Finite-Dimensional RHC Control of Linear Time-Varying Parabolic PDEs: Stability Analysis and Model-Order Reduction
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911759601762304 |
|---|---|
| author | Azmi, Behzad Rohleff, Jan Volkwein, Stefan |
| author_facet | Azmi, Behzad Rohleff, Jan Volkwein, Stefan |
| contents | This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear combination of finitely many indicator functions whose total supports cover only a small part of the spatial domain. Further, we consider the squared l1-norm as the control cost. This leads to a nonsmooth infinite-horizon problem which allows a stabilizing optimal control with a low number of active actuators over time. First, the stabilizability of RHC is investigated. Then, to speed-up numerical computation, the data-driven model-order reduction (MOR) approaches are adequately incorporated within the RHC framework. Numerical experiments are also reported which illustrate the advantages of our MOR approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-Dimensional RHC Control of Linear Time-Varying Parabolic PDEs: Stability Analysis and Model-Order Reduction Azmi, Behzad Rohleff, Jan Volkwein, Stefan Optimization and Control This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear combination of finitely many indicator functions whose total supports cover only a small part of the spatial domain. Further, we consider the squared l1-norm as the control cost. This leads to a nonsmooth infinite-horizon problem which allows a stabilizing optimal control with a low number of active actuators over time. First, the stabilizability of RHC is investigated. Then, to speed-up numerical computation, the data-driven model-order reduction (MOR) approaches are adequately incorporated within the RHC framework. Numerical experiments are also reported which illustrate the advantages of our MOR approaches. |
| title | Finite-Dimensional RHC Control of Linear Time-Varying Parabolic PDEs: Stability Analysis and Model-Order Reduction |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.09111 |