Solving a Single-Pursuer, Dual-Evader Pursuit-Evasion Differential Game and Analogous Optimal Control Problems

Differential games provide a framework for solving dynamic systems of two competing interests.One family of differential games focuses on two competing agents.Another family of differential games has competing teams of agents known as teaming games.Solutions to teaming games have inherit challenges due to the number of agents.By increasing the number of agents on each team, the dimension of the state space increases and additional termination cases are created.Singularities are a challenge in the majority of differential games and increasing the number of agents compounds that difficulty.This study aimed to overcome the challenges presented in solving teaming differential games by solving corresponding optimal control problems.The teaming game in question is a single pursuer, dual evader pursuit-evasion differential game.By fixing the control strategy of the pursuer, the teaming differential game is transformed into an optimal control problem for the team of evaders.Conversely, fixing the control strategies of the evaders results in an optimal control problem for the pursuer.For both problems, the optimal control strategy for the team in question is determined along with any singularities present within the control strategies.The teaming game is then reconsidered.Similarities between the optimal control problems and differential game allow for a simplified development of the solution to teaming game.The work concludes by demonstrating how solving the corresponding optimal control problems helps to overcome the inherit challenges of solving a teaming differential game.