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arXiv · 2512.07749

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

Emilio Benenati·Giuseppe Belgioioso
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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.

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Emilio Benenati, Giuseppe Belgioioso. 2025-12-08. The explicit game-theoretic linear quadratic regulator for constrained multi-agent systems. https://arxiv.org/abs/2512.07749

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