Intermittent Boundary Control for Synchronization of Fractional Delay Neural Networks With Diffusion Terms

Abstract

This article studies the synchronization of new coupled fractional delayed reaction–diffusion neural networks with reaction terms satisfying the global Lipschitz condition via time-continuous and time-discontinuous boundary controllers. The realization of neural networks inevitably involves diffusion phenomena and time delays, and all the neurons of neural networks are interrelated. Considering these aspects, this study focuses on coupled fractional neural networks with time-delay and diffusion terms. A state-dependent boundary control (BC) is designed for when the state information is available, and a criterion is presented to ensure the synchronization of the considered systems. Considering the advantages of a time-discontinuous controller, an intermittent BC and a criterion of synchronization are given. When the state information cannot be fully obtained, a boundary-output-based observer is provided for estimating the states. Then, an observer-based intermittent boundary controller is given to ensure the synchronization. From the given criteria, the effects of time delay and the control time length on synchronization are analyzed. This research involves two key challenges: 1) consideration of the BC and intermittent control parameters in the system performance analysis and 2) clarification of the influence of system parameters on synchronization. These challenges are addressed using Poincaré’s inequality, the fractional Razumikhin-type theorem, and several properties of the Mittag-Leffler function are used to deal with the above difficulties. Examples show that our results are valid.