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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.
Aiming at the chaos control and anti-control problem of deterministic discrete dynamic system, a general method to realize chaos control and anti-control is proposed based on Lyapunov exponent allocation. Firstly, the eigenvalue condition of chaos judgment of controlled system is given, The system of this condition will produce the chaos in the sense of Devaney and the chaos in the sense of Li-Yorke, and then adjust the system Jacobian matrix elements by introducing non-diagonal feedback and flexibly configure the values and symbols of the system Lyapunov exponents to achieve discrete The chaotic control or anti-control of the system is given.The necessary proofs and simulation examples are given, and the simulation results show the effectiveness of the algorithm.