Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.07283 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912717505298432 |
|---|---|
| author | Corella, Alberto Domínguez Jork, Nicolai Nečasová, Šarká Simon, John Sebastian H. |
| author_facet | Corella, Alberto Domínguez Jork, Nicolai Nečasová, Šarká Simon, John Sebastian H. |
| contents | This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the Hölder subregularity of the optimality mapping, which stems from the necessary conditions of the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07283 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls Corella, Alberto Domínguez Jork, Nicolai Nečasová, Šarká Simon, John Sebastian H. Optimization and Control This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the Hölder subregularity of the optimality mapping, which stems from the necessary conditions of the problem. |
| title | Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2307.07283 |