The explicit game-theoretic linear quadratic regulator for constrained multi-agent systems

TL;DR

This paper introduces an efficient algorithm for solving constrained multi-agent dynamic games, enabling real-time linear-quadratic game-theoretic MPC with significant computational improvements.

Contribution

It extends explicit constrained LQR and MPC frameworks to multi-agent non-cooperative settings using a novel variational inequality approach.

Findings

Order-of-magnitude faster online computation compared to existing solvers.

Achieves high solution accuracy at high sampling rates.

Demonstrates practical viability for multi-agent systems.

Abstract

We present an efficient algorithm to compute the explicit open-loop solution to both finite and infinite-horizon dynamic games subject to state and input constraints. Our approach relies on a multiparametric affine variational inequality characterization of the open-loop Nash equilibria and extends the classical explicit constrained LQR and MPC frameworks to multi-agent non-cooperative settings. A key practical implication is that linear-quadratic game-theoretic MPC becomes viable even at very high sampling rates for multi-agent systems of moderate size. Extensive numerical experiments demonstrate order-of-magnitude improvements in online computation time and solution accuracy compared with state-of-the-art game-theoretic solvers.