The maximum principle for discrete-time control systems and applications to dynamic games
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917206614343680 |
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| author | Corella, Alberto Domínguez Hernández-Lerma, Onésimo |
| author_facet | Corella, Alberto Domínguez Hernández-Lerma, Onésimo |
| contents | We study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known continuous-time maximum principle. We show that this maximum principle, together with a transversality condition, is a necessary condition for optimality; we also show that it is sufficient under additional hypotheses. We use Gateaux differentials as a natural setting to derive first-order conditions. Additionally, we use the discrete-time maximum principle to derive the discrete-time Euler equation and to characterize Nash equilibria for discrete-time dynamic games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The maximum principle for discrete-time control systems and applications to dynamic games Corella, Alberto Domínguez Hernández-Lerma, Onésimo Optimization and Control We study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known continuous-time maximum principle. We show that this maximum principle, together with a transversality condition, is a necessary condition for optimality; we also show that it is sufficient under additional hypotheses. We use Gateaux differentials as a natural setting to derive first-order conditions. Additionally, we use the discrete-time maximum principle to derive the discrete-time Euler equation and to characterize Nash equilibria for discrete-time dynamic games. |
| title | The maximum principle for discrete-time control systems and applications to dynamic games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.11395 |