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Pontryagin maximum principle, relaxation, and controllability

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Abstract

The relations between the necessary minimum conditions in an optimal control problem (Pontryagin maximum principle), the minimum conditions in the corresponding relaxation (weakened) problem, and sufficient conditions for the local controllability of the controlled system specifying the constraints in the original formulation are studied. An abstract optimization problem that models the basic properties of the optimal control problem is considered.

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References

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya ul. 65, Moscow, 117997, Russia

    E. R. Avakov

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    G. G. Magaril-Il’yaev

  3. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoi Karetnyi per. 19/1, Moscow, 127994, Russia

    G. G. Magaril-Il’yaev

Authors
  1. E. R. Avakov
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  2. G. G. Magaril-Il’yaev
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Correspondence to G. G. Magaril-Il’yaev.

Additional information

Original Russian Text © E.R. Avakov, G.G. Magaril-Il’yaev, 2016, published in Doklady Akademii Nauk, 2016, Vol. 467, No. 5, pp. 505–508.

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Avakov, E.R., Magaril-Il’yaev, G.G. Pontryagin maximum principle, relaxation, and controllability. Dokl. Math. 93, 193–196 (2016). https://doi.org/10.1134/S1064562416020216

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  • DOI: https://doi.org/10.1134/S1064562416020216

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