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.

中文翻译：

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不确定非线性时变系统的自适应模糊容错跟踪控制

本文研究了具有非仿射非线性故障的不确定非线性时变延迟系统的基于模糊近似的自适应容错 (FT) 跟踪控制问题。与现有结果相比，所提出的控制方案避免了Lyapunov-Krasovskii泛函的使用，放宽了对未知时变延迟（${\dot\tau(t)<1}$）导数的限制。利用有限覆盖引理和模糊逻辑系统（FLS），将所考虑的时变延迟系统转化为具有已知恒定延迟的新型切换非线性系统。此外，非仿射非线性故障使控制设计更加复杂。为了克服这个困难，利用均值定理对故障函数进行解耦。在设计过程中，产生了未知控制增益和控制方向的问题。为了解决这个问题，引入了 Nussbaum 型函数。将反推技术与FLSs相结合，提出了一种自适应逼近FT跟踪控制方案。最后，所开发的控制方法确保所有闭环信号最终一致有界，并且跟踪误差可以收敛到原点的一个小邻域。给出了一个仿真例子来说明所开发的控制方案的有效性。所开发的控制方法确保所有闭环信号最终一致有界，跟踪误差可以收敛到原点的一个小邻域。给出了一个仿真例子来说明所开发的控制方案的有效性。所开发的控制方法确保所有闭环信号最终一致有界，跟踪误差可以收敛到原点的一个小邻域。给出了一个仿真例子来说明所开发的控制方案的有效性。