The Cesàro Value Iteration
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910126570471424 |
|---|---|
| author | Mair, Jonas Schwenkel, Lukas Müller, Matthias A. Allgöwer, Frank |
| author_facet | Mair, Jonas Schwenkel, Lukas Müller, Matthias A. Allgöwer, Frank |
| contents | In this paper, we consider undiscouted infinite-horizon optimal control for deterministic systems with an uncountable state and input space. We specifically address the case when the classic value iteration does not converge. For such systems, we use the Ces`aro mean to define the infinite-horizon optimal control problem and the corresponding infinite-horizon value function. Moreover, for this value function, we introduce the Cesàro value iteration and prove its convergence for the special case of systems with periodic optimal operating behavior. For this instance, we also show that the Cesàro value function recovers the undiscounted infinite-horizon optimal cost, if the latter is well-defined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Cesàro Value Iteration Mair, Jonas Schwenkel, Lukas Müller, Matthias A. Allgöwer, Frank Systems and Control Optimization and Control In this paper, we consider undiscouted infinite-horizon optimal control for deterministic systems with an uncountable state and input space. We specifically address the case when the classic value iteration does not converge. For such systems, we use the Ces`aro mean to define the infinite-horizon optimal control problem and the corresponding infinite-horizon value function. Moreover, for this value function, we introduce the Cesàro value iteration and prove its convergence for the special case of systems with periodic optimal operating behavior. For this instance, we also show that the Cesàro value function recovers the undiscounted infinite-horizon optimal cost, if the latter is well-defined. |
| title | The Cesàro Value Iteration |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2504.04889 |