Synchronization Control for Coupled Delayed Neural Networks With Time-Varying Coupling via Markov Pinning Strategy

Abstract

In this article, a novel Markov pinning strategy, where each mode corresponds to a specific pinning strategy and the switches from one specific pinning strategy to another are governed by the transition probability matrix, is proposed for synchronization control problem of coupled delayed neural networks. With consideration that topological structures of networks are usually time-dependent, a general polytopic time-varying coupling model is studied. In coupled delayed neural networks, each node frequently exchanges information with its neighboring nodes so as to realize synchronization. Since communization network is with limited transmission resource, network congestion may occur, and thus information of neighboring nodes may not be available. Furthermore, as the amount of information that needs to be transmitted will change with the number of pinned nodes, packet dropout rate is considered to be random switching. By Lyapunov function method, a sufficient condition is obtained to globally synchronize the coupled delayed neural networks, and then the Markov pinning controller is designed. Finally, an illustrative example, where all nodes synchronize quickly under the control of Markov pinning controller, is used to demonstrate the advantages and potential of the new design strategy.