离散混沌系统的最小能量控制

Energy minimization control for a discrete chaotic system

对于离散混沌系统的最小能量控制问题 ,提出了一种框架性方法 ,该方法具有通用性 .首先 ,设计一个二次目标函数 ,同时把混沌系统分解为线性部分和非线性部分两项和 .然后 ,提出了求解非线性最优控制问题的两级算法 :第一级对混沌系统中的非线性部分进行预估 ,以使原系统变为带有常数项的线性系统 ;第二级用动态规划求解一个非典型线性二次最优控制问题 ,并把解返回第一级 ,第一级根据第二级的解对非线性部分重新预估 .这样通过两级间不断的信息交换 ,最终得到混沌系统的最优控制律 .该方法不仅实现了对混沌系统的控制 ,而且在整个控制过程中消耗的控制能量最小 .

A general framework algorithm is proposed for energy minimization control for a discrete chaotic system. A quadratic performance function is first given and the chaotic system is decomposed into a linear and a nonlinear parts. Then, the two-level algorithm is presented to solve the nonlinear optimal control problem: The first level predicates the nonlinear part of the chaos system; the second level solves a nonlinear quadratic optimization control problem by dynamic programming. The solution is fed back into the first level. The first level re-estimates the nonlinear part according to the solution from the second level. The information has been exchanged between the two levels by this means such that the optimal control law is obtained eventually. This method not only can make the control of chaos system be realized but also makes the energy consumed minimal during the whole control process.Simulations show the effectiveness of this algorithms.