Fault-Tolerant Fuzzy Control for Semi-Markov Jump Nonlinear Systems Subject to Incomplete SMK and Actuator Failures

Abstract

This article focuses on the problem of fuzzy-model-based fault-tolerant control for nonlinear semi-Markov jump systems in the discrete-time context. The discrete-time semi-Markov process is employed to describe the mode jumping among several subsystems in the investigated systems. Moreover, the nonlinear characteristics are effectively tackled through utilizing the Takagi–Sugeno fuzzy model. Unlike some previous results, the information of the semi-Markov kernel (SMK) in this article is assumed to be partially available, which conforms better with the practical scenarios. Besides, considering the case that actuators may encounter some unexpected failures during system operation, the fault-tolerant mechanism is introduced in the process of controller design to enhance the fault tolerance of the studied systems. By means of SMK approach and Lyapunov stability theory, some elapsed-time-dependent criteria for guaranteeing the mean-square stability of the closed-loop system are established. According to these criteria, the design methodology of the reliable fuzzy state feedback controller is developed. Eventually, in order to verify the practicability and rationality of the developed control scheme, a single-link robot arm model is presented.