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On a One-Dimensional Differential Game with a Non-convex Terminal Payoff

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Mathematical Optimization Theory and Operations Research (MOTOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12095))

Abstract

A one-dimensional differential game is considered, in which the payoff is determined by the modulus of the deviation of the phase variable at a fixed time from the set value, taking into account the periodicity. The first player seeks to minimize the payoff. The goal of the second player is the opposite. For this problem, the price of the game is calculated and optimal player controls are constructed. As an example, we consider the problem of controlling a rotational mechanical system in which the goal of the first player acquires the meaning of minimizing the modulus of deviation of the angle from the desired state.

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

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Authors and Affiliations

  1. N.N. Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaya Street, 16, 620108, Yekaterinburg, Russia

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

  2. Chelyabinsk State University, Br. Kashirinykh Street, 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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Corresponding author

Correspondence to Igor’ V. Izmest’ev .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov

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

    Michael Khachay

  3. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A Kalyagin

  4. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Izmest’ev, I.V., Ukhobotov, V.I. (2020). On a One-Dimensional Differential Game with a Non-convex Terminal Payoff. In: Kononov, A., Khachay, M., Kalyagin, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Lecture Notes in Computer Science(), vol 12095. Springer, Cham. https://doi.org/10.1007/978-3-030-49988-4_14

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