Linear-quadratic pursuit-evasion game with zero-order players’ dynamics and terminal constraint for the evader

Pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional is considered. The dynamics of each player is ideal, meaning that the controls of the players are their accelerations. The objective of the pursuer is minimizing the cost functional, while the evader has two objectives: maximizing the cost functional and keeping a given terminal inequality constraint. The game is solved both in open-loop and in feedback controls. Solution properties for small control penalties in the cost functional are analyzed. Simulation of the pursuit by the game optimal feedback control against a realistic bang-bang evader's control is presented.