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On a Single-Type Differential Game with a Non-convex Terminal Set

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

We consider the problem of controlling a rod attached to a rotor. A rotating flywheel is attached to one end of the rod. The rotor is controlled by the first player. The flywheel is controlled by the second player. The goal of the first player is to bring the rotor to a vertical position at a given time. The goal of the second player is the opposite. This problem is an example of a more general linear differential game with a one-dimensional aim. Using a linear change of variables, this problem is reduced to a single-type one-dimensional differential game with a non-convex terminal set, for which we have found the necessary and sufficient conditions of termination and constructed the corresponding controls of the players.

This work was funded by the Russian Science Foundation (project no. 19-11-00105).

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Authors and Affiliations

  1. Chelyabinsk State University, Br. Kashirinykh str., 129, 454001, Chelyabinsk, Russia

    Igor’ V. Izmest’ev & Viktor I. Ukhobotov

Authors
  1. Igor’ V. Izmest’ev
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  2. Viktor I. Ukhobotov
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Correspondence to Igor’ V. Izmest’ev .

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Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Izmest’ev, I.V., Ukhobotov, V.I. (2019). On a Single-Type Differential Game with a Non-convex Terminal Set. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_42

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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