Numerical Solution to Optimal Feedback Control by Dynamic Programming Approach: A Local Approximation Algorithm

doi:10.1007/s11424-017-5149-1

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	Numerical Solution to Optimal Feedback Control by Dynamic Programming Approach: A Local Approximation Algorithm
	Guo Bao-Zhu1,2 ; Wu Tao-Tao 1
	2017-08-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	30 期号:4 页码:782-802
摘要	This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.
关键词	Curse of dimensionality Hamilton-Jacobi-Bellman equation optimal feedback control upwind finite difference viscosity solutions.
DOI	10.1007/s11424-017-5149-1
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000407482800003
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26199
专题	系统科学研究所
通讯作者	Guo Bao-Zhu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Guo Bao-Zhu,Wu Tao-Tao. Numerical Solution to Optimal Feedback Control by Dynamic Programming Approach: A Local Approximation Algorithm[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2017,30(4):782-802.
APA	Guo Bao-Zhu,&Wu Tao-Tao.(2017).Numerical Solution to Optimal Feedback Control by Dynamic Programming Approach: A Local Approximation Algorithm.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,30(4),782-802.
MLA	Guo Bao-Zhu,et al."Numerical Solution to Optimal Feedback Control by Dynamic Programming Approach: A Local Approximation Algorithm".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 30.4(2017):782-802.