Noether's Theorem of Nonholonomic Systems in Optimal Control

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	Noether's Theorem of Nonholonomic Systems in Optimal Control
Alternative Title	Noether's Theorem of Nonholonomic Systems in Optimal Control
	Cai Pingping 1; Song Duan 2; Fu Jingli 1
	2016
Source Publication	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
Volume	32 Issue:4 Pages:875-882
Abstract	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.
Other Abstract	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.
Keyword	SYMMETRIES nonholonommic system symmetry conservation law Noether's theorem optimal control
Indexed By	CSCD
Language	英语
Funding Project	[National Natural Science Foundation of China]
CSCD ID	CSCD:5854032
Citation statistics
Document Type	期刊论文
Identifier	http://ir.imr.ac.cn/handle/321006/153953
Collection	中国科学院金属研究所
Affiliation	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
Recommended Citation 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.

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