Nonzero-sum differential game guidance laws in target-missile-defender engagement

Abstract The guidance law design is considered for an engagement scenario of a missile attacking an actively defended target. A three-player nonzero-sum differential game is formulated to describe players’ respective behaviours including the attacking missile’s evading the target’s defender and thereafter attacking the target, the target’s evading the attacking missile under the assistance of the defender, and the defender’s intercepting the attacking missile to assist the target evading the attacking missile. It is considered that the missile hits the target at a specific terminal angle to enhance the destructive effect by attacking the vulnerable regions of the target. The advantages of norm-bounded and linear quadratic differential game guidance laws are combined and the cost functions segmented by relative distances between the players are proposed. The equilibrium solutions of the nonzero-sum differential game are derived and used as the respective guidance laws of the players. Simulations in various engagement scenarios are conducted to verify the reliability and robustness of the design.