Dynamic Nash Equilibrium Seeking for a Class of Nonlinear Uncertain Multi-agent Systems

TL;DR

This paper develops a distributed control framework for multi-agent systems with nonlinear uncertainties to seek Nash equilibria, ensuring convergence through robust stabilization and backstepping techniques.

Contribution

It introduces a novel approach converting NE seeking into a distributed stabilization problem for uncertain nonlinear multi-agent systems.

Findings

Successfully stabilizes the augmented system to reach NE

Designs a distributed state-feedback controller

Handles nonlinear uncertainties and external disturbances

Abstract

We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that converts the problem into a distributed robust stabilization problem of an appropriately augmented system. To be specific, we construct a virtual single-integrator multi-agent system, as a reference signal generator, to compute an NE in a fully distributed manner. By introducing internal models to tackle the disturbances, as well as embedding the virtual system, we derive an augmented system. Following that, we show that the outputs of all agents reach an NE of the game if the augmented system can be stabilized by a control law. Finally, resorting to a backstepping procedure, we design a distributed state-feedback controller to stabilize the augmented system semi-globally.