The problem of direct adaptive compensation for infinite number of time-varying actuator failures/faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems. However, due to the technical difficulties, so far, very limited result is available in addressing such an issue, which thus motivates us to propose a new fuzzy control methodology in this paper. The proposed scheme is established from the techniques of projection adaptation design, a new piecewise Lyapunov function analysis, and an optimized fuzzy adaptation. It is shown that all the closed-loop signals are bounded and the steady-state tracking error converges to a residual around zero, irrespective of a possibility that there are infinite number of time-varying actuator failures. Simulations are provided to illustrate the effectiveness and applicability of the proposed scheme.

中文翻译：

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不确定非线性系统模糊跟踪控制中无限次数时变执行器故障的自适应补偿

在不确定非线性系统的模糊跟踪控制中，对无限数量的时变执行器故障/故障的直接自适应补偿问题具有理论和实践意义。然而，由于技术上的困难，到目前为止，解决这个问题的结果非常有限，这促使我们在本文中提出一种新的模糊控制方法。该方案是从投影自适应设计技术、新的分段李雅普诺夫函数分析和优化的模糊自适应技术建立的。结果表明，所有闭环信号都是有界的，稳态跟踪误差收敛到零附近的残差，而不管存在无限数量的随时间变化的致动器故障的可能性。