LQ optimal control for infinite-dimensional passive systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913875075530752 |
|---|---|
| author | Hastir, Anthony Jacob, Birgit |
| author_facet | Hastir, Anthony Jacob, Birgit |
| contents | We study the Linear-Quadratic optimal control problem for a general class of infinite-dimensional passive systems, allowing for unbounded input and output operators. We show that under mild assumptions, the finite cost condition is always satisfied. Moreover, we show that the optimal cost operator is a contraction. In the case where the system is energy preserving, the optimal cost operator is shown to be the identity, which allows to deduce easily the unique stabilizing optimal control. In this case, we derive an explicit solution to an adapted operator Riccati equation. We apply our results to boundary control systems, first-order port-Hamiltonian systems and an Euler-Bernoulli beam with shear force control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LQ optimal control for infinite-dimensional passive systems Hastir, Anthony Jacob, Birgit Optimization and Control Analysis of PDEs We study the Linear-Quadratic optimal control problem for a general class of infinite-dimensional passive systems, allowing for unbounded input and output operators. We show that under mild assumptions, the finite cost condition is always satisfied. Moreover, we show that the optimal cost operator is a contraction. In the case where the system is energy preserving, the optimal cost operator is shown to be the identity, which allows to deduce easily the unique stabilizing optimal control. In this case, we derive an explicit solution to an adapted operator Riccati equation. We apply our results to boundary control systems, first-order port-Hamiltonian systems and an Euler-Bernoulli beam with shear force control. |
| title | LQ optimal control for infinite-dimensional passive systems |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2506.03882 |