SOLVABILITY OF LINEAR-QUADRATIC DIFFERENTIAL GAMES ASSOCIATED WITH PURSUIT-EVASION PROBLEMS

Josef Shinar (), Vladimir Turetsky (), Valery Y. Glizer () and Eduard Ianovsky ()
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Josef Shinar: Faculty of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel
Vladimir Turetsky: Faculty of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel
Valery Y. Glizer: Department of Mathematics, Ort Braude College, P.O. Box 78, Karmiel 21982, Israel
Eduard Ianovsky: Faculty of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel

International Game Theory Review (IGTR), 2008, vol. 10, issue 04, 481-515

Abstract: A finite horizon zero-sum linear-quadratic differential game with a generalized cost functional, involving a Lebesgue integral with a measure that has both discrete and distributed parts, is considered. Sufficient conditions for the solvability of such a game are established in terms of the eigenvalues of an integral operator in Hilbert space. The game solution is based on solving an impulsive Riccati matrix differential equation. These results are applied for two games associated with pursuit-evasion problems. Illustrative examples are presented.

Keywords: Linear-quadratic differential game; solvability conditions; pursuit-evasion; Subject Classification: 49N70; Subject Classification: 49N90; Subject Classification: 91A23 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219198908002060

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