Noether's Theorem of Nonholonomic Systems in Optimal Control

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	Noether's Theorem of Nonholonomic Systems in Optimal Control
其他题名	Noether's Theorem of Nonholonomic Systems in Optimal Control
	Cai Pingping 1; Song Duan 2; Fu Jingli 1
	2016
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	32 期号:4 页码:875-882
摘要	In this paper, we extend Noether's theorem to nonholonomic constraints systems in optimal control. We present a systematic way to calculate conserved quantities along the Pontryagin extremals for optimal control problems with nonholonomic constraints, which are invariant under the parameter groups of infinitesimal transformations that change all (time, state, control) variables. Meanwhile, the Noether equalities corresponding to the conservation laws are given. Then, we obtain a new version of Noether's theorem to optimal control systems. An example is given to illustrate the application of these results.
其他摘要	In this paper, we extend Noether's theorem to nonholonomic constraints systems in optimal control. We present a systematic way to calculate conserved quantities along the Pontryagin extremals for optimal control problems with nonholonomic constraints, which are invariant under the parameter groups of infinitesimal transformations that change all (time, state, control) variables. Meanwhile, the Noether equalities corresponding to the conservation laws are given. Then, we obtain a new version of Noether's theorem to optimal control systems. An example is given to illustrate the application of these results.
关键词	SYMMETRIES nonholonommic system symmetry conservation law Noether's theorem optimal control
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China]
CSCD记录号	CSCD:5854032
引用统计
文献类型	期刊论文
条目标识符	http://ir.imr.ac.cn/handle/321006/153953
专题	中国科学院金属研究所
作者单位	1.Zhejiang Sci Tech Univ, Institute Math Phys, Hangzhou 310018, Zhejiang, Peoples R China 2.中国科学院金属研究所
推荐引用方式 GB/T 7714	Cai Pingping,Song Duan,Fu Jingli. Noether's Theorem of Nonholonomic Systems in Optimal Control[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2016,32(4):875-882.
APA	Cai Pingping,Song Duan,&Fu Jingli.(2016).Noether's Theorem of Nonholonomic Systems in Optimal Control.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,32(4),875-882.
MLA	Cai Pingping,et al."Noether's Theorem of Nonholonomic Systems in Optimal Control".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 32.4(2016):875-882.