From ivan@cresotech.com Mon Jul 16 15:49:56 2001 Date: Mon, 4 Jun 2001 12:02:50 +0300 From: ivan <ivan@cresotech.com> To: congress@imath.kiev.ua Subject: ABSTRACT (13) \documentclass[10pt]{article} \renewcommand{\baselinestretch}{1.3} \textwidth=140mm \textheight=235mm \hoffset=-5mm \voffset=4.2mm %\sloppy \pagestyle{empty} \begin{document} \title{\textbf{On One Differential Game of Approach with Variable Structure}} \author{\textbf{Ivan Matychyn} \\ (Institute of Cybernetics)} \date{} \maketitle \centerline{ivan\_mat@yahoo.com} \bigskip %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% A quasilinear game problem of approach for differential systems with variable structure and discontinuous trajectories, for which the dimension of phase space can change by switches, is treated here. An approach to this problem based on the Method of Resolving Functions \cite{S1} is considered. This method essentially engages the apparatus of the set-valued mapping theory. At the heart of the approach proposed lies Pontrjagin's condition \cite{S1} reflecting some advantage of the pursuer over the evader in control resources. In addition, it provides means for the appropriate control choice on the basis of Filippov-Castaing theorem on measurable choice. Presented in the paper ideas allowed to obtain the sufficient conditions of approach with the terminal set for one class of differential games with variable structure \cite{S2}, \cite{S3}. Theoretical results are supported by model example \cite{S2}, in which the pursuer has dynamic of a `crocodile' while the evader is a moving object of the type `boy' \cite{S4}. For this game the full solution of the approach problem is obtained and an explicit formula for the game termination time is derived. \begin{thebibliography}{99} \bibitem{S1} Chikrii A.A. Conflict-Controlled Processes, Kluwer Academic Publishers, Boston-London-Dordrecht, 1997, 424p. \bibitem{S2} Chikrii A.A., Matychyn I.I. Quasilinear Conflict Controlled Processes with Variable Structure, Journal of Automation and Information Sciences, Vol.31, No.6, p.24-32, 1999 by Begell House. \bibitem{S3} Matychyn I.I. On One Class of Approach Game Problems with Variable Structure, Journal of Automation and Information Sciences, Vol.31, No.10, p.47-53, 1999 by Begell House. \bibitem{S4} Isaacs R. Differential Games. New York: John Wiley \& Sons, 1965. \end{thebibliography} \end{document}

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