一个超混沌系统的最优控制与同步  

Optimal Control and Synchronization of a Hyperchaotic System

作　　者：朱红兰[1,2] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]淮阴工学院数理学院,江苏淮安223003

出　　处：《重庆师范大学学报（自然科学版）》2013年第3期65-68,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11211120155)

摘　　要：在参数未知的情况下,对于一个新的超混沌系统,首先设计最优控制器和参数自适应律实现了混沌系统的控制,并根据最优化原理和Lyapunov方法,选取适当的Lyapunov函数,应用Lyapunov第二方法通过推导得到Lyapunov函数关于系统的全导数是恒小于零的,根据Lyapunov稳定性定理,系统在零点是一致渐近稳定的,从而从理论上证明了控制器的有效性,紧接着对两个相同结构的混沌系统,根据最优化原理设计最优控制器和参数自适应律,实现了混沌系统的同步,并应用Lyapunov第二方法从理论上给予了证明,最后通过Matlab软件对控制与同步的效果进行了数值仿真,数值仿真的结果显示同步系统在很短的时间内很快达到了同步,进一步说明了同步方法的正确性与有效性。In order to realize the control and synchronization of a new chaotic system through optimal controller. In this paper the optimal control and synchronization of a new chaotic system is achieved with fully unknown parameters through design optimal con- troller and parameters updating rule. It is proved that the derivatives of Lyapunov function are constant less than zero. According to the Lyapunov stability theory, the system is uniformly asymptotically stable at zero, thus the validity of this synchronous method theoretically is feasible by Lyapunov method and Hamihon-Jacobi-Bellman equation. Finally, a simulation is conducted with Matlab to prove the optimal control and synchronization of the chaotic system. Simulation results show that synchronization system achieve the synchronization in a short time. Simulation results are provided to demonstrate the effectiveness of the suggested scheme.

关 键 词：混沌 控制 同步 最优化 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置] O415.5[自动化与计算机技术—控制科学与工程]