Reachable-Set-Based Strategies for Attacker-Defender-Target Games with a Non-Dominant Attacker

The Attacker-Defender-Target (ADT) differential game provides an important framework for modeling modern aerial combat and missile defense. This paper aims to address the limitations in existing research, which typically assumes scenarios where the attacker possesses overwhelming superiority, fails to account for coordination between the defender and the target, and often neglects singular surfaces in the state space, leading to incomplete strategy solutions. To overcome these issues, the following contributions are made. First, this paper considers a relatively balanced scenario, characterized by the fact that the attacker’s reachable set does not completely contain the target’s reachable set. Second, based on a reachable-set analysis, the payoff function is reformulated as the distance between the boundaries of the players' reachable sets, enabling the derivation of strategies that achieve coordination between the defender and the target. Third, the singular surfaces arising in the game are thoroughly analyzed, allowing for the derivation of complete strategies. Finally, simulations under both linearized and nonlinear planar engagement kinematics are conducted. The nonlinear results show close agreement with the analytically predicted switching times and attacker-target miss distance, demonstrating the applicability of the proposed framework beyond the linearized terminal-projection model.