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From chik@d165.icyb.kiev.ua Mon Jul 16 15:49:07 2001
Date: Thu, 31 May 2001 15:31:10 +0300 (EET)
From: Arkadii Chikrii <chik@d165.icyb.kiev.ua>
To: congress@imath.kiev.ua
Subject: ABSTRACT(13)

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\title{\textbf{One Method for Solution of Complex Problems of Pursuit}
   }
\date{}
%Cybernetics Institute, Kiev, Ukraine \\
%e-mail:chik@d165.icyb.kiev.ua

\author{\textbf{Greta Ts. Chikrii} \\
{Institute of Cybernetics, 40 Glushkov Prsp., 03187 Kiev,
 Ukraine,} \\ {e-mail: chik@d165.icyb.kiev.ua} \\
{fax: (38044)2667418; tel: (38044)2662178}
 }
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The game problem of pursuit with delayed information for linear
evolutionary system of general kind  is treated
here. It is shown that like the case of differential dynamics [1]
this problem is equivalent to a
certain perfect-information game with somewhat changed dynamics and
terminal set.
On the one hand, this makes it feasible in the case of
delayed information to apply methods of pursuit, developed for the games
with perfect information.
On the other hand, on the basis of this equivalence an
approach to solving perfect-information linear problems of pursuit,
for which
fundamental Pontryagin's condition fails was suggested [2].
This approach consists in a passage from original game
to an auxiliary one with special-kind variable
information delay and subsequent analysis of the game, equivalent
to the latter.
Sufficient conditions for terminating the
perfect-information
linear dynamic games of pursuit, for which Pontryagin's condition
fails, were established. One model  game of soft
meeting of two moving objects with second-order differential dynamics was
analysed in detail [3]. An explicit formula for the control of the pursuer,
ensuring the soft meeting in a finite time and constructed
on the basis of control of the
evader in the past, was  obtained.

\vspace{1cm}

1. G.Ts. Chikrii. An Approach to the Solution of Linear Differential
Games with Variable Information Delay, ``Journal of Automation
and Information Sciences'', Vol.27, No.3\&4, pp.163-170, 1997 by Begell
House.

2. G.Ts. Chikrii. Using Impact of Information Delay for Solution
of Came Problems of Pursuit, ``Dopovidi Academ. Nauk Ukrainy'',
1999, No.12, pp.107-111.

3. G.Ts. Chikrii. On One Method of Pursuit in Tracks, Dopovidi
Academ. Nauk Ukrainy, 2000, No.6, pp.109-113.

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