Research ArticleOpen AccessGoogle Scholar indexed
Differential Games of Pursung in the Systems with Distributed Parameters and Geometrical Restrictions
Department “Geometry”, National University of Uzbekistan Named After M. Ulugbek, Tashkent, Uzbekistan
Department “Geometry”, National University of Uzbekistan Named After M. Ulugbek, Tashkent, Uzbekistan
Department “Geometry”, National University of Uzbekistan Named After M. Ulugbek, Tashkent, Uzbekistan
- 1 Department “Geometry”, National University of Uzbekistan Named After M. Ulugbek, Tashkent, Uzbekistan
- 2 Department “Geometry”, National University of Uzbekistan Named After M. Ulugbek, Tashkent, Uzbekistan
- 3 Department “Geometry”, National University of Uzbekistan Named After M. Ulugbek, Tashkent, Uzbekistan
American Journal of Computational Mathematics·Volume 03 (2013)·Pages 56–61·Published 30 September 2013·DOI10.4236/ajcm.2013.33B010
Copy link · social · email
Abstract
A problem of pursuit in the controlled systems of elliptic type without mixed derivatives with variable coefficients was considered. The model of the considered system is described by partial differential equations. The players (opponents) control parameters occur on the right-hand side of the equation and are subjected to various constraints. The first player’s goal is to bring the system from one state into another desired state; the second player’s goal is to prevent this from happening. We represent new sufficient conditions for bringing the system from one state into another. The finite-difference method is used to solve this problem.
KeywordsPursuitPursuerEvaderTerminal SetPursuit ControlEvasion control
- O. A. Ladyzhenskaya, “Kraevye Zadachi Matemati-cheskoi Fiziki,” (Boundary Problems of Mathematical Physics), Moscow, Nauka, 1973.
- O. A. Ladyz-henskaya, V. A. Solonnikov and N. N. Ural’tseva, “Lineinye I Kvazilineinye Uravneniya Parabolicheskogo Tipa,” (Linear and Quasi linear Functions of Parabolic Type), Moscow, Nauka, 1967.
- V. A. Il’in, “Boundary Control of String Oscillations at One End with Other End Fixed, Provided that Finite Energy Exists,” Dokl. Ross. Akad. Nauk, Vol. 378, No. 6, 2001, pp. 743-747.
- V. A. Il’in and V. V. Tikhomirov, “Wave Equation with Boundary Control at Two Ends and Problem of Complate Oscillation Damping ,” Diff. Uravn., Vol. 35, No. 5, 1999, pp. 692-704.
- Yu. S. Osipov and S. P. Okhezin, “On the Theory of Differential Games in Parabolic Systems,” Dokl. Akad. Nauk SSSR, Vol. 226, No. 6, 1976, pp. 1267-1270.
- F. L. Chernous’ko, “Bounded Controls in Distributed-parameter Systems,” Prikl. Mat. Mekh., Vol. 56, No. 5, 1992, pp. 810-826.
- N. Satimov and M. Sh. Mamatov, “On a Class of Linear Differential and Discrete Games between Groups of Pursuers and Evaders,” Diff. Uravn., Vol. 26, No. 9, 1990, pp. 1541-1551.
- N. Satimov and M. Tukhtasinov, “On some Game Problems in the Distributed Controlled Systems,” Prikl. Mat. Mekh., Vol. 69, No. 6, 2005, pp. 997-1003.
- N. Satimov and M. Tukhtasinov, “On some Game Problems in Controlled First-order Evolutionary Equations,” Diff. Uravn., Vol. 41, No. 8, 2005, pp. 1114 -1121.
- M. Sh. Mamatov, “On the Theory of Differential Pursuit Games in Distributed Parameter Systems,” Automatic Control and Computer Sciences, Vol. 43, No. 1, 2009, pp. 1-8. doi:10.3103/S0146411609010015
- M. Sh. Mamatov, “About Application of a Method of Final Differences to the Decision a Prosecution Problem in Systems with the Distributed Parameters,” Automation and Remote Control, Vol. 70, No. 8, 2009, pp. 1376-1384. doi:10.1134/S0005117909080104
- M. Tukhtasinov and M. Sh. Mamatov, “On Pursuit Problems in Controlled Distributed Systems,” Mathematical notes, Vol. 84, No. 2, 2008, pp. 273-280.
- M. Tukhtasinov and M. Sh. Mamatov, “About Transition Problems in Operated Systems,” Diff. Uravn., Vol. 45, No.3, 2009, pp. 1-6.
- M. Sh. Mamatov and M. Tukhtasinov, “Pursuit Problem in Distributed Control Systems,” Cybernetics and Systems Analysis, Vol. 45, No. 2, 2009, pp. 297-302. doi:10.1007/s10559-009-9100-x