Neural Network-Based Adaptive Sliding-Mode Control for Fractional Order Fuzzy System With Unmatched Disturbances and Time-Varying Delays

This article concentrates on the neural network (NN)-based adaptive sliding-mode control (SMC) for fuzzy fractional-order system (FOS),
$\alpha \in (0,1)$
. 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.