离散时间系统线性状态反馈混沌化

摘要

针对给定的确定性离散时间动力学系统,提出一种新的线性状态反馈加非线性模运算的混沌化算法.给定离散时间系统可以是线性、非线性、低阶、高阶、渐近稳定、不稳定、甚至混沌的.算法的结果是受控系统所有李雅普诺夫指数均不为零而其中至少一个为正,符合混沌的定义.给出了证明和一个混沌化实例.仿真结果显示了算法的良好效果.%A control algorithm that combines a linear state-feedback with a nonlinear mod-operation is proposed to make an arbitrarily given, deterministic, discrete-time dynamical system chaotic. The given system can be either linear or nonlinear, lower or higher dimensional, asymptotically stable, unstable, or even chaotic. The resulting controlled system fitting the definition of chaos very well with all Lyapunov exponents non-zero is chaotic, with at least one positive Lyapunov exponent larger than a given positive constant, c. The corresponding proof as well as an example has been presented. The results of simulation show effectiveness of the algorithm.