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Time Optimal Control for Some Ordinary Differential Equations with Multiple Solutions

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Abstract

This paper studies a time optimal control problem for a class of ordinary differential equations. The control systems may have multiple solutions. Based on the properties fulfilled by the solutions of the concerned equations, we get both the existence and the Pontryagin maximum principle for optimal controls.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grant 11471070, 11301472, the Natural Science Foundation of Guangdong Province under Grant 2014A030307011, the Training Program Project for Outstanding Young Teachers of Colleges and Universities in Guangdong Province under Grant Yq2014116 and the Characteristic Innovation Project of Common Colleges and Universities in Guangdong Province under Grant 2014KTSCX158.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Ping Lin

  2. School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang, 524048, China

    Shu Luan

Authors
  1. Ping Lin
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  2. Shu Luan
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Correspondence to Ping Lin.

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Communicated by Boris Vexler.

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Lin, P., Luan, S. Time Optimal Control for Some Ordinary Differential Equations with Multiple Solutions. J Optim Theory Appl 173, 78–90 (2017). https://doi.org/10.1007/s10957-017-1064-9

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  • DOI: https://doi.org/10.1007/s10957-017-1064-9

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