An Engage or Retreat differential game with Mobile Agents

The thesis is aimed at developing optimal defensive strategies that dissuade an attacker from engaging a defender while simultaneously persuading the attacker to retreat. A two-player Engage or Retreat differential game is developed in which one player represents a mobile attacker and the other player represents a mobile defender. Both players are modeled as massless particles moving with constant velocity. The choice to terminate the game in engagement or retreat lies with the attacker. The defender indirectly influences the choice of the attacker by manipulating the latter\u27s utility function. In other words, the defender co-operates with the attacker so that retreat appears to be the best option available. The solution to the differential game is obtained by solving two related optimization problems namely the Game Of Engagement and Optimal Constrained Retreat. In the Game of Engagement, the attacker terminates the game by capturing the defender.In the Optimal Constrained Retreat, a value function constraint is imposed which deters the attacker\u27s retreat trajectory from entering into a region where it may lead to engagement. Such regions where constrained retreat occurs are known as escort regions. The solutions to these two problems are used to construct the global equilibrium solutions to the Engage or Retreat differential game.The global equilibrium solution divides the admissible state space into two regions that contain qualitatively different equilibrium control strategies. Numerical solutions are included to support the theory presented