Controlling the Rates of a Chain of Harmonic Oscillators with a Point Langevin Thermostat
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915107718561792 |
|---|---|
| author | Hannani, Amirali Tran, Minh-Binh Phung, Minh Nhat Trélat, Emmanuel |
| author_facet | Hannani, Amirali Tran, Minh-Binh Phung, Minh Nhat Trélat, Emmanuel |
| contents | We consider the control problem of controlling the rates of an infinite chain of coupled harmonic oscillators with a Langevin thermostat at the origin. We study the effect of two types of open-loop boundary controls, impulsive control and linear memory-feedback control, in the high frequency limit. We investigate their action on the reflection-transmission coefficients for the wave energy for the scattering of the thermostat. Our study shows that the impulsive boundary controls have no impact on the rates and are thus not appropriate to act on the system, despite their physical meaning and relevance. In contrast, the second kind of control that we propose, which is less standard and uses the past of the state solution of the system, is adequate and relevant. We prove that any triple of rates satisfying appropriate assumptions is asymptotically reachable thanks to the linear memory-feedback controls that we design explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Controlling the Rates of a Chain of Harmonic Oscillators with a Point Langevin Thermostat Hannani, Amirali Tran, Minh-Binh Phung, Minh Nhat Trélat, Emmanuel Optimization and Control We consider the control problem of controlling the rates of an infinite chain of coupled harmonic oscillators with a Langevin thermostat at the origin. We study the effect of two types of open-loop boundary controls, impulsive control and linear memory-feedback control, in the high frequency limit. We investigate their action on the reflection-transmission coefficients for the wave energy for the scattering of the thermostat. Our study shows that the impulsive boundary controls have no impact on the rates and are thus not appropriate to act on the system, despite their physical meaning and relevance. In contrast, the second kind of control that we propose, which is less standard and uses the past of the state solution of the system, is adequate and relevant. We prove that any triple of rates satisfying appropriate assumptions is asymptotically reachable thanks to the linear memory-feedback controls that we design explicitly. |
| title | Controlling the Rates of a Chain of Harmonic Oscillators with a Point Langevin Thermostat |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.06536 |