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Noether’s theorem of nonholonomic systems in optimal control

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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.

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Authors and Affiliations

  1. Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Ping-ping Cai

  2. Eastern Liaodong University, Shenyang, 118000, China

    Duan Song

  3. Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Jing-li Fu

Authors
  1. Ping-ping Cai
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  2. Duan Song
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  3. Jing-li Fu
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Corresponding author

Correspondence to Jing-li Fu.

Additional information

Supported by the National Natural Science Foundation of China (No. 11272287, 11472247).

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Cai, Pp., Song, D. & Fu, Jl. Noether’s theorem of nonholonomic systems in optimal control. Acta Math. Appl. Sin. Engl. Ser. 32, 875–882 (2016). https://doi.org/10.1007/s10255-016-0607-4

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  • DOI: https://doi.org/10.1007/s10255-016-0607-4

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