KMS Of Academy of mathematics and systems sciences, CAS
Approximation of optimal feedback control: a dynamic programming approach | |
Guo, Bao-Zhu1,2; Wu, Tao-Tao1,3 | |
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. |
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