Asymptotic Analysis for Optimal Control of the Cattaneo Model
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_ | 1866918158818869248 |
|---|---|
| author | Blauth, Sebastian Pinnau, René Andres, Matthias Totzeck, Claudia |
| author_facet | Blauth, Sebastian Pinnau, René Andres, Matthias Totzeck, Claudia |
| contents | We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal control problems for a vanishing delay time $τ\rightarrow 0$. First, we show the convergence of solutions of the Cattaneo equation to the ones of the heat equation. Assuming the same right-hand side and compatible initial conditions for the equations, we prove a linear convergence rate. Moreover, we show linear convergence of the optimal states and optimal controls for the Cattaneo equation towards the ones for the heat equation. We present numerical results for both, the forward and the optimal control problem confirming these linear convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07630 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic Analysis for Optimal Control of the Cattaneo Model Blauth, Sebastian Pinnau, René Andres, Matthias Totzeck, Claudia Optimization and Control Analysis of PDEs We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal control problems for a vanishing delay time $τ\rightarrow 0$. First, we show the convergence of solutions of the Cattaneo equation to the ones of the heat equation. Assuming the same right-hand side and compatible initial conditions for the equations, we prove a linear convergence rate. Moreover, we show linear convergence of the optimal states and optimal controls for the Cattaneo equation towards the ones for the heat equation. We present numerical results for both, the forward and the optimal control problem confirming these linear convergence rates. |
| title | Asymptotic Analysis for Optimal Control of the Cattaneo Model |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2302.07630 |