Step-like contrast structure for class of nonlinear singularly perturbed optimal control problem

被引：1

作者：

Wu, Li-meng ^{[1
,2
]}

Ni, Ming-kang ^{[2
,3
]}

Lu, Hai-bo ^{[2
]}

机构：

[1] Hebei Normal Univ Sci & Technol, Sch Math & Informat Technol, Qinhuangdao 066004, Hebei Province, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[3] Shanghai Jiao Tong Univ, E Inst Shanghai Univ, Div Computat Sci, Shanghai 200240, Peoples R China

来源：

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2013年 / 34卷 / 07期

基金：

中国国家自然科学基金;

关键词：

optimal control; contrast structure; singular perturbation; SLOW-FAST DECOMPOSITION;

D O I：

10.1007/s10483-013-1714-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result.

引用

页码：875 / 888

页数：14

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