basic reproduction numbers R₀ is less than unity while the disease persists if R₀ is greater than unity. The global stability of the Transfusion–Transmitted Malaria model at the disease-free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion–Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.

Human African Trypanosomiasis (HAT) commonly known as sleeping sickness, is a neglected tropical vector borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments while in the human population, the HAT is modelled by four compartments. The next generation matrix approach is used to derive the basic reproduction number, R₀, and also it is proved that if R₀ ≤ 1 the disease free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persist in the population if the value of R₀ > 1. Furthermore, the optimal control model is determined by using the Pontryagin’s maximum principle with control measures such as education, treatment and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures are very efficient and effective to eliminate HAT in Africa.

The paper deals with the modelization and optimization of an integrated multi-component energy system. On-off operation and presence-absence of components must be described by means of binary decision variables, besides equality and inequality constraints; furthermore, the synthesis and the operation of the energy system should be optimized at the same time. In this paper a hierarchical optimization strategy is used, adopting a genetic algorithm in the higher optimization level, to choose the main binary decision variables, whilst a MILP algorithm is used in the lower level, to choose the optimal operation of the system and to supply the merit function to the genetic algorithm. The method is then applied to a distributed generation system, which has to be designed for a set of users located in the center of a small town in the North-East of Italy. The results show the advantage of distributed cogeneration, when the optimal synthesis and operation of the whole system are adopted, and significant reduction in the computing time by using the proposed two-level optimization procedure.

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

The maritime environment is the setting for a variety of economic activities, such as offshore wind energy, aquaculture, salt extraction, and oil and gas platforms. While some of these activities have a long-term presence, others require decarbonisation as they head towards their demise. In this context, the aim of this study is to develop a methodology to replace the electrical energy from high-emission industrial processes offshore with clean electricity generated by offshore wind energy. The proposal is structured in three phases: Initiation, which involves the collection of quantitative, technical and geospatial information of the study area; Indicators, where the main indicators are calculated and the best alternative is selected using multi-criteria evaluation methods; and finally, short, medium and long-term scenarios are proposed. The methodology is evaluated in Spain, the best alternative with a nominal power of 225 MW, is capable of avoiding up to 1.44 MtCO₂ by 2050.

Modeling the reaction time required for the removal of chemical oxygen demand (COD) from wastewater is important because can be an indicator of harmful pollutants that may pose risks to human health.. Here, we evaluate the use of an inverse artificial neural network (ANNi) to optimize the removal of COD from aqueous herbicide solutions using sonophotocatalysis as the treatment process.. This algorithm takes the operating conditions as input and estimates the optimal reaction time to reach the required effluent COD. This model was validated by comparison with both experimental measurements and simulated analysis, resulting in low error (0.5%), high Pearson correlation (R2 = 0.9956), and short computing time (less than one minute). The results for the proposed methodology (ANNi-GAs) were efficient and attractive in a reasonable way providing a satisfactory picture of the relationships between the optimal input parameters. Such parameters control the degradation process of herbicides online and can be used to predict the behavior of COD removal, thus taking actions to reduce the impact of aqueous treatment with alazine and gesaprim herbicides on aquatic, soil biota, and human health. Therefore, this technique constitutes a promising framework for predicting the environmental impact of herbicides within a tolerable degree of error.

This work presents an innovative application of optimal control theory to the strategic scheduling of battery storage in the day-ahead electricity market, with a focus on enhancing profitability while factoring in battery degradation. The study incorporates in the optimisation framework the cost of battery capacity degradation, the effects of capacity degradation and internal resistance degradation into dynamics. We employ a continuous-time representation of the dynamics, in contrast with many other studies that use a discrete-time approximation with rather coarse intervals. We adopt an equivalent circuit model coupled with empirical degradation parameters to simulate a battery cell’s behaviour and degradation mechanisms with good support from experimental data. Utilising direct collocation methods with mesh refinement allows for precise numerical solutions to the complex, nonlinear dynamics involved. Through a detailed case study of Belgium’s day-ahead electricity market, we determine the optimal charging and discharging schedules under varying objectives: maximizing net revenues, profits considering capacity degradation, and profits considering both capacity degradation and internal resistance increase due to degradation. The results demonstrate the viability of our approach and underscore the significance of integrating degradation costs into the market strategy for battery operators, alongside its effects on the battery’s dynamic behaviour. Our methodology extends previous work by offering a more comprehensive model that empirically captures the intricacies of battery degradation, including a fine and adaptive time domain representation, focusing on the day-ahead market, and utilising accurate direct methods for optimal control. The paper concludes with insights into the potential of optimal control applications in energy markets and suggestions for future research avenues.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

This study entailed the design and analysis of a 400 m-class underwater glider operated by a bladder-type buoyancy engine. The underwater glider was designed for high-speed movement with a maximum velocity of 2 knots. The shape of the hull was designed to reduce water resistance using the Myring hull profile equation. The reliability was verified by performing simulations using resistance coefficients. The relationship between the control value of the ballast discharged from the buoyancy engine and the glider's speed according to the path angle was analyzed. Further, the relationship between the optimal glide angle and the design control value of the ballast was derived, and the optimal glider speed was estimated accordingly. Based on the analysis results, a bladder-type buoyancy engine was developed, and the maximum speed of the tested underwater glider was measured via sea trials.

This paper discusses two major applications of SU(3) theory, the first being the question of quantum brachistochrones and problems in time optimal control theory, the second being the use of spherical tensor decompositions of the special functions which are associated to SU(3) via the isotropic oscillator. We discuss the derivation of the quantum brachistochrone problem more generally from the perspective of von Neumann equations and matrix mechanics, arriving at an equivalent formulation to the Lagrangian method. Discussion is given to the application of such advanced methods in quantum computation, and some future directions that may be amenable to a similar sort of an

The present work concerns with presenting an explicit formula for new shifted wavelet (NSW) functions. Wavelet functions have many applications and advantages in both applied and theoretical fields. They are formulated with different orthogonal polynomials to construct new techniques for treating some problems in sciences, and engineering. A new important differentiation property of NSW in terms of NSW themselves is obtained and proved in this paper. Then it is utilized together with the state parameterization technique to find solution of optimal control problem (OCP) approximately. The suggested method converts the OCP into a quadratic programming problem, which can be easily determined on computer. As a result, the approximate solution closes with the exact solution even with a small number of NSW utilized in estimation. The error bound estimation for the proposed method is also discussed. Some test numerical examples are solved to demonstrate the applicability of the suggested method. For comparison, the exact known solutions against the obtained approximate results are listed in Tables.

Computer network attacks are evolving in parallel with the evolution of hardware and neural network architecture. Despite major advancements in Network Intrusion Detection System (NIDS) technology, most implementations still depend on signature-based intrusion detection systems, which can’t identify unknown attacks. Deep learning can help NIDS to detect novel threats since it has a strong generalization ability. The deep neural network’s architecture has a significant impact on the model’s results. We propose a genetic algorithm based model to find the optimal number of hidden layers and the number of neurons in each layer of the deep neural network (DNN) architecture for the network intrusion detection binary classification problem. Experimental results demonstrate that the proposed DNN architecture shows better performance than classical machine learning algorithms at a lower computational cost.

The main goal of this paper is to show that Bayesian optimization could be regarded as a general framework for the data driven modelling and solution of problems arising in water distribution systems. Hydraulic simulation, both scenario based, and Monte Carlo is a key tool in modelling in water distribution systems. The related optimization problems fall in a simulation/optimization framework in which objectives and constraints are often black-box. Bayesian Optimization (BO) is characterized by a surrogate model, usually a Gaussian process, but also a random forest and increasingly neural networks and an acquisition function which drives the search for new evaluation points. These modelling options make BO nonparametric, robust, flexible and sample efficient particularly suitable for simulation/optimization problems. A defining characteristic of BO is its versatility and flexibility, given for instance by different probabilistic models, in particular different kernels, different acquisition functions. These characteristics of the Bayesian optimization approach are exemplified by the two problems: cost/energy optimization in pump scheduling and optimal sensor placement for early detection on contaminant intrusion. Different surrogate models have been used both in explicit and implicit control schemes. Showing that BO can drive the process of learning control rules directly from operational data. BO can also be extended to multi-objective optimization. Two algorithms have been proposed for multi-objective detection problem using two different acquisition functions.

The incorporation of renewable energy into power systems poses serious challenges to the transmission and distribution power system operators (TSOs and DSOs). To fully leverage these resources there is a need for a new market design with improved coordination between TSOs and DSOs. In this paper we propose two coordination schemes between TSOs and DSOs: one centralised and another decentralised that facilitate the integration of distributed based generation; minimise operational cost; relieve congestion; and promote a sustainable system. To this end, we approximate the power equations with linearised equations so that the resulting optimal power flows (OPFs) in both the TSO and DSO become convex optimisation problems. In the resulting decentralised scheme, the TSO and DSO collaborate to optimally allocate all resources in the system. In particular, we propose an iterative bi-level optimisation technique where the upper level is the TSO that solves its own OPF and determines the locational marginal prices at substations. We demonstrate numerically that the algorithm converges to a near optimal solution. We study the interaction of TSOs and DSOs and the existence of any conflicting objectives with the centralised scheme. More specifically, we approximate the Pareto front of the multi-objective optimal power flow problem where the entire system, i.e., transmission and distribution systems, is modelled. The proposed ideas are illustrated through a five bus transmission system connected with distribution systems, represented by the IEEE 33 and 69 bus feeders.

Recently, the mapping industry has been focusing on the possibility of large-scale mapping from unmanned aerial vehicles (UAVs) owing to advantages such as easy operation and cost reduction. In order to produce large-scale maps from UAV images, it is important to obtain precise orientation parameters. For this, various techniques have been developed and are included in most of the commercial UAV image processing software. For mapping, it is equally important to select images that can cover a region of interest (ROI) with the fewest possible images. Otherwise, to map the ROI, one may have to handle too many images, and commercial software does not provide information needed to select images, nor does it explicitly explain how to select images for mapping. For these reasons, stereo mapping of UAV images in particular is time consuming and costly. In order to solve these problems, this study proposes a method to select images intelligently. We can select a minimum number of image pairs to cover the ROI with the fewest possible images. We can also select optimal image pairs to cover the ROI with the most accurate stereo pairs. We group images by strips, and generate the initial image pairs. We then apply an intelligent scheme to iteratively select optimal image pairs from the start to the end of an image strip. According to the results of the experiment, the number of images selected is greatly reduced by applying the proposed optimal image–composition algorithm. The selected image pairs produce a dense 3D point cloud over the ROI without any holes. For stereoscopic plotting, the selected image pairs were map the ROI successfully on a digital photogrammetric workstation (DPW), and a digital map covering the ROI is generated. The proposed method should contribute to time and cost reductions in UAV mapping.

The bending performance of a basalt-polypropylene fiber-reinforced concrete (HBPFRC) was characterized by testing 24 400×100×100 mm3 prismatic specimens in a four-point bending test JSCE-SF4 configuration. The type and content of both fibers was varied in order to guarantee different target levels of post-cracking flexural performance. The results evidenced that mono-micro basalt fiber reinforced concrete (BFRC) allows the increase of the flexural strength (pre-cracking stage), while macro polypropylene fiber reinforced concrete can effectively improve both bearing capacity and ductility of the composite for a wide crack width range. Compared with the plain concrete specimens, flexural toughness and equivalent flexural strength of macro polypropylene fiber-reinforced concrete (PPFRC) and the hybrid fiber-reinforced concrete (HFRC) increased by 3.7~7.1 times and 10%~42.5%, respectively. From both technical and economic points of view, the optimal mass ratio of basalt fiber to polypropylene fiber resulted to be 1:2, with a total content of 6 kg/m3. This HFRC is seen as a suitable material to be used in sewerage pipes where cracking control (crack formation and crack width control) is of paramount importance to guarantee the durability and functionality of the pipeline as well as the ductility of the system in case of local failures.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

In this study, the thermal behavior of a PCM-based heat sink in the presence of horizontal fins was numerically investigated. These types of heat sink can be effective in electronic cooling applications. Independent variables included aspect ratio (AR), number of horizontal fins (n) and their length (LR), while the objective function was defined to maximize the safe operation time (tmax). The incorporation of horizontal fins has a positive effect (thermal conductivity enhancement) as well as a negative effect (latent heat reduction). Based on the results, the optimal number of horizontal fins was five. As the number of fins rises up to five, the incremental effect of thermal conductivity improvement (positive effect) was superior to the decremental effect of the latent heat reduction (negative effect), hence the objective function (tmax) improved. However, with a further increase in the number of fins upon five, the negative effect prevailed over the positive effect and therefore the safe operation time diminished.