Linear quadratic control for multiple time-delayed uncertain random systems

This study focuses on time-delayed linear quadratic control problems (LQCPs). Firstly, a general time-delayed control problem for a linear time-varying system is investigated. This problem is equivalent to an optimization problem without time delays, and corresponding recurrence equations are proposed accordingly. Furthermore, based on recurrence equations and chance theory, two different types of LQCPs are researched, where the control weighting matrices are positive definite and indefinite, respectively. Exact solutions for the optimal results of these LQCPs are provided. Finally, numerical examples are provided to demonstrate the findings.