Solution of a Linear Pursuit-Evasion Differential Game with Closed and Convex Terminal Set

Gafurjan I. Ibragimov, Marzieh Khakestari, Atamurat Sh. Kuchkarov


A linear two-person zero-sum pursuit-evasion differential game is considered. Control functions of players are subject to integral constraints. Terminal set is a closed convex subset of  The Pursuer tries to bring the state of the system to the terminal set and the Evader  prevents bringing of the state to the terminal set where control resource of the Pursuer is greater than that of Evader.   We obtain a formula for the optimal pursuit time and construct optimal strategies of the players in explicit form.

Full Text:



Pshenichnii, B.N. & Onopchuk, Yu., N., Linear Differential Games with Integral Constraints, Izvestige Akademii Nauk SSSR, Tekhnicheskaya Kibernetika, 1, pp. 13-22, 1968.

Mezentsev A.V., A Direct Method in Linear Differential Games with Different Constraints, Zh. vyhisl. Mat. Mat. Fiz. 11(2), pp. 365-374, 1971.

Nikolskii M.S., A Direct Method In Linear Differential Pursuit-Evasion Games, V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, 33(2), pp. 885-891, 1983.

Ibragimov, G.I., A Problem of Optimal Pursuit in Systems with Distributed Parameter, J. Appl. Math. Mech., 66(5), pp. 719-724, 2003.

Ibragimov, G.I., A Game Problem on A Closed Convex Set, Siberian Advances in Mathematics, 12(3), pp. 16-31, 2002.

Azimov, A.Ya., Linear Differential Pursuit Games with Integral Constraints on The Control, Differentsial’nye Uravneniya 11, 1975, English transl. in Differential Equations, 11, pp. 1723-1731, 1975.

Azimov, A.Ya., A Linear Differential Evasion Game with Integral Constraints on The Controls, Zh. Vychisl. Mat. Mat. Fiz, 14(6), pp. 1427-1436, 1974.

Azamov, A.A., Samatov, B., Strategy, An Elementary Introduction to the Theory of Differential Games, National University of Uzbekistan, Tashkent, Uzbekistan, p. 32, 2000.

Krasovskii, N.N., Upravlenie Dinamicheskoi Sistemoi (Control of a dynamical system), Moscow, 1985.

Lee, E.B. & Markus, L., Foundations of Optimal Control Theory, John Wiley & Sons, Inc., New York, 1967.

Hajek, O., Pursuit Games, Academic Press, New York-San Francisco, 1975.

Krasovskii, N.N., Upravlenie Dinamicheskoi Sistemoi (Control of a Dynamical System), Moscow, 1985.

Petrosyan, L.A., Differential Games of Pursuit, World Scientific, Singapore, London, 1993.

Pontryagin, L.S. & Mishchenko, E.F., On Evasion Problem of One Controlled Object from Another, Dokl. AN. SSSR., 189(4), 721-723, 1969.



  • There are currently no refbacks.

View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.


Lembaga Penelitian dan Pengabdian kepada Masyarakat (LPPM), Center for Research and Community Services (CRCS) Building, 6th & 7th Floor, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia, Tel. +62-22-86010080, Fax.: +62-22-86010051; E-mail: