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Program Iterations Method and Relaxation of a Pursuit-Evasion Differential Game

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Advanced Control Techniques in Complex Engineering Systems: Theory and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 203))

Abstract

We consider special case of non-linear zero-sum pursuit-evasion differential game. This game is defined by two closed sets - target set and one defining state constraints. We find an optimal non-anticipating strategy for player I (the pursuer). Namely, we construct his successful solvability set specified by limit function of the iterative procedure in space of positions. For positions outside of the successful solvability set, we consider relaxation of our game by determining the smallest size of a neighborhoods of two mentioned sets, for which the pursuer can solve his problem. Then, we construct his successful solvability set in terms of those neighborhoods.

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Authors and Affiliations

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

    Alexander Chentsov & Daniel Khachay

  2. Ural Federal University, Ekaterinburg, Russia

    Alexander Chentsov & Daniel Khachay

Authors
  1. Alexander Chentsov
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  2. Daniel Khachay
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Corresponding author

Correspondence to Alexander Chentsov .

Editor information

Editors and Affiliations

  1. Department of Intelligent Information Systems, Petro Mohyla Black Sea National University, Mykolaiv, Ukraine

    Yuriy P. Kondratenko

  2. Glushkov Cybernetics Institute of NAS of Ukraine, Kyiv, Ukraine

    Arkadii A. Chikrii

  3. Space Research Institute of NAS and SSA of Ukraine, Kyiv, Ukraine

    Vyacheslav F. Gubarev

  4. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Chentsov, A., Khachay, D. (2019). Program Iterations Method and Relaxation of a Pursuit-Evasion Differential Game. In: Kondratenko, Y., Chikrii, A., Gubarev, V., Kacprzyk, J. (eds) Advanced Control Techniques in Complex Engineering Systems: Theory and Applications. Studies in Systems, Decision and Control, vol 203. Springer, Cham. https://doi.org/10.1007/978-3-030-21927-7_7

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