Fault Isolation and Fault-Tolerant Control for Takagi–Sugeno Fuzzy Time-Varying Delay Stochastic Distribution Systems

A fault isolation, estimation, and fault-tolerant control (FTC) scheme for nonlinear time-varying delay stochastic distribution control systems was presented in this article. The Takagi–Sugeno fuzzy model was adopted to represent the nonlinear dynamics of time-varying delay systems. According to the output equivalence principle and Laplace transformation, an augmented state vector was given to solve the time-varying delay problem. When multiple actuator faults and interference occur simultaneously, fault detection, isolation, and fault estimation were designed to obtain the fault information. To decouple faults and obtain the size and location information of the fault, the system was separated into two parts through the designed multiple conversion matrices, in which one subsystem was only affected by one actuator fault. This has simplified the design of fault isolation and estimation. An adaptive observer for fault estimation was given. Then, the fault information such as the time, location, and size was determined. The observer gain matrices were calculated using linear matrix inequality. When a fault was detected and diagnosed, an FTC algorithm was devised using the proportional–integral control scheme to compensate the fault as much as possible. It has been shown that even if multiple faults actuator occurred simultaneously, the FTC controller still ensured that the output probability density function of the system traces the desired probability density function. Finally, the expected results were obtained through simulation example, which confirms the effectiveness of the method.