Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities

Emilio Benenati; Sergio Grammatico

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arXiv · 2408.15703

Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities

Emilio Benenati·Sergio Grammatico

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Abstract

We consider dynamic games with linear dynamics and quadratic objective functions. We observe that the unconstrained open-loop Nash equilibrium coincides with a linear quadratic regulator in an augmented space, thus deriving an explicit expression of the cost-to-go. With such cost-to-go as a terminal cost, we show asymptotic stability for the receding-horizon solution of the finite-horizon, constrained game. Furthermore, we show that the problem is equivalent to a non-symmetric variational inequality, which does not correspond to any Nash equilibrium problem. For unconstrained closed-loop Nash equilibria, we derive a receding-horizon controller that is equivalent to the infinite-horizon one and ensures asymptotic stability.

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BibTeX RIS

Emilio Benenati, Sergio Grammatico. 2024-08-28. Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities. https://arxiv.org/abs/2408.15703

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