Observer-based Fault Estimation and Tolerant Control for Stochastic Takagi-Sugeno Fuzzy Systems with Brownian Parameter Perturbations

In this paper, robust fault estimation and fault tolerant control for stochastic Takagi-Sugeno fuzzy systems, subjected to Brownian parameter perturbations, unknown process uncertainties and unexpected faults, are investigated. Augmented system approach, unknown input observer techniques and sliding mode control strategies are integrated to decouple the influences from the unknown input uncertainties, and drive the trajectories of the estimation error dynamics to enter and subsequently remain within a desired surface of the error space. As a result, a robustly simultaneous estimate of the means of the faults concerned and the full system states can be achieved. In the meanwhile, the actuator/sensor signal compensation techniques are used to formulate the tolerant control strategy to eliminate or offset the influences from the faults to the systems dynamics and ensure the robust stabilization of the closed-loop control system. In terms of linear matrix inequalities, sufficient conditions are proposed to ensure the robust stability of the overall closed-loop system composed of system state and estimation error dynamics, as well as the reachability of the sliding mode surface. Furthermore, the systematic design procedures for the robust fault estimation and fault tolerant control scheme are addressed. Finally, simulation studies on a single-link manipulator and a three-tank system are illustrated to demonstrate the effectiveness of the suggested methodologies.