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Alternative Theorem for Differential Games with Strongly Convex Admissible Control Sets

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Optimization and Applications (OPTIMA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

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Abstract

A linear differential game with strongly convex admissible control sets and a smooth target set is considered. For such a differential game we obtain the alternative theorem. This theorem states that for any initial position either there is a program strategy of pursuer that guarantees the capture or there is a program strategy of evader that guarantees the evasion. This result is based on the commutativity of the Minkowski sum and difference for sets with special properties of strong and weak convexity in a Banach space.

Supported by the Russian Foundation for Basic Research, grant 18-01-00209.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation

    Grigorii E. Ivanov & Maxim O. Golubev

Authors
  1. Grigorii E. Ivanov
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  2. Maxim O. Golubev
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Corresponding author

Correspondence to Maxim O. Golubev .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Ivanov, G.E., Golubev, M.O. (2019). Alternative Theorem for Differential Games with Strongly Convex Admissible Control Sets. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_23

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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