Finite-time and fixed-time sliding mode control for discontinuous nonidentical recurrent neural networks with time-varying delays

This article investigates the synchronization problem in finite-time and fixed-time of the drive-response delayed recurrent neural networks (RNNs). Moreover, it is assumed that the parameters of the RNNs are nonidentical and the activation functions are discontinuous. For addressing the synchronization problem in finite-time and fixed-time, an improved sliding mode control (SMC) approach is presented. In a first time, by applying the drive-response concept and the synchronization error between the drive-response model, two novel integral sliding mode surfaces are constructed such that the synchronization error can converge to zero in finite-time and fixed-time. In second time, two SMC is created to overcome the finite-time and fixed-time synchronization problem of delayed RNNs. On the basis of Lyapunov stability theory, several sufficient criteria are obtained for the considered discontinuous nonidentical RNNs with time-varying delays models to achieve finite-time synchronization and fixed-time synchronization. Moreover, two types of setting time, which are dependent and independent on the initial values, are given respectively. In the end, three numerical simulations are given to illustrate the effectiveness of the synchronization criteria.