A combined fractional tracking controller based on backstepping and active disturbance rejection control (ADRC) is proposed in this work to control uncertain fractional-order systems (FOSs). The proposed method is constructed in two parts: first, all internal and external uncertainties are estimated by a fractional-order extended state observer (FO-ESO). Second, fractional backstepping method is used to determine the control law and lead the system to the desired control objectives. The control system stability is verified by fractional Lyapunov-like lemma and two numerical simulations confirm the efficiency of the proposed combined ADRC-based backstepping controller.

在这项工作中，提出了一种基于反步法和主动抗扰控制（ADRC）的组合分数跟踪控制器来控制不确定分数阶系统（FOS）。所提出的方法分为两部分：首先，所有内部和外部不确定性都由分数阶扩展状态观测器（FO-ESO）估计。其次，采用分数反推法确定控制规律，引导系统达到预期的控制目标。控制系统稳定性通过分数李雅普诺夫引理验证，两个数值模拟证实了所提出的基于 ADRC 的组合反步控制器的效率。