Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908458314366976 |
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| author | Benenati, Emilio Grammatico, Sergio |
| author_facet | Benenati, Emilio Grammatico, Sergio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities Benenati, Emilio Grammatico, Sergio Systems and Control Optimization and Control 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. |
| title | Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2408.15703 |