Stability Certificates for Receding Horizon Games

TL;DR

This paper introduces a formal stability analysis framework for receding horizon game-based control of multi-agent systems, providing verifiable certificates and scalable methods for ensuring asymptotic stability.

Contribution

It develops the first stability certificates based on dissipativity and monotone operator theory applicable to non-potential games in receding horizon control.

Findings

LMI-based certificates guarantee asymptotic stability.

Scalable verification for decoupled agent dynamics.

Guidelines for tuning cost functions to satisfy stability certificates.

Abstract

Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This control paradigm has recently received an increasing attention in various application fields, including robotics, autonomous driving, traffic networks, and energy grids, due to its ability to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process. In this work, we present the first formal stability analysis based on dissipativity and monotone operator theory that is valid also for non-potential games. Specifically, we derive LMI-based certificates that ensure asymptotic stability and are numerically verifiable. Moreover, we show that, if the agents have decoupled dynamics, the numerical verification can be performed in a scalable manner. Finally, we present tuning guidelines for the agents' cost function weights to fulfill the certificates and, thus, ensure stability.