基于秩一摄动理论配置Lyapunov指数的新方法
A New Method of Placing Lyapunov Exponents Via Rank One Perturbation

本文提出一种混沌控制与反控制的新算法。利用秩一摄动理论精确摄动离散受控系统矩阵的特征值，来配置Lyapunov指数。新算法完全吻合混沌的Lyapunov指数判据。既能更准确地配置正的Lyapunov指数，又能配置传统算法无法获得的负Lyapunov指数。仿真结果显示了新算法的有效性。
Lyapunov exponents are important metrics to determine chaos in discrete systems. A new algorithm configuring Lyapunov exponents is proposed for chaos control and chaos anti-control. By introducing specific types of feedback and modulus operations, the algorithm uses eigenvalues of the system matrix via rank one perturbations theory to configure Lyapunov exponents. The proposed algorithm is inline with the Lyapunov exponent criterion for chaos. The proposed algorithm is able to accurately configure the positive Lyapunov exponents of chaos control, and the negative Lyapunov exponents that cannot be obtained in traditional algorithms. The simulation results illustrate the effectiveness of the proposed algorithm.