Robust Distributed Nash Equilibrium Seeking Subject to Communication Constraints

In this article, we address the robust distributed Nash equilibrium seeking problem of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula>-player games under switching networks and communication delays. The salient feature of this work is that the switching communication networks can be uniformly strongly connected, and the communication delays are allowed to be arbitrarily unknown, time-varying and bounded. To solve the problem, we construct a distributed estimator for each player to estimate all players' strategies through unreliable communication networks. Based on the gradient play technique, we design a distributed Nash equilibrium seeking law. Then, we obtain the closed-loop system, which is an interconnected system of a nonlinear subsystem and a linear time-delay subsystem. By constructing the Lyapunov–Krasovskii functional, and designing the controller parameter in the sense of the small gain theorem, we achieve robust Nash equilibrium seeking asymptotically in spite of unreliable communication networks. Finally, we illustrate our proposed approach by its application to practical motion control of mobile robots with an experiment.