Doklady Mathematics

, Volume 98, Issue 3, pp 575–578 | Cite as

Generalized Maximum Principle in Optimal Control

  • E. R. AvakovEmail author
  • G. G. Magaril-Il’yaev


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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  1. 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).Google Scholar
  2. 2.
    A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems (Nauka, Moscow, 1974; Elsevier, Amsterdam, 1978).Google Scholar
  3. 3.
    R. V. Gamkrelidze, Foundations of Optimal Control (Tbilis. Univ., Tbilisi, 1977) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia
  3. 3.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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