Fully Distributed Nash Equilibrium Seeking: A Double-Layer Adaptive Approach

Abstract

This article is concerned with fully distributed Nash equilibrium seeking in networked games under both undirected and directed communication graphs. New fully Nash equilibrium seeking strategies incorporating gradient-based optimization algorithms, consensus algorithms, and double-layer adaptive control laws are presented. In particular, the double-layer adaptive control laws are introduced to ensure that the control gains are not overlarge and free of dependence on any global information. This is achieved by adding a damping term to the adaptive parameter design such that the continuous increase in control gains is avoided. Theoretical analyses are conducted to prove that players’ actions can be convergent to the Nash equilibrium under the proposed strategies. Moreover, it is shown that the developed strategies can be extended to accommodate the players with heterogeneous linear dynamics. Finally, numerical examples are provided to illustrate the effectiveness of the proposed methods.