Stability Certificates for Receding Horizon Games
CoRR(2024)
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.
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