The explicit game-theoretic linear quadratic regulator for constrained multi-agent systems
This work enables real-time game-theoretic model predictive control for multi-agent systems of moderate size, addressing a key computational bottleneck in constrained multi-agent control.
The paper presents an efficient algorithm for computing explicit open-loop Nash equilibria in finite and infinite-horizon dynamic games with state and input constraints, achieving order-of-magnitude improvements in online computation time and solution accuracy compared to state-of-the-art solvers.
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.