Game-Based Formation Control of High-Order Multi-Agent Systems

This paper studies the formation control of high-order multi-agent systems, where the dynamics of agents are $n$-order integrators. Different from existing results, this paper investigates the problem from the viewpoint of aggregative games. An interesting discovery is that the Nash equilibrium of a quadratic aggregative game constitutes the desired formation. Moreover, a distributed algorithm is designed for these high-order agents to form the desired formation by seeking the Nash equilibrium, where every agent estimates the aggregate of the game. Furthermore, the convergence of the algorithm is analyzed via Lyapunov stability theory. In contrast with existing formation protocols, the high-order agents with the proposed algorithm exponentially converge to the desired formation without using the (relative) positions and velocities of formation neighbors. Finally, two examples illustrate the algorithm.

Automated summary

This paper studies the formation control of high-order multi-agent systems using aggregative games. The Nash equilibrium of a quadratic aggregative game is found to constitute the desired formation. A distributed algorithm is designed to achieve the desired formation by seeking the Nash equilibrium, with each agent estimating the game aggregate. The convergence of the algorithm is analyzed using Lyapunov stability theory.