基于轨道引导和可控域的混沌系统控制研究

Control of Chaotic Systems Based on Directing Orbits and Controllable Target

把最短时间最优控制思想用于混沌轨道引导 ,并通过可控域 ,把混沌轨道引导和不稳定周期轨道的稳定化方法有机地结合在一起 ,提出了一种离散混沌系统的控制方法 ,该方法是先利用最短时间的混沌轨道引导控制使系统快速进入可控域 ,然后激发局部状态反馈控制器来实现控制混沌系统 ,最后以Henon系统为例 ,进行了数字仿真 ,仿真中对系统进入可控域的时间和噪声对所提方法控制效果的影响等问题进行了讨论 。

The idea of minimum time optimal control is applied to chaotic orbit targeting.Based on a combination of chaotic orbit targeting with a stabilization method for unstable periodic orbit via controllable target,a new method for controlling discrete chaotic systems is proposed.The control method consists of first directing the orbit of the given chaotic system from a given initial point to the controllable target by using minimum time optimal control,and then applying the appropriate close loop control to stabilize the given chaotic system.Henon system is used as an illustration to discuss the important issues including the length of the transient before reaching the controllable target and the effect of noise,and to demonstrates the effectiveness of the proposed method.