Adaptive sliding mode control for a class of uncertain nonlinear fractional-order Hopfield neural networks

Abstract

The stabilization problem for a class of uncertain nonlinear fractional-order Hopfield neural networks (FOHNNs) is solved by adaptive sliding mode control (ASMC). The uncertain internal parameters and the unknown external nonlinear perturbations are estimated by adaptive techniques. Firstly, a switched sliding mode surface (SMS) of uncertain nonlinear FOHNNs is presented. Secondly, in order to guarantee the stability of uncertain nonlinear FOHNNs, an effective sliding mode controller (SMC) is designed. According to the fractional-order Lyapunov theory, the sliding mode asymptotically converges to the origin in finite time. Finally, a numerical example of a three-dimensional uncertain nonlinear FOHNNs is given to demonstrate the effectiveness of the proposed method.