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.