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The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited

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Abstract

A maximum principle in the form given by R.V. Gamkrelidze is obtained, although without a priori regularity assumptions to be satisfied by the optimal trajectory. After its formulation and proof, we propose various regularity concepts that guarantee, in one sense or another, the nondegeneracy of the maximum principle. Finally, we show how the already known first-order necessary conditions can be deduced from the proposed theorem.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    A. V. Arutyunov

  2. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia

    D. Y. Karamzin

  3. University of Porto, Porto, Portugal

    D. Y. Karamzin

  4. Faculty of Engineering, University of Porto, Institute for Systems & Robotics, Porto, Portugal

    F. L. Pereira

Authors
  1. A. V. Arutyunov
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  2. D. Y. Karamzin
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  3. F. L. Pereira
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Corresponding author

Correspondence to D. Y. Karamzin.

Additional information

Communicated by B. Mordukhovich.

This research was supported by the Russian Foundation for Basic Research, project 09-01-00619, by a grant from the President of the Russian Federation, MK-119.2009.1, by the Russian Federal Program “Scientific and pedagogical staff of innovative Russia in 2009–2013” (contract 16.740.11.0426 of 11/26/2010), and by the Foundation for Science and Technology (Portugal), support of R&D unit 147 (ISRP), and projects PTDC/EEA-CRO/104901/2008, and SFRH/BPD/26231/2006.

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Arutyunov, A.V., Karamzin, D.Y. & Pereira, F.L. The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited. J Optim Theory Appl 149, 474–493 (2011). https://doi.org/10.1007/s10957-011-9807-5

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  • DOI: https://doi.org/10.1007/s10957-011-9807-5

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