This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

本文提出了一种基于观测器的自适应神经网络反推滑模控制器，以确保在存在任意切换和未测量状态的情况下切换分数阶严格反馈非线性系统的稳定性。为避免“复杂度爆炸”并不断获得虚拟控制函数的分数阶导数，在控制器中引入分数阶动态表面控制（DSC）技术。观测器用于分数阶系统的状态估计。引入滑模控制技术以增强鲁棒性。未知的非线性函数和不确定的扰动由径向基函数神经网络 (RBFNNs) 逼近。系统的稳定性由构造的李雅普诺夫函数保证。提出了分数自适应律来更新不确定参数。所提出的控制器可以确保跟踪误差的收敛，并且所有状态在闭环系统中保持有界。最后，通过两个例子证明了所提出的控制方法的可行性。