One-Sided Capture in Nonlinear Differential Games

K. A. Shchelchkov ()
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K. A. Shchelchkov: Institute of Mathematics, Information Technologies and Physics, Udmurt State University, Universitetskaya ul. 1, Izhevsk 426034, Russia

International Game Theory Review (IGTR), 2023, vol. 25, issue 02, 1-14

Abstract: A differential game described by a nonlinear system of differential equations is considered in a finite-dimensional Euclidean space. The value set of the pursuer control is a finite set. The value set of the evader control is a compact set. The purpose of the pursuer is a translation of the system in a finite time to any given neighborhood of zero. The pursuer uses a piecewise open-loop strategy constructed only by using information on the state coordinates and the velocity in the partition points of a time interval. In the past work, sufficient conditions were obtained for existence of a neighborhood of zero from which the capture occurs. The statement of the capture theorem contains such a condition that some vectors set up a positive basis. In this research, we consider the case when these vectors set up a one-sided set. For this case, sufficient conditions are obtained for existence of a set of initial position, from which the capture occurs.

Keywords: Differential game; nonlinear system; pursuer; evader; capture (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0219198923500068

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