Adaptive Fault-Tolerant Tracking Control for Continuous-Time Interval Type-2 Fuzzy Systems

This paper investigated the tracking problem of mixed ${\mathcal{H}}_{\infty }$ and $L_2-L_{\infty }$ adaptive fault-tolerant control (FTC) for continuous-time interval type-2 fuzzy systems (IT2FSs). For the membership function mismatch and uncertainty between the modules of the nonlinear system, the IT2 fuzzy model is applied to linearly approximate it. The observer can sensitively estimate the system state, and the adaptive fault estimation functions can estimate adaptively the fault signals, which enables the designed adaptive FTC scheme to ensure the asymptotic stability of the closed-loop control system and achieve the desired mixed ${\mathcal{H}}_{\infty }$ and $L_2-L_{\infty }$ tracking performance. The designed adaptive control law can achieve the purpose of dynamic compensation for faults and disturbances, and the introduced lemmas further reduce the design conservatism by adjusting the slack parameters and matrices. Finally, a mass-spring-damping system is used to illustrate the effectiveness of the designed method.