一类复杂动力学网络的滑模控制混沌同步

Chaos Synchronization of a Class of Complex Networks on Sliding Mode Control

滑模控制作为一种重要的鲁棒控制策略,得到广泛的应用,运用滑模控制实现多个具有相互关联的混沌系统的同步问题还鲜有报道。本文利用滑模控制方法研究了一类复杂动力学网络的同步控制问题,该系统的驱动系统为i=Cxi+1+f(xi+1),n=g(x1,x2,…,xn),而响应系统为j i=Cxj i+1+f(xj i+1),j n=g(xj1,xj2,…,xj n)+ξj+uj,结果表明选取适当的滑模面和控制律,该混沌系统是同步的。文章基于Lyapunov稳定性理论,设计了网络滑模面以及控制输入,如果选取适当的可调参数,可得到V·<0,从而在滑模控制方法下多个混沌系统构成的复杂动力学网络是混沌同步的,仿真算例说明了该方法的有效性。

Sliding mode control get comprehensive application as important robust control strategy. The sychronation problem is scarcely reported for multiple synchrophic chaos systems by using sliding mode approach. Chaos synchronization of a class of com- plex networks on sliding mode control is studied in the paper. The drive systems is systems as following x·i=Cxi＋1＋f（xi＋1）,x·n=g（x1,x2,…,xn）, and systems x·ji=Cxji＋1＋f（xji＋1）,x·jn=g（xj1,xj2,…,xjn）＋ξj＋ujas it＇s response systems. The research results illustrated that by choosing appropriate sliding mode surface and control law, systems is chaos synchroniziation. The effectiveness of the method is analyzed based on Lyapunov stability theory. The last results proved that complex networks are chaos synchronized selecting proper adjustable parameter. It can get that the derivative of V is less then zero. So the complex dy- namics network comprised of multiple synchrophic chaos systems is synchronized using sliding mode approach. The simulation ex- ample proved that the approach is effective.