Adaptive Fuzzy Fault-Tolerant Tracking Control of Uncertain Nonlinear Time-Varying Delay Systems

This paper investigates the problem of fuzzy-approximation-based adaptive fault-tolerant (FT) tracking control for uncertain nonlinear time-varying delay systems with nonaffine nonlinear faults. Compared with the existing results, the proposed control scheme avoids the use of the Lyapunov–Krasovskii functional, which relaxes the restriction on the derivative of unknown time-varying delay ( ${\dot \tau (t)< 1}$ ). By utilizing the finite covering lemma and fuzzy logic systems (FLSs), the considered time-varying delay system is transformed into novel switched nonlinear system with known constant delays. In addition, the nonaffine nonlinear faults make the control design more complicated. To overcome the difficulty, the fault function is decoupled by utilizing the mean-value theorem. In the design procedure, the problem of unknown control gain and control direction is produced. To solve this problem, the Nussbaum-type function is introduced. Combined backstepping technique with FLSs, an adaptive approximation FT tracking control scheme is proposed. Finally, the developed control method ensures that all the closed-loop signals are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin. A simulation example is presented to illustrate the effectiveness of the developed control scheme.