Approximation of optimal feedback control: a dynamic programming approach

doi:10.1007/s10898-009-9432-0

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	Approximation of optimal feedback control: a dynamic programming approach
	Guo, Bao-Zhu1,2 ; Wu, Tao-Tao 1,3
	2010-03-01
发表期刊	JOURNAL OF GLOBAL OPTIMIZATION
ISSN	0925-5001
卷号	46 期号:3 页码:395-422
摘要	We consider the general continuous time finite-dimensional deterministic system under a finite horizon cost functional. Our aim is to calculate approximate solutions to the optimal feedback control. First we apply the dynamic programming principle to obtain the evolutive Hamilton-Jacobi-Bellman (HJB) equation satisfied by the value function of the optimal control problem. We then propose two schemes to solve the equation numerically. One is in terms of the time difference approximation and the other the time-space approximation. For each scheme, we prove that (a) the algorithm is convergent, that is, the solution of the discrete scheme converges to the viscosity solution of the HJB equation, and (b) the optimal control of the discrete system determined by the corresponding dynamic programming is a minimizing sequence of the optimal feedback control of the continuous counterpart. An example is presented for the time-space algorithm; the results illustrate that the scheme is effective.
关键词	Viscosity solution Hamilton-Jacobi-Bellman equation Finite difference Optimal feedback control
DOI	10.1007/s10898-009-9432-0
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	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000274461400006
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9749
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 100190, Peoples R China 2.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa 3.Chinese Acad Sci, Grad Univ, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Guo, Bao-Zhu,Wu, Tao-Tao. Approximation of optimal feedback control: a dynamic programming approach[J]. JOURNAL OF GLOBAL OPTIMIZATION,2010,46(3):395-422.
APA	Guo, Bao-Zhu,&Wu, Tao-Tao.(2010).Approximation of optimal feedback control: a dynamic programming approach.JOURNAL OF GLOBAL OPTIMIZATION,46(3),395-422.
MLA	Guo, Bao-Zhu,et al."Approximation of optimal feedback control: a dynamic programming approach".JOURNAL OF GLOBAL OPTIMIZATION 46.3(2010):395-422.