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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 Pingping1; Song Duan2; Fu Jingli1 2016 Source Publication ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES ISSN 0168-9673 Volume 32Issue:4Pages: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/321006/153950 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 China2.中国科学院金属研究所 Recommended CitationGB/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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