奇摄动最优控制问题中的内部转移层解

数学物理学报 ›› 2013, Vol. 33 ›› Issue (2): 206-215.

奇摄动最优控制问题中的内部转移层解

武利猛¹|倪明康^1,2|陆海波¹

1.华东师范大学数学系上海 |200241;
2.上海高校计算科学E -研究院, 上海交通大学研究所上海 |200240

收稿日期:2011-09-20 修回日期:2012-12-01 出版日期:2013-04-25 发布日期:2013-04-25
基金资助:
国家自然科学基金 (11071075, 30921064, 90820307)、上海市自然科学基金 (10ZR1409200)、上海市教育委员会E -研究院建设项目(E03004)和中国科学院知识创新工程项目资助

Internal Transition Layer Solution of Singularly Perturbed Optimal Control Problem

WU Li-Meng¹, NI Ming-Kang^1,2, LIU Hai-Bo¹

1.Department of Mathematics, East China Normal University, Shanghai 200241;
2.Division of Computational Science, E-Institute of Shanghai Universities, SJTU, Shanghai 200240

Received:2011-09-20 Revised:2012-12-01 Online:2013-04-25 Published:2013-04-25
Supported by:
国家自然科学基金 (11071075, 30921064, 90820307)、上海市自然科学基金 (10ZR1409200)、上海市教育委员会E -研究院建设项目(E03004)和中国科学院知识创新工程项目资助

摘要/Abstract

摘要：

利用奇摄动理论证明了一类最优控制问题中内部转移层解的存在性, 不但给出了内部转移层存在的条件而且确定了转移点的位置. 同时利用边界层函数法基础上发展起来的直接展开法构造了该最优控制问题的一致有效渐近解. 最后, 通过例子验证了主要结果.

关键词: 奇摄动, 最优控制, 转移层

Abstract:

The existence of internal transition layer solution for a class of optimal control problem is proved by the singularly perturbed theory. In the framework of this paper, the authors not only give the conditions under which there exists an internal transition layer but also determine where an internal transition time is. Meanwhile, the uniformly valid asymptotic solution for the optimal control problem is constructed by the direct scheme method, which is based on the boundary function method. Finally, an example is presented to show the result.

Key words: Singular perturbation, Optimal control, Transition layer

中图分类号:

34B15

武利猛, 倪明康, 陆海波. 奇摄动最优控制问题中的内部转移层解[J]. 数学物理学报, 2013, 33(2): 206-215.

WU Li-Meng, NI Ming-Kang, LIU Hai-Bo. Internal Transition Layer Solution of Singularly Perturbed Optimal Control Problem [J]. Acta mathematica scientia,Series A, 2013, 33(2): 206-215.

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