多个时滞混沌系统自适应有限时间同步控制

Adaptive finite-time synchronization of multiple chaotic systems with time-varying delay

针对多个时滞混沌系统,研究了其有限时间同步控制问题,所考虑的混沌系统具有不同的结构和时变状态时滞,通过设计适当的自适应更新律,用以在线更新控制器的增益,从而达到更快地收敛速度,并给出了自适应控制器设计方法。利用Lyapunov稳定性定理和有限时间稳定性理论,证明了所设计的自适应控制器和相应的控制增益自适应更新律,均能保证多个误差动态系统的状态在有限时间内达到同步,并给出了同步过渡时间的估计。最后,通过对3个典型的混沌系统,即Lorenz系统、Chen系统和Lü系统的算例仿真,进一步验证了所提自适应有限时间同步控制方法的可行性和有效性。

In this paper, the issue of adaptive finite-time synchronization of multiple chaotic systems with time-varying delay is investigated. The chaotic systems with different structures and time-varying state delays were considered. Firstly, by designing appropriate adaptive update law, the gain of the controller can be updated online to achieve faster convergence speed. The design method of adaptive controller is presented. Then by using Lyapunov stability theorem and finite-time stability theory, it is proved that the designed adaptive controller and the corresponding control gain adaptive update law can guarantee the synchronization of states of multiple error dynamic systems in finite time, and the estimation of synchronization settling time is also given. Finally, the feasibility and effectiveness of the proposed adaptive finite-time synchronization control method is further validated by numerical simulation of three typical chaotic systems i.e. Lorenz system, Chen system and Lü system.