Optimal control of third grade fluids with multiplicative noise
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915155876511744 |
|---|---|
| author | Tahraoui, Yassine Cipriano, Fernanda |
| author_facet | Tahraoui, Yassine Cipriano, Fernanda |
| contents | This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to achieve a predefined velocity profile under a minimal cost. Due to the strong nonlinearity of the stochastic state equations, strong solutions are available just locally in time, and the cost functional includes an appropriate stopping time. First, we show the existence of an optimal pair. Then,we show that the solution of the stochastic forward linearized equation coincides with the Gâteaux derivative of the control-to-state mapping, after establishing some stability results. Next, we analyse the backward stochastic adjoint equation; where the uniqueness of solution holds only when $d=2$. Finally, we establish a duality relation and deduce the necessary optimality conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13231 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal control of third grade fluids with multiplicative noise Tahraoui, Yassine Cipriano, Fernanda Optimization and Control Analysis of PDEs Probability 35R60, 49K20, 76A05, 76D55, 60H15 This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to achieve a predefined velocity profile under a minimal cost. Due to the strong nonlinearity of the stochastic state equations, strong solutions are available just locally in time, and the cost functional includes an appropriate stopping time. First, we show the existence of an optimal pair. Then,we show that the solution of the stochastic forward linearized equation coincides with the Gâteaux derivative of the control-to-state mapping, after establishing some stability results. Next, we analyse the backward stochastic adjoint equation; where the uniqueness of solution holds only when $d=2$. Finally, we establish a duality relation and deduce the necessary optimality conditions. |
| title | Optimal control of third grade fluids with multiplicative noise |
| topic | Optimization and Control Analysis of PDEs Probability 35R60, 49K20, 76A05, 76D55, 60H15 |
| url | https://arxiv.org/abs/2306.13231 |