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On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems

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Abstract

We consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied and provide appropriate examples. The sufficient conditions are shown to be both necessary and sufficient when the Hamiltonian is linear with respect to state and control. We obtain a new form of sufficient optimality conditions in the case when the Hamiltonian is neither concave nor differentiable with respect to control.

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Acknowledgments

The author is grateful for valuable comments to S. M. Aseev and all participants of the seminar “Problems of Mathematical Control Theory” at the Steklov Mathematical Institute of Russian Academy of Sciences, as well to the participants of the International Seminar School of Young Scientists “Modelling and Optimization of Complex Systems MOCS-2019.”

Funding

This work is supported by the Russian Science Foundation under grant 19-11-00223.

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Authors and Affiliations

  1. Moscow School of Economics, Lomonosov Moscow State University, Leninskie Gory 1, str. 61, Moscow, 119234, Russia

    Anton O. Belyakov

  2. National Research Nuclear University “MEPhI,”, Kashirskoe sh. 31, Moscow, 115409, Russia

    Anton O. Belyakov

  3. National University of Science and Technology “MISiS,”, Leninskii pr. 4, Moscow, 119049, Russia

    Anton O. Belyakov

  4. Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia

    Anton O. Belyakov

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  1. Anton O. Belyakov
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Correspondence to Anton O. Belyakov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 308, pp. 65–75.

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Belyakov, A.O. On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems. Proc. Steklov Inst. Math. 308, 56–66 (2020). https://doi.org/10.1134/S0081543820010058

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  • DOI: https://doi.org/10.1134/S0081543820010058

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