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Generalized Maximum Principle in Optimal Control

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Abstract

The concept of a local infimum for an optimal control problem is introduced, and necessary conditions for it are formulated in the form of a family of “maximum principles.” If the infimum coincides with a strong minimum, then this family contains the classical Pontryagin maximum principle. Examples are given to show that the obtained necessary conditions strengthen and generalize previously known results.

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References

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1969; Gordon and Breach, New York, 1986).

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  2. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems (Nauka, Moscow, 1974; Elsevier, Amsterdam, 1978).

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  3. R. V. Gamkrelidze, Foundations of Optimal Control (Tbilis. Univ., Tbilisi, 1977) [in Russian].

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Authors and Affiliations

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

    E. R. Avakov

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia

    E. R. Avakov & G. G. Magaril-Il’yaev

  3. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, 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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Corresponding author

Correspondence to E. R. Avakov.

Additional information

Original Russian Text © E.R. Avakov, G.G. Magaril-Il’yaev, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 3.

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Avakov, E.R., Magaril-Il’yaev, G.G. Generalized Maximum Principle in Optimal Control. Dokl. Math. 98, 575–578 (2018). https://doi.org/10.1134/S1064562418070116

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  • DOI: https://doi.org/10.1134/S1064562418070116

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