Differential Game of Pursuit Time Satisfy the Geometric Constraints in l ₂ Space

Abstract

In the present article, we present a differential game of pursuit problem with the case of geometric constraint in the Hilbert space l 2. The game is given by system of 2-infinite systems of first order ordinary differential equations (ODEs). Geometric constraint are imposed on the control functions of players. The game is began from a given point z 0 called the initial position. It is given another point z 1 in the space l 2. The Pursuer targeting to bring the state of the system from z 0 to z 1 where an equation to find a guaranteed pursuit time is obtained while that of the Evader action is opposite. The game is assumed to be completed if z(t) = z 1 at some time t. Moreover, a control problem is studied and then extended to the differential game of pursuit where the strategy for the Pursuer is constructed explicitly.

On a Control Problem and a Pursuit Game of Transferring States Described by An Infinite Three-Systems of Differential Equations

“…In the context of pursuit differential game, the completion of pursuit is solely based on the motive of the first player, that is the pursuer. For the case of a pursuit game in an infinite system, the pursuer's conventional objective is to transfer the state of the system into another state of the system, which could be the origin (see, for example, [12][13][14]) or a non-zero state (see, for instance, [15][16][17][18][19]), to complete the pursuit.…”

“…By bearing pursuer of similar objective, differential game theorists continued to investigate pursuit game in a higher level of infinite system. The papers of [17] and [18] aimed to investigate the pursuit game of transferring states for an infinite 2-system of differential equations described by…”