Performance-Driven Fault Detection for Uncertain Takagi–Sugeno Fuzzy Feedback Control Systems

This article mainly studies the performance-driven fault detection for general uncertain Takagi–Sugeno fuzzy feedback control systems, where the infinite-horizon quadratic index is introduced to describe the concerned system performance. Different from the existing output-driven fault detection methods, the proposed approach aims to detect the performance degradations induced by faults. For this purpose, the performance index embedded with the information of system dynamics is reformulated for linear feedback control systems with reference inputs. The performance residual, which is adopted as the evaluation function, is derived based on the Bellman equation and further represented into an explainable form. Then, for uncertain linear feedback control systems, the boundaries of the performance residual are analyzed via the linear matrix inequality technique, and an advantaged threshold setting scheme is proposed with the aid of randomized algorithm. Concerning the main objective, a novel approximation method that combines the fuzzy blend of local performance indexes and the radial basis function neural network is developed to approximate the global performance index for Takagi–Sugeno fuzzy systems. Based on the result in the linear case, the performance residual is constructed along the closed-loop system trajectory, and the threshold is determined for the fuzzy control systems with reference inputs and model uncertainties. Finally, simulation studies are provided to show the effectiveness of the proposed theoretical results.