Distributed Nash Equilibrium Seeking in Aggregative Games for High-Order Integrator Dynamics Over Switching Networks

In this paper, we study the distributed Nash equilibrium (DNE) seeking problem for aggregative games with players whose actions are governed by high-order integrator dynamics over jointly connected and weight-balanced switching networks. Since the existing approaches critically depend on the connectivity of the communication network, they are not applicable to jointly connected switching networks, which can be disconnected at any time instant. To deal with the jointly connected networks, we present a different approach from the existing methods, which involves finding a time-varying quadratic Lyapunov function for the closed-loop system by using converse Lyapunov theorem. Our result is applied to a formation control problem of unmanned aerial vehicles (UAVs).