Distributed Robust Synchronization of Dynamical Networks With Stochastic Coupling

Abstract

This paper deals with the problem of robust adaptive synchronization of dynamical networks with stochastic coupling by means of evolutionary algorithms. The complex networks under consideration are subject to: 1) the coupling term in a stochastic way is considered; 2) uncertainties exist in the node's dynamics; and 3) pinning distributed synchronization is also considered. By resorting to Lyapunov function methods and stochastic analysis techniques, the tasks to get the distributed robust synchronization and distributed robust pinning synchronization of dynamical networks are solved in terms of a set of inequalities, respectively. The impacts of degree information, stochastic coupling, and uncertainties on synchronization performance, i.e., mean control gain and convergence rate, are derived theoretically. The potential conservativeness for the distributed robust pinning synchronization problem is solved by means of an evolutionary algorithm-based optimization method, which includes a constraint optimization evolutionary algorithm and a convex optimization method and aims at improving the traditional optimization methods. Simulations are provided to illustrate the effectiveness and applicability of the obtained results.