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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2406.11009 |
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| _version_ | 1866916519275921408 |
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| author | Gong, Jiayin Wang, Tianxiao |
| author_facet | Gong, Jiayin Wang, Tianxiao |
| contents | This paper is concerned with a unified treatment of linear quadratic control problem for stochastic Volterra integral equations (SVIEs), motivated by the various approaches and scattered results in the existing literature. A novel class of optimal causal feedback strategy is introduced and characterized by means of a new Riccati system. To this end, a fundamental function space and an appropriate multiplicative rule among functions are defined for the first time. In contrast with the existing works, our unified treatment not only provides a new approach, but also extends or improves the known conclusions in stochastic differential equations, convolution SVIEs, stochastic Volterra integro-differential equations (VIDEs), deterministic VIEs, deterministic VIDEs. In addition, an interesting phenomenon is reveal by the current study: for SVIEs the conventional structure of state feedback is replaced by a suitable causal form, and the original state process no longer plays indispensable role in the feedbacks while an auxiliary state process does. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Causal feedback strategies for controlled stochastic Volterra systems: a unified treatment Gong, Jiayin Wang, Tianxiao Optimization and Control This paper is concerned with a unified treatment of linear quadratic control problem for stochastic Volterra integral equations (SVIEs), motivated by the various approaches and scattered results in the existing literature. A novel class of optimal causal feedback strategy is introduced and characterized by means of a new Riccati system. To this end, a fundamental function space and an appropriate multiplicative rule among functions are defined for the first time. In contrast with the existing works, our unified treatment not only provides a new approach, but also extends or improves the known conclusions in stochastic differential equations, convolution SVIEs, stochastic Volterra integro-differential equations (VIDEs), deterministic VIEs, deterministic VIDEs. In addition, an interesting phenomenon is reveal by the current study: for SVIEs the conventional structure of state feedback is replaced by a suitable causal form, and the original state process no longer plays indispensable role in the feedbacks while an auxiliary state process does. |
| title | Causal feedback strategies for controlled stochastic Volterra systems: a unified treatment |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.11009 |