Passivity-based Gradient-Play Dynamics for Distributed Generalized Nash Equilibrium Seeking

TL;DR

This paper introduces passivity-based gradient-play dynamics with novel compensators for distributed GNE seeking, ensuring convergence under monotone conditions and extending to partial information scenarios.

Contribution

It proposes new passivity-based gradient-play dynamics with compensators that guarantee convergence to GNEs under less restrictive conditions and extends the framework to partial-decision information.

Findings

Proposed dynamics reach GNEs in monotone regimes.

Passivity-based framework unifies and generalizes existing methods.

Extended results to partial-decision information settings.

Abstract

We consider seeking generalized Nash equilibria (GNE) for noncooperative games with coupled nonlinear constraints over networks. We first revisit a well-known gradientplay dynamics from a passivity-based perspective, and address that the strict monotonicity on pseudo-gradients is a critical assumption to ensure the exact convergence of the dynamics. Then we propose two novel passivity-based gradient-play dynamics by introducing parallel feedforward compensators (PFCs) and output feedback compensators (OFCs). We show that the proposed dynamics can reach exact GNEs in merely monotone regimes if the PFCs are strictly passive or the OFCs are output strictly passive. Following that, resorting to passivity, we develop a unifying framework to generalize the gradient-play dynamics, and moreover, design a class of explicit passive-based dynamics with convergence guarantees. In addition, we explore the relation between the proposed dynamics and some existing methods, and extend our results to partial-decision information settings.