Neural Network-Based Adaptive Sliding-Mode Control for Fractional Order Fuzzy System With Unmatched Disturbances and Time-Varying Delays
针对带有不匹配扰动和时变时滞的分数阶模糊系统，提出一种基于神经网络的自适应滑模控制方法，利用自适应动态规划和积分滑模确保系统有限时间到达滑模面，并通过李雅普诺夫稳定性证明系统渐近稳定。
This article concentrates on the neural network (NN)-based adaptive sliding-mode control (SMC) for fuzzy fractional-order system (FOS), <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (0,1)$ </tex-math></inline-formula> . First of all, a novel method of optimal SMC approach is developed for fuzzy FOSs by using the adaptive dynamic program (ADP), integral sliding mode, and NN with unmatched disturbances and time-varying delays. Next, to weaken the influence of the nonlinearities, the SMC strategy is proposed for the specific system, which is established on the corresponding SMD to ensure that the FOS reach the SMS in a finite time. Moreover, it shows that the matrix of SMS can be described by the linear matrix inequality (LMI). Furthermore, the Hamilton–Jacobi–Bell man (HJB) equation can be approximated by a single NN method, and the Lyapunov stability principle proves that the weight errors are convergent, further guaranteeing the asymptotically stability of the fuzzy FOS. Finally, to display that the above-presented policy is effective, simulation results are presented.