Backstepping control for fractional-order nonlinear systems (FONSs) requires the analytic calculation of fractional derivatives of certain complicated stabilizing functions, which becomes prohibitive as the order of the system increases. This article aims to facilitate the adaptive neural network (NN) backstepping control design for FONSs with actuator faults whose parameters and patterns are fully unknown. A fractional filtering approach, which obviates the requirement of analytic fractional differentiation, is used to generate command signals together with their fractional derivatives. Compensated tracking errors that can eliminate approximation errors of command signals are generated by fractional filters. The proposed adaptive NN command filtered backstepping control (ANNCFBC) approach, together with fractional adaptive laws, guarantees not only the boundedness of all involved variables but also the convergence of both the tracking error and the compensated tracking error to a sufficiently small region. Finally, simulation studies are given to indicate the effectiveness of the proposed control method.

中文翻译：

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具有执行器故障的分数阶非线性系统的自适应神经网络Backstepping控制。

分数阶非线性系统（FONS）的反步控制需要对某些复杂的稳定函数的分数导数进行解析计算，随着系统阶数的增加，这种计算变得难以实现。本文旨在促进参数和模式完全未知的执行器故障的FONS的自适应神经网络（NN）反步控制设计。一种分数滤波方法，它消除了解析分数微分的要求，可用于生成命令信号及其分数导数。小数滤波器会生成可消除命令信号近似误差的补偿跟踪误差。提出的自适应NN命令过滤反推控制（ANNCFBC）方法以及分数自适应律，不仅保证了所有相关变量的有界性，而且还保证了跟踪误差和补偿后的跟踪误差都收敛到足够小的区域。最后，仿真研究表明了该控制方法的有效性。