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Differential Stability of a Class of Convex Optimal Control Problems

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Abstract

A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular subdifferential of the optimal value function at a given parameter are obtained by means of some recent results on differential stability in mathematical programming. The computation procedures and illustrative examples are presented.

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Acknowledgements

This work was supported by College of Sciences, Thai Nguyen University (Vietnam), the Grant MOST 105-2221-E-039-009-MY3 (Taiwan), and National Foundation for Science & Technology Development (Vietnam). The authors would like to thank the anonymous referees for their careful readings and valuable suggestions for corrections, which have helped to improve the paper presentation.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, College of Sciences, Thai Nguyen University, Thai Nguyen City, Vietnam

    D. T. V. An

  2. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    J.-C. Yao

  3. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam

    N. D. Yen

Authors
  1. D. T. V. An
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  2. J.-C. Yao
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  3. N. D. Yen
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Correspondence to N. D. Yen.

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An, D.T.V., Yao, JC. & Yen, N.D. Differential Stability of a Class of Convex Optimal Control Problems. Appl Math Optim 81, 1–22 (2020). https://doi.org/10.1007/s00245-017-9475-4

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  • DOI: https://doi.org/10.1007/s00245-017-9475-4

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