Event-triggered heterogeneous master-slave synchronization with sampled-data control

Abstract

As is well known, chaos synchronization has a good performance in secret communication. However, in most existing researches, chaos synchronization is realized between master chaotic system and slave chaotic system with real-time communication. A lot of network bandwidths are wasted in useless communication which may bring great economic costs and increase the likelihood of network congestion. In this paper, the synchronization for the heterogeneous master-slave system is studied. Compared with the homogeneous synchronization, the heterogeneous synchronization has a broad application prospect. Then the sampling controller based on event trigger is designed to achieve the heterogeneous master-slave synchronization which can save network bandwidth, with the control performance maintained. Because transmission time delay is universal in communication system, the delay model of the system is constructed and utilized firstly. Based on the proposed system model, the master-slave heterogeneous synchronization problem is equivalently converted into the asymptotical stability problem of a time-delay system by using the input delayed approach. Then, according to the Lyapunov stability theory and linear matrix inequality, we may rigouously prove that the synchronization of heteogeneous master-slave chaotic system can be achieved. Meanwhile, the heterogeneous master-slave system synchronization conditions and sampling controller can be given based on the constructing Lyapunov-Krasovskii functional with the Wirtinger inequality and free weight matrix method. The sampling controller actually is a stateback controller. But for the purpose of reducing the network usage rate, wheter the state can be transmitted can be determined by the event-triggered rules. The event-triggered rules are designed based on the error state between master chaotic system and slave chaotic system, and the synchronization performance index can be determined by choosing the system parameter. The designed sampling controller updates the control parameters when the event-triggered rules are satisfied. Finally, numerical simulation experiments are employed to verify the correctness and effectiveness of the proposed method. Results indicate that the hetergeneous master-slave chaotic system with transimission time delay can indeed achieve synchronization by event-triggerd sample control. Moreover, the number of communications between master chaotic system and slave chaotic system is less than before and the synchroization performance is also at an idea level.