高维奇异摄动最优控制问题中的空间对照结构

武利猛; 倪明康; 陆海波; 张娟

doi:10.3969/j.issn.1000-5641.2016.01.003

高维奇异摄动最优控制问题中的空间对照结构

doi: 10.3969/j.issn.1000-5641.2016.01.003

1.
河北科技师范学院~~数学与信息科技学院,
2.
河北~~秦皇岛066004;
3.
华东师范大学~~数学系, 上海200241;
4.
上海应用技术学院~~经管学院, 上海201418) 3. 上海应用技术学院~~经管学院, 上海201418

基金项目:

国家自然科学基金(11401385, 11371140); 河北省自然科学基金(A2015407063); 秦皇岛市科学技术研究与发展计划项目(201401A038); 河北科技师范学院博士基金(2013YB008)

详细信息

作者简介:
武利猛, 男, 博士,研究方向为奇异摄动最优控制理论.

通讯作者:
第一作者:\;\;武利猛, 男, 博士,研究方向为奇异摄动最优控制理论.

中图分类号: O175.14
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出版历程
- 收稿日期: 2014-12-29
- 刊出日期: 2016-01-25

Contrast structure of higher dimensional singularly perturbed optimal control problem

摘要

摘要: 研究了一类线性高维奇异摄动最优控制问题的空间对照结构解,利用\ k+\sigma 交换引理证明了空间对照结构解的存在性. 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问题一致有效的形式渐近解.最后, 通过例子验证了主要结果.
- 奇异摄动 /
- 最优控制 /
- 空间对照结构
Abstract: In this paper, a class of linear high-dimensional singularly perturbed optimal control problem is discussed. By means of k+\sigma exchange lemma, we prove the existence\linebreak of contrast structure solution for the singularly perturbed optimal control problem. Meanwhile, by virtue of the direct scheme method which is based on boundary function method, we construct the uniformly valid formal asymptotic solution. Finally, an example is presented to illustrate the main results.
- singular perturbation optimal control contrast structure /

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参考文献(1)

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