Formation Tracking in Noncooperative Game-Theoretic Framework

This article addresses a class of formation tracking problems of multiple agents from the perspective of game theory. In the game, the private interests of all followers are permitted. Each follower aims to minimize its own objective function by updating the control input. When each follower cannot unilaterally change its state to reduce the objective function, the followers reach the dynamic Nash equilibrium, and the formation is achieved in the meantime. Specifically, the resulting formation geometry depends on the dynamic Nash equilibrium. Considering the single- and double-integrator dynamics in the form of Newton's second law, some strategies are proposed to seek the dynamic Nash equilibrium. Based on the Lyapunov analysis technique, it is proved that the states of all followers converge exponentially to the dynamic Nash equilibrium point. The effectiveness of the proposed strategies is demonstrated by some numerical examples.