An adaptive generalized Nash equilibrium seeking algorithm under high-dimensional input dead-zone

Abstract

In this paper, a novel adaptive generalized Nash equilibrium (GNE) seeking algorithm is designed, in order to address the non-cooperative game with private inequality constraints under high-dimensional input dead-zone. That is to say, the dead-zone dynamics may be thought of as a generic high-dimensional convex set, and the introduction of two methods distinguishes our works in seeking the GNE of non-cooperative games. On the one hand, a two-time-scale structure based on singular perturbation method is led into the design of GNE seeking algorithm, where the fast dynamics part rapidly eliminates the influence of input dead-zone, and the slow dynamics part drives the players’ action to the GNE. On the other hand, adaptive penalty method is utilized to ensure the player’s action enters the inequality constraints set without a prior estimation of centralized information for penalty parameters. The algorithm in this paper realizes complete distribution and parameter independence, making it easy to apply in practical programming. At last, several numerical examples regarding the electricity markets are employed to verify the effectiveness of the theoretical results.