Stackelberg-Nash null controllability for stochastic parabolic equations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916339175653376 |
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| author | Oukdach, Omar Boulite, Said Elgrou, Abdellatif Maniar, Lahcen |
| author_facet | Oukdach, Omar Boulite, Said Elgrou, Abdellatif Maniar, Lahcen |
| contents | We study a hierarchical control problem for stochastic parabolic equations involving gradient terms. We employ the Stackelberg-Nash strategy with two leaders and two followers. The leaders are responsible for selecting the policy targeting null controllability, while the followers solve a bi-objective optimal control problem which consists of maintaining the solution process close to prefixed targets. Once the Nash equilibrium is determined, the problem reduces to achieving null controllability of a coupled forward-backward stochastic system. To solve this problem, via Carleman estimates, we establish a suitable observability inequality. Subsequently, we achieve the desired controllability result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stackelberg-Nash null controllability for stochastic parabolic equations Oukdach, Omar Boulite, Said Elgrou, Abdellatif Maniar, Lahcen Optimization and Control Analysis of PDEs We study a hierarchical control problem for stochastic parabolic equations involving gradient terms. We employ the Stackelberg-Nash strategy with two leaders and two followers. The leaders are responsible for selecting the policy targeting null controllability, while the followers solve a bi-objective optimal control problem which consists of maintaining the solution process close to prefixed targets. Once the Nash equilibrium is determined, the problem reduces to achieving null controllability of a coupled forward-backward stochastic system. To solve this problem, via Carleman estimates, we establish a suitable observability inequality. Subsequently, we achieve the desired controllability result. |
| title | Stackelberg-Nash null controllability for stochastic parabolic equations |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2407.20366 |