Indefinite LQ optimal control for stochastic Takagi–Sugeno fuzzy system under sensor data scheduling: Finite‐horizon case

Abstract

The present paper considers the finite‐horizon indefinite linear quadratic (LQ) control problem for stochastic Takagi–Sugeno (T‐S) fuzzy systems with input delay. In this paper, we consider the presence of sensor data scheduling, which imposes a communication energy constraint and necessitates optimal state estimation for measurements. Then, by utilizing dynamic programming principles, the stochastic LQ problem under consideration can be solved, while the optimal control policy is developed in terms of the unique solutions to a set of coupled difference Riccati equations (CDREs). Specifically, for simple delay‐free case, the linear matrix inequalities based conditions are also proposed, whose feasibility is shown to be equivalent to the well‐posedness of the indefinite LQ control under consideration. As an application, our theoretic analysis is extended to study the intermittent observation model caused by random denial‐of‐service attack.