ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS

doi:10.1016/S0252-9602(16)30081-9

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1457-1466.doi: 10.1016/S0252-9602(16)30081-9

ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS

武利猛¹, 张娟¹, 倪明康², 陆海波³

1. School of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China;
2. Department of Mathematics, East China Normal University, Shanghai 200241, China;
3. School of Economics and Management, Shanghai Institute of Technology, Shanghai 201418, China

收稿日期:2014-12-06 修回日期:2016-04-25 出版日期:2016-10-25 发布日期:2016-10-25
作者简介:Limeng WU,neamou123@163.com;Juan ZHANG,neamou123@163.com;Mingkang NI,wulmmath2010@163.com;Haibo LU,classten@163.com
基金资助:
This project is supported by the National Natural Science Foundation of China (11471118, 11401385 and 11371140), Natural Science Foundation of Hebei Province (A2015407063) and Doctoral Foundation of Hebei Normal University of Science and Technology(2013YB008).

ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS

Limeng WU¹, Juan ZHANG¹, Mingkang NI², Haibo LU³

1. School of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China;
2. Department of Mathematics, East China Normal University, Shanghai 200241, China;
3. School of Economics and Management, Shanghai Institute of Technology, Shanghai 201418, China

Received:2014-12-06 Revised:2016-04-25 Online:2016-10-25 Published:2016-10-25
Supported by:
This project is supported by the National Natural Science Foundation of China (11471118, 11401385 and 11371140), Natural Science Foundation of Hebei Province (A2015407063) and Doctoral Foundation of Hebei Normal University of Science and Technology(2013YB008).

摘要/Abstract

摘要：

In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. Meanwhile, the existence of solution for the hybrid dynamical system is proved by the sewing method and the uniformly valid asymptotic expansion of the optimal trajectory is constructed by the boundary function method. Finally, an example is presented to illustrate the result.

关键词: optimal control, hybrid dynamical system, singular perturbation

Abstract:

Key words: optimal control, hybrid dynamical system, singular perturbation

中图分类号:

34B15

武利猛, 张娟, 倪明康, 陆海波. ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS[J]. 数学物理学报(英文版), 2016, 36(5): 1457-1466.

Limeng WU, Juan ZHANG, Mingkang NI, Haibo LU. ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS[J]. Acta mathematica scientia,Series B, 2016, 36(5): 1457-1466.

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ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS

ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS

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