This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system with multiple input delays and multiplicative noises. The main contributions are two-fold. Firstly, when the state variables can be observed exactly, we obtain a necessary and suffcient condition for the multiple-delays system in terms of the non-homogeneous relationship between the state and costate, which is the solution to the coupled forward and backward stochastic difference equations. Secondly, when the state variables are partially observed, we derive a suboptimal linear output feedback controller for the discrete-time system based on the obtained results of the optimal LQG control. Numerical examples are shown to illustrate the proposed algorithm.

Optical micro-angiography (OMAG) is a new method of detecting flow rate and widely used for in vivo imaging. Although OMAG can distinguish between flowing and stationary parts, it cannot obtain accurate flow rate information. This study proposed a range formula for OMAG and the ultrahigh-sensitivity OMAG (UHS-OMAG) method to quantify the measurement range of an entire system. The parameters of the angle between beam scanning and flow directions, the angular velocity of the galvanometer, and the offset of incident light were introduced, and a formula for calculating the range was derived. Experiments were conducted to measure fine and ultra-fine flow rates by using OMAG and UHS-OMAG methods. The minimum measured flow rate was approximately 30 μm/s, and the maximum measured flow rate was approximately 8 mm/s. Experimental results are in good agreement with the preset results.

To accurately and non-destructively monitor the growth of spring wheat in the Hetao Irrigation Area, UAV remote sensing was employed during various fertility stages. Digital image indices from diverse fertilization treatments were calculated and compared with physiological indices to identify the most sensitive digital image indices corresponding to these indices. The study underscored the critical importance of the flowering stage in the growth of spring wheat, thus highlighting the necessity of focusing on this stage. This finding reiterated that the flowering stage was pivotal for spring wheat development in the Hetao Irrigation Area. Several digital image indices, such as GLA, R, G, INT, g, GRVI, MGRVI, RGBVI, EXG, and GRRI, exhibited a high frequency of significant correlations with physiological indices during the four primary reproductive stages of wheat. Consequently, these sensitive digital image indices during the flowering stage can more effectively characterize the physiological indices of spring wheat.