Regulation cooperative control for heterogeneous uncertain chaotic systems with time delay: A synchronization errors estimation framework

This paper addresses the regulation cooperative control problem of heterogeneous uncertain chaotic systems with nonlinear dynamics and time delay. By proposing a robust estimation framework for synchronization error level, this paper investigates the case that complete synchronization for heterogeneous uncertain chaotic systems cannot be achieved since multiple heterogeneous uncertain chaotic systems do not have a common equilibrium point. By introducing a virtual leader node, it is proven that the regulation cooperative control for heterogeneous uncertain chaotic systems can be achieved with an error level by constructing an appropriate synchronization tracking condition with free parameters. To demonstrate the proposed approach in engineering applications, it is applied to the secure communication with multiple heterogeneous uncertain chaotic systems, in which each chaotic synchronization state is treated as an information signal that is injected into the transmitter and simultaneously transmitted to the receiver. Simulation results on heterogeneous uncertain chaotic systems and secure communication consisting of six nonidentical Chua's circuits are presented to demonstrate the effectiveness of the proposed approaches.