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

Abstract

This article addresses fault-tolerant event-triggered sampled-data (SD) fuzzy control for nonlinear delayed parabolic partial differential equation (PDE) systems under spatially point measurements (SPMs). First, a Takagi–Sugeno fuzzy delayed PDE model is presented to accurately describe the nonlinear delayed parabolic PDE systems. Second, a fault-tolerant event-triggered SD fuzzy control strategy under SPMs is designed to cope with Markov jump faults occurring in actuators, which can effectively reduce the unnecessary data transmission and be achieved by finite sensors and actuators. The membership functions of the proposed controller are determined by the measurement output and independent of the fuzzy delayed PDE plant model. Then, by constructing a Lyapunov functional, sufficient conditions that guarantee the stochastically exponential stability of closed-loop nonlinear delayed parabolic PDE systems are obtained based on linear matrix inequalities. Finally, two examples are given to illustrate the designed approach.