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A new algorithm for finding numerical solutions of optimal feedback control
Guo, Bao-Zhu1,2; Sun, Bing2,3
2009-03-01
发表期刊IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
ISSN0265-0754
卷号26期号:1页码:95-104
摘要A new algorithm for finding numerical solutions of optimal feedback control based on dynamic programming is developed. The algorithm is based on two observations: (1) the value function of the optimal control problem considered is the viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation and (2) the appearance of the gradient of the value function in the HJB equation is in the form of directional derivative. The algorithm proposes a discretization method for seeking optimal control-trajectory pairs based on a finite-difference scheme in time through solving the HJB equation and state equation. We apply the algorithm to a simple optimal control problem, which can be solved analytically. The consistence of the numerical solution obtained to its analytical counterpart indicates the effectiveness of the algorithm.
关键词optimal feedback control viscosity solution dynamic programming numerical solution exponential stability
DOI10.1093/imamci/dnn001
语种英语
资助项目National Natural Science Foundation of China ; National Research Foundation of South Africa
WOS研究方向Automation & Control Systems ; Mathematics
WOS类目Automation & Control Systems ; Mathematics, Applied
WOS记录号WOS:000264190900006
出版者OXFORD UNIV PRESS
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/8671
专题系统科学研究所
通讯作者Guo, Bao-Zhu
作者单位1.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China
2.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
3.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
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Guo, Bao-Zhu,Sun, Bing. A new algorithm for finding numerical solutions of optimal feedback control[J]. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION,2009,26(1):95-104.
APA Guo, Bao-Zhu,&Sun, Bing.(2009).A new algorithm for finding numerical solutions of optimal feedback control.IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION,26(1),95-104.
MLA Guo, Bao-Zhu,et al."A new algorithm for finding numerical solutions of optimal feedback control".IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 26.1(2009):95-104.
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