Generalized Engage or Retreat Differential Game With Escort Regions

Abstract

This paper is motivated by the desire to develop optimal defensive control strategies that discourage an attacker from engaging in attack while simultaneously encouraging retreat. We develop a general, two-player, differential game in which one player represents an attacker and the opposing player represents the defender. The attacker possesses superior dynamics such that it is capable of terminating the game either in engagement or retreat as it so chooses. The defender is incapable of directly preventing engagement. Instead, the defender uses the manipulation of the attacker's utility function as a form of indirect control in an attempt to make retreat a more attractive option over engagement. The solution to the overall engage or retreat differential game is found by solving two related optimization problems: the differential game of engagement and the optimal constrained retreat. The equilibrium open-loop control strategies and resulting game values of the attack or retreat game are expressed in terms of the solutions to these subproblems. Within the optimal constrained retreat problem, a value function constraint is imposed in order to prevent the attacker from moving into regions where engagement becomes optimal. This leads to regions of constrained retreat which we refer to as escort regions.

Dynamic network analysis of a target defense differential game with limited observations

“…Role switching of attacker in TAD games was studied recently in [24]. In [25], the defender's strategies force the attacker to retreat instead of engaging the target. In [26], the authors study the possibility of role switch as well as the cooperation between the target and defender.…”

Engage or Retreat Differential Game with Two Targets

“…Using the solutions of the Game of Engagement and the Optimal Constrained retreat, we can develop the overall solution to the Engage or Retreat Game [4] . It is possible that a solution may not exist to the OCR for some values of x 0 .…”

“…The game is solved using the general solution technique developed in [4] . Using this technique, the solution for the game is obtained by solving two related optimization problems called Game of Engagement (GoE) and Optimal Constrained Retreat (OCR).…”

“…This creates some constrained retreat trajectories which we will refer to as escort trajectories. It was shown in [4] that for a given initial state, the equilibrium solution to the Engage or Retreat game is provided by the solution of either the GoE or OCR.…”

An Optimal Engagement Zone Avoidance Scenario in 2-D

“…In this case, the target vehicle must maneuver from a pre-specified initial state to a goal state. A similar scenario was investigated in [19] under the name of optimal constrained retreat (OCR). There, a vehicle sought to maneuver past a static defender to a pre-specified retreat zone in minimum time subject to the constraint that it never became advantageous (optimal) to engage the defender in lieu of retreat.…”