具有长期平均最优性准则的奇摄动最优控制问题的平均控制生成族
On average control generating families for singularly perturbed optimal control problems with long run average optimality criteria
摘要：
本文的目的是开发工具，用于分析和构造具有长期平均最优性准则的奇异摄动（SP）最优控制问题的近最优解。我们利用的思想是，首先渐近近似一个给定的问题的最优控制的SP系统的某一平均最优控制问题，然后将此平均问题转化为一个无限维（ID）的线性规划（LP）问题，然后近似后者的半无限LP问题。我们表明，这些半无限LP问题的最优解和它们的最优解（可以找到一个可用的LP软件的修改的帮助下）允许一个构建近最优控制的SP系统。我们证明了一个数值例子的建设。
英文摘要：
The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.
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