Distributed Nash Equilibrium Seeking in Aggregative Games Over Jointly Connected and Weight-Balanced Networks

The problem of the distributed Nash equilibrium (NE) seeking for aggregative games has been studied over strongly connected and weight-balanced static networks and every time strongly connected and weight-balanced switching networks. In this article, we further study the same problem over jointly connected and weight-balanced networks. The existing approaches critically rely on the connectedness of the network and these approaches fail if the network is not connected. To overcome this difficulty, we propose a novel approach to showing the exponential convergence of the output of the closed-loop system to the unknown NE point under a set of mild conditions. For this purpose, we need to establish the exponential stability for a time-varying ancillary system. By the converse Lyapunov theorem, this result guarantees the existence of a time-varying quadratic Lyapunov function for the ancillary system, which in turn leads to the construction of a suitable Lyapunov function for the closed-loop system, thus leading to the solution of the problem. A numerical example is presented to validate the effectiveness of our distributed algorithm.