摘要
针对确定性离散动力学系统的混沌控制与反控制问题,从配置Lyapunov指数出发,提出一种实现混沌控制与反控制的一般性方法.首先给出了受控系统混沌判断的特征值条件,满足该条件的系统,将产生Devaney意义下的混沌和Li-Yorke意义下的混沌.然后通过引入非对角型反馈来调整系统雅可比矩阵元素,灵活配置系统Lyapunov指数的数值和符号,从而实现离散系统的混沌控制或反控制.给出了必要的证明和仿真实例,仿真结果表明了算法的有效性.
A generalized control method, which based the configuration of the signs and values of Lyapunov exponents and used to control or anti-control a chaotic deterministic discrete-time dynamical system, is presented in this paper. A criterion is given to detect the chaos in controlled systems. The systems satisfied the criterion have Devaney＇s chaos and Li ＋ Yorke＇s chaos. The control or anti-control a discrete-time system is realized by the used of none-diagonal feedback, and the elements in Jacobian matrix of the system are arranged to place the Lyapunov exponents well. The necessary proofs and example are presented in the paper, and simulation results depict the effectiveness of the proposed method.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第23期206-212,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(61074185)
