基于秩一摄动理论配置Lyapunov指数的新算法  

A new method of placing Lyapunov exponents via rank one perturbation

作　　者：于永进 陈旭 程学珍 YU Yong-jin;CHEN Xu;CHENG Xue-zhen(College of Electical Engineering and Automation, Shandong University of Science and Techonology,Qingdao Shandong 266590, China)

机构地区：[1]山东科技大学电气与自动化工程学院,山东青岛266590

出　　处：《控制理论与应用》2017年第7期980-985,共6页Control Theory & Applications

基　　金：国家自然科学基金项目(61503224;61273197)资助~~

摘　　要：本文提出一种为混沌控制与反控制配置Lyapunov指数的新算法.该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,使其完全吻合混沌判据.该算法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 configuringLyapunov exponents is proposed for chaos control and chaos anti-control.By introducing specific types of feedbackand modulus operations,the algorithm uses eigenvalues of the system matrix via rank one perturbations theory to configureLyapunov exponents.The proposed algorithm is inline with the Lyapunov exponent criterion for chaos.The proposedalgorithm is able to accurately configure the positive Lyapunov exponents of chaos control,and the negative Lyapunov exponentsthat cannot be obtained in traditional algorithms.The simulation results illustrate the effectiveness of the proposedalgorithm.

关 键 词：LYAPUNOV指数 秩一摄动 混沌控制 混沌反控制 

分 类 号：O231[理学—运筹学与控制论] O415.5[理学—数学]