Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities
<|reference_start|>Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities: We consider dynamic games with linear dynamics and quadratic objective functions. We observe that the unconstrained open-loop Nash equilibrium coincides with the LQR 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.<|reference_end|>
@article{benenati2024linear-quadratic,
    title={Linear-Quadratic Dynamic Games as Receding-Horizon Variational
  Inequalities},
    author={Emilio Benenati and Sergio Grammatico},
    journal={arXiv preprint arXiv:2408.15703},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.15703},
    primaryClass={eess.SY cs.SY math.OC}
}