Adaptive fixed‐time prescribed performance regulation for switched stochastic systems subject to time‐varying state constraints and input delay

Abstract In this article, the adaptive fixed‐time prescribed performance (FTPP) regulation is investigated for a class of time‐varying state constrained switched stochastic systems with input delay. The time‐varying barrier Lyapunov function and a compensation system are presented, respectively, to deal with the design problems caused by the existence of both time‐varying state constraints and input delay. Some radial basis function neural networks are used to approximate unknown functions, and the common Lyapunov function method is displayed to handle the switched signals. Besides, by designing a fixed‐time prescribed performance function, the desired adaptive neural controller is constructed. Compared with the existing works for state constrained control problem, the FTPP regulation control scheme is first proposed for time‐varying state constrained stochastic switched systems under input delay, and the adaptive dynamic surface control scheme with the nonlinear filter is designed to solve the problem of “explosion of complexity.” Based on the stochastic stability theory, the FTPP of system output is achieved, other system state variables are restricted in the predefined regions, and all signals of this closed‐loop system remain bounded in probability. Finally, the availability of the proposed control scheme is illustrated via two simulation examples.