大时间区间优化问题的“两分法”变换次优解

A Suboptimal Solution to Optimal Control Problem Over Large Time Interval with Dichotomy Transformation

本文对于两端固定的大时间区间 LQ 优化问题,提出了一种基于“两分法”变换(Dichotomy Transformatinn)的次优解法.该解法避免了对高阶矩阵的求逆运算,并具有较高的精度.在此基础上,运用次优性的有关概念,给出了估计上述次优控制引起的性能损失的方法,从而使次优解的可靠性建立在定量的基础上.

This paper presents a suboptimal solution,based on the dichotomy tran-sformation [1]～[3] to the LQ optimal control problem over a large time intervalwith end states prescribed.With a relatively high accuracy,the solution avoidsthe inverse operation of high-order matrices.Furthermore,using the ideas ofsuboptimality,this paper gives the method for estimating the performance losscaused by the suboptimal control.Hence,the reliability of the suboptimal solu-tion is ensured on the basis of quantitative analysis.