Pursuit-evasion games are the next logical stage in the exploring of
powerful, intelligent, adaptive performance. In fact the optimal
strategy is known for games in an infinitely sized playing field. The
quality of the machine learning methods can thus be compared to the
optimal performance possible. Therefore, we consider in this study a
pursuit-evasion differential game in Hilbert space
l2 with a hybrid system of dynamics. The game
consists of a non-inertial pursuer and an inertial evader where controls
of the pursuer and the evader are satisfied to the integral constraints.
The duration of the game, φ, is fixed. The position of the evader at
time φ satisfies to the phase constraint. We obtain attainability
domains of the players and then we make a winning strategy for the
pursuer which guarantees capturing the evader. We show that our
constructed strategy is admissible as well.