Formation Control Against Attack: An Integrated Design of Stackelberg and Zero-Sum Games

This paper proposes a game framework that integrates Stackelberg and zero-sum games, in order to handle formation control under attacks. In this framework, two agents adopt a Stackelberg game approach for formation control, in which the follower encounters attacks. In order to resist the attack, a zero-sum game is played between the follower agent and attacker, such that the game framework is reconstructed for formation by adjusting the weight parameters. According to the maximum principle, the optimal control strategies of agents and the optimal attack strategy of the attacker are designed in the integrated game framework. It is rigorously proved that when the agents adopt the optimal control strategies, the leader agent and follower agent can achieve their formation goals even under the influence of attacks.