Stochastic synchronization of complex networks via a novel adaptive composite nonlinear feedback controller

Abstract

In this paper, a novel adaptive composite nonlinear feedback controller is designed to synchronize complex networks. The proposed adaptive composite nonlinear feedback controller consists of an adaptive linear feedback control law and an adaptive nonlinear feedback control law. The adaptive linear feedback control part is designed to achieve a quick response. However, too fast convergent speed may cause overshoot or oscillations. So in order to achieve precise control, we design the adaptive nonlinear feedback control law to reduce the overshoot or oscillations caused by the adaptive linear feedback part. By using the properties of Weiner process and adding the proposed control strategy to the nodes, stochastic synchronization of complex networks with quickly convergent speed and high control precision can be achieved. Numerical simulations demonstrate the superior performance of this novel adaptive composite nonlinear feedback controller as compared to the conventional adaptive linear feedback controller.