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Approximation of optimal feedback control: a dynamic programming approach

文献类型：期刊论文

作者Guo, Bao-Zhu1,2; Wu, Tao-Tao1,3
刊名JOURNAL OF GLOBAL OPTIMIZATION
出版日期2010-03-01
卷号46期号:3页码:395-422
关键词Viscosity solution Hamilton-Jacobi-Bellman equation Finite difference Optimal feedback control
ISSN号0925-5001
DOI10.1007/s10898-009-9432-0
英文摘要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.
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
语种英语
WOS记录号WOS:000274461400006
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/9748]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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