Finite-Time Fuzzy Bounded Control for Semilinear PDE Systems with Quantized Measurements and Markov Jump Actuator Failures

This article presents a novel reliable fuzzy output feedback controller for a class of semilinear parabolic partial differential equation systems with Markov jump actuator failures. First, the control strategy's novelties include the following aspects: 1) the considered system is represented by using a fuzzy modeling approach, based on which a new asynchronous fuzzy observer is constructed via utilizing a series of discrete output signals that are induced by samplers and quantizers; 2) a novel Markov jump input model, which is more fit for real applications, is introduced to depict various stochastically occurring actuator faults; and 3) inspired by the above discussion, a reliable mode-dependent fuzzy piecewise control strategy, which only needs limited actuators, is developed. Then, some new conditions, which can ensure that the closed-loop system is finite-time bounded, are established. Furthermore, some slave matrices are introduced to relax the strict constraints caused by asynchronous membership functions. Finally, two simulation examples are provided to support the validity of the proposed method.