摘要
分数阶混沌系统大多都是三维或者四维的,关于分数阶高维系统的研究较少.通过构造一个5D分数阶系统,对于这个5D超混沌系统,根据分数阶系统稳定性理论,分析了其平衡点的稳定性.然后基于Lyapunov理论和分数阶系统性理论,设计参数未知的自适应控制与同步,使得5D分数阶系统可以实现不稳定点的控制,并且实现参数未知的同结构自适应同步.最后通过数值模拟,对理论分析加以验证.
Fractional order chaotic systems are often three or four dimension. There are few results about high dimension fractional order systems. Now we construct a 5D fractional order system. For this 5D hyperchaotic system, the stability of equilibrium points is analyzed by means of the stability theory of fractional systems. Then, according to Lyapunov stability theory and theory of fractional systems, adaptive synchronization and control of such systems with unknown parameters are studied~ so that the 5D fractional order system could be stabilized to the unstable point, and the adaptive synchronization with unknown parameters is realized. Finally, numerical simulations are presented to verify the analytical results.
出处
《合肥学院学报（自然科学版）》
2015年第4期20-23,共4页
Journal of Hefei University :Natural Sciences
基金
安徽省自然科学基金项目(11040606M12)资助
