Singular Linear Quadratic Optimal Control Problem for Stochastic Nonregular Descriptor Systems

Abstract

AbstractThis paper is concerned with the singular linear quadratic (SLQ) optimal control problem for stochastic nonregular descriptor systems with time‐delay. By means of some reasonable assumptions and a series of equivalent transformations, the problem is finally transformed into a positive linear quadratic (LQ) problem for standard stochastic systems. Then dynamic programming principle is used to establish the solvability of the original problem, and the desired explicit presentation of the optimal controller is given in terms of matrix iterative form. The results due to Feng et al. are generalized and improved. As an application, a numerical example is presented to demonstrate the efficiency of the proposed approach.