Linear discrete pursuit game with phase constraints.

Asqar Raxmanov,Gafurjan Ibragimov

doi:10.1155/2014/435103

Asqar Raxmanov, Gafurjan Ibragimov

Open Access

https://doi.org/10.1155/2014/435103

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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 R n. 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 R n 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.

Highlights

A number of works were devoted to investigate differential and discrete pursuit games with various constraints on controls
We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints
Differential games with phase constraints on a position of one or several players are studied in many works

Summary

Introduction

A number of works were devoted to investigate differential and discrete pursuit games with various constraints on controls (see, e.g., [1,2,3,4,5,6,7,8]). In the work [11], a simple motion pursuit-evasion game problem of many pursuers and one evader is considered on a compact set. In [13], simple motion pursuit game problem is solved for all initial positions of space when the maximum speeds of players are equal and the evader moves on a convex bounded set with nonempty interior. In [15], sufficient conditions of completion of pursuit are obtained for a linear differential game when the evader moves in a bounded convex set. We consider a linear discrete pursuit game of one pursuer and one evader We will study both total and geometric constraints on controls of players under assumption that the terminal set M consists of an interior point in Rn. The evader can move only in a given bounded convex set.

Statement of the Problem

Main Result

Findings

Conclusion