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Stability Property in the Convergence Game Problem in the Presence of Phase Constraints

  • CONTROL IN DETERMINISTIC SYSTEMS
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Abstract

In this paper, we consider a nonlinear conflict-controlled system on a finite time interval and in a finite-dimensional space that is constrained by nonstationary phase constraints. A convergence game problem at a fixed moment of time with a compact in the phase space of the system is studied. The stability property that is central to the theory of positional differential games is studied. Some modifications of the definition of a u-stable bridge and the system of sets approximating this bridge are presented. These modifications are focused on the development of algorithms for the approximate calculation of solutions in specific convergence game problems in the presence of phase constraints on the system. Two specific approach problems for which mathematical modeling is performed and the simulation results are presented are described.

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Funding

The research by V.N. Ushakov and A.V. Ushakov was supported by the Russian Science Foundation, grant no. 19-11-00105.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 620108, Yekaterinburg, Russia

    A. A. Zimovets, A. R. Matviichuk, A. V. Ushakov & V. N. Ushakov

Authors
  1. A. A. Zimovets
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  2. A. R. Matviichuk
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  3. A. V. Ushakov
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  4. V. N. Ushakov
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Corresponding authors

Correspondence to A. A. Zimovets, A. R. Matviichuk, A. V. Ushakov or V. N. Ushakov.

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Translated by A. Ivanov

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Zimovets, A.A., Matviichuk, A.R., Ushakov, A.V. et al. Stability Property in the Convergence Game Problem in the Presence of Phase Constraints. J. Comput. Syst. Sci. Int. 60, 530–548 (2021). https://doi.org/10.1134/S1064230721040110

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  • DOI: https://doi.org/10.1134/S1064230721040110

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