title: Linear discrete pursuit game with phase constraints.
abstract: We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints: y∈G, where G is a subset of Rn. We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints. Terminal set M is a subset of Rn and it is assumed to have a nonempty interior. Game is said to be completed if y(k)-x(k)∈M at some step k; thus, the evader has not the right to leave set G. To construct the control of the pursuer, at each step i, we use the value of the control parameter of the evader at the step i. We obtain sufficient conditions of completion of pursuit from certain initial positions of the players in finite time interval and construct a control for the pursuer in explicit form.
authors.affiliation: Department of Informatics, Tashkent University of Information Technologies, (TUIT), Amir Temur Street 108, 100202 Tashkent, Uzbekistan.
authors.forename: Asqar
authors.initials: A
authors.lastname: Raxmanov
authors.affiliation: Institute for Mathematical Research & Department of Mathematics, FS, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
authors.forename: Gafurjan
authors.initials: G
authors.lastname: Ibragimov
mesh_terms: D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical