An observer‐based adaptive fuzzy backstepping approach is proposed for nonlinear systems with respect to fractional‐order differential equations, unmatched uncertainties, unmeasured states, and actuator faults. The approximation capability of fuzzy logic system and minimal learning parameter approaches are applied to identify uncertain functions in a simultaneous manner. For estimating the unavailable conditions, a fuzzy fractional‐order state‐observer is extended. Applying fault‐tolerant approach in a backstepping design methodology would provide a new fault‐tolerant adaptive fuzzy output‐feedback approach for fractional‐order strict‐feedback systems. This control structure would assure the considered system stability through selection of the appropriate Lyapunov candidate function. Two numerical simulations are run to exhibit the validity herein.

中文翻译：

---

分数阶非线性系统的基于近似的自适应故障补偿反推控制：一种输出反馈方案

针对分数阶微分方程，不匹配的不确定性，无法测量的状态和执行器故障，针对非线性系统提出了一种基于观测器的自适应模糊反推方法。模糊逻辑系统的逼近能力和最小学习参数方法可用于同时识别不确定函数。为了估计不可用条件，对模糊分数阶状态观测器进行了扩展。在后推设计方法中应用容错方法将为分数阶严格反馈系统提供一种新的容错自适应模糊输出反馈方法。该控制结构将通过选择适当的Lyapunov候选函数来确保所考虑的系统稳定性。运行两个数值模拟以证明此处的有效性。