Passivity-based Gradient-Play Dynamics for Distributed GNE Seeking via Parallel Feedforward Compensation
Wei‐Jian Li, Lacra Pavel · 2024
We consider seeking generalized Nash equilibria for games with coupled nonlinear constraints over networks. We first revisit a well-known gradient-play dynamics to solve the problem from a passivity-based perspective, and address that the strict monotonicity on pseudo-gradients is a critical assumption to guarantee its convergence. Then we develop a novel passivity-based gradient-play dynamics by introducing parallel feedforward compensators. We prove that the dynamics achieves asymptotic convergence in merely monotone regimes. Moreover, in the absence of coupled constraints, we surprisingly find that the dynamics can handle hypomonotone games with inverse Lipschitz pseudo-gradients.