An Inexact-Penalty Method for GNE Seeking in Games With Dynamic Agents

Abstract

In this article, we consider a network of autonomous agents, whose outputs are actions in a game with coupled constraints. In such network scenarios, agents seek to minimize coupled cost functions using distributed information while satisfying the coupled constraints. Current methods consider a small class of multiintegrator agents using primal-dual methods. These methods can only ensure constraint satisfaction in steady state. In contrast, we propose an inexact penalty method using a barrier function for nonlinear agents with equilibrium-independent passive dynamics. We show that these dynamics converge to an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -GNE while satisfying the constraints for all time, not just in steady state. We develop these dynamics in both full-information and partial-information settings. In the partial-information setting, dynamic estimates of the others' actions are used to make decisions and are updated through local communication. Applications to optical networks, velocity synchronization of flexible robots, and wind farm optimization are provided.