Adaptive PI Control for Synchronization of Complex Networks With Stochastic Coupling and Nonlinear Dynamics

In the paper, synchronization of nonlinear dynamical complex networks with stochastic coupling under adaptive PI control is considered. In light of the relative states information of the network nodes, node- and edge-based adaptive PI synchronization protocols are proposed and several sufficient conditions are derived. By employing stochastic analysis techniques combined with a version of the LaSalle's invariant principles applied to stochastic process and Lyapunov function approaches, synchronization of complex networks with nonlinear dynamics and stochastic coupling reaches in mean square via these two types of adaptive PI control protocols are proved. The proposed adaptive PI control protocols for synchronization of complex dynamical networks are useful for future realistic engineering systems design. Numerical examples are finally simulated to validate the theoretical analysis.