Bounded Control based on Norm Differential Game for Three - Player Conflict

A Three-player conflict with bounded controls is considered in this paper. Optimal pursuit-evasion strategy based on differential game with bounded control is derived assuming that the attacker, target and it’s defender have linearized kinematics, arbitrary-order linear adversaries’ dynamics, and perfect information. The obtained strategy is dependent on the zero-effort miss distance of two pursuer-evader pairs: attacker with target and defender with attacker. For adversaries with first-order dynamics, this paper presents algebraic conditions for the three-player problem and gives an analytical hybrid strategy for the attacker to capture the target while evading the defender is obtained. The simulation results shows that, by using the hybrid strategy, the attacker will evade form the defender successfully and guarantee the miss distance from the target. Keywords—Bounded control, Norm differential game, Three-player conflict, Optimal strategies.