Fault-Tolerant Stochastic Sampled-Data Fuzzy Control for Nonlinear Delayed Parabolic PDE Systems

Abstract

For nonlinear delayed parabolic partial differential equation (PDE) systems, this paper addresses fault-tolerant stochastic sampled-data (SD) fuzzy control under spatially point measurements (SPMs). Initially, a T–S fuzzy PDE model is given to accurately describe the nonlinear delayed parabolic PDE system. Secondly, in consideration of possible actuator failure, a fault-tolerant SD fuzzy controller with stochastic sampling under SPMs is designed for nonlinear delayed parabolic PDE system, where two sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. Then, by constructing a novel time-dependent Lyapunov functional, sufficient conditions that guarantee the mean square exponential stability of closed-loop delayed PDE system are obtained based on linear matrix inequalities (LMIs). Lastly, three examples are given to illustrate the designed approach.