混沌系统的时滞反馈控制研究

This project studies the problem of stabilization of unstable periodic orbits of chaotic systems by using time-delayed state or output feedback. The focus of the project is the well known open problem related to the "Odd Number Limitation" of the time-delayed feedback control method. Some important results obtained in the project are as follows: 1) We are among the first researchers who study the problem of stabilization of unstable periodic orbits of chaotic systems in continuous-time form by using time-delayed dynamic output feedback. For the first time, we establish a separation principle of the design of dynamic output feedback for time-delayed periodic systems. And we point out that the odd number limitation cannot be overcome by this kind of controller. 2) For the first time we study the problem of stabilization of unstable periodic orbits in hybrid chaotic systems. We creatively propose a time-delayed impulsive control method to solve this problem, and give the rigorous stability analysis for this method. 3) Based on an optimality principle we first propose a nonlinear time-delayed feedback control method to overcome the odd number limitation in the problem of stabilization of unstable periodic orbits of chaotic systems in continuous-time form. 4) For chaotic system with unknown parameters, we propose an identification method based on chaos synchronization, and give some sufficient conditions of the convergence of the identification algorithm. We further apply this identification method to the adaptive stabilization of unstable periodic orbits of chaotic systems with unknown parameters.

本项目着重研究混沌系统时滞反馈控制中的若干基础理论问题：1）利用混沌同步建立未知煦缦低车哪Ｐ停?）分析混沌系统的能控性和小能量控制设计原理；3）分析混沌系统在线允敝头蠢∠碌奈榷ㄐ裕⒃鲆婢卣蟮纳杓圃颍?）探讨线性时滞反馈的“奇数限制”的本质及克服方法，建立用时滞状态镇定混沌系统内嵌周期轨道的一般原则和设计方法。