Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910921807364096 |
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| author | Moldenhauer, Robert H. Nešić, Dragan Granzotto, Mathieu Postoyan, Romain Teel, Andrew R. |
| author_facet | Moldenhauer, Robert H. Nešić, Dragan Granzotto, Mathieu Postoyan, Romain Teel, Andrew R. |
| contents | We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability assumptions inspired by the related literature on deterministic systems, we prove that uniform semi-global practical recurrence holds for the closed-loop system, where the adjustable parameter is the discount factor. Under additional continuity assumptions, we further prove that this property is robust. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost Moldenhauer, Robert H. Nešić, Dragan Granzotto, Mathieu Postoyan, Romain Teel, Andrew R. Optimization and Control Systems and Control 93E20, 93D09, 93D30 We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability assumptions inspired by the related literature on deterministic systems, we prove that uniform semi-global practical recurrence holds for the closed-loop system, where the adjustable parameter is the discount factor. Under additional continuity assumptions, we further prove that this property is robust. |
| title | Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost |
| topic | Optimization and Control Systems and Control 93E20, 93D09, 93D30 |
| url | https://arxiv.org/abs/2504.20705 |