The system identification problem with multiple nonlinearities is relevant. Its decision depends on many factors. These include: feedbacks, the method of connecting nonlinear links, signal properties. They affect the identifiability of the system parameters. We introduced a condition for the excitation constancy for state variables, which considers the S-identifiability of the system. We propose system decomposition by measuring input to identify parameters. Each subsystem has an implicit identification representation. It guarantees obtaining estimates of subsystem parameters based on experimental data. The trajectories boundedness of adaptive system proved in parametric and coordinate spaces. Conditions guaranteeing exponential stability of the system obtained. Systems of self-oscillation generation and nonlinear correction of a nonlinear system consider. Conditions for the trajectories boundedness of the adaptive system obtained for these cases. The influence of nonlinearity and feedback on the system performance estimated.

. Interconnected control systems (ICS) widely apply to various technical systems. ICS has a complex description. Therefore, simplified models use, which the specifics of an object do not always reflect. So, the problem of synthesizing mathematical models is topical. The work purpose is to develop an approach to obtaining models in conditions of incomplete a priori information. We use an adaptive approach. As examples, two-channel systems (TCS) with cross-links and identical channels consider, and a method for mathematical model design. We consider the system with asymmetric cross-links and evaluate their impact on properties of an adaptive identification system. Approach proposed to assessing the TCS identifiability with cross-links. The excitation constancy influence on TСS parameter estimates is studied. A generalization of the proposed approach is given for an interconnected system.

The structural identification (SI) problem of control objects has not been solved. The formalization and interpretation complexity of the structure concept is the main problem. In identification systems, the form of the model (its structure) choice is intuitive and bases on the experience and knowledge of the researcher in most cases. The task of parametric identification is often interpreted as SI. It introduces certain confusion in understanding of the task and decision-making. This is two different areas of research. The structural identification problem is multifaceted and includes many subtasks, and their solution gives the final result. Some tasks have been solved. The purpose of this work is to review existing approaches and methods to the structural identification problem of control objects from a system perspective. It is necessary to give the SI problem statement at the multiple-informational level to reflect the difficulties of formalizing SI. New directions to analyse that were not SI areas until now.

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation.

The complexity of objects and control systems increases the requirements for mathematical models. The structural identifiability (SI) assessment of nonlinear systems is one of the identification problems. Until now, this problem solves by parametric methods using various approximation methods. This approach is not always effective under uncertainty. We apply an approach to SI estimation based on the analysis of virtual structures. The requirements form for the system input based on the expansion of the excitation constancy property and S-synchronizability. The approach generalization to structural identifiability used in the analysis of systems with symmetric nonlinearity is given. homothety and identifiability conditions for systems with non-symmetric nonlinearities (SNN) obtained. The detectability and recoverability proofed for virtual frameworks (VF) guaranteed the SI estimation under uncertainty. The conditions under which the non-symmetric nonlinearity is hypothetical symmetric nonlinearity obtained. SI estimation examples considered for closed nonlinear systems under uncertainty.