Exact controllability for a Rayleigh beam with piezoelectric actuator - Archive ouverte HAL Access content directly
Reports (Research Report) Year : 2023

## Exact controllability for a Rayleigh beam with piezoelectric actuator

Yubo Bai
• Function : Correspondent author
• PersonId : 1221560

Connectez-vous pour contacter l'auteur
Christophe Prieur
Zhiqiang Wang
• Function : Author
• PersonId : 1221561

#### Abstract

In this paper, exact controllability for a Rayleigh beam with piezoelectric actuator is considered. Controllability results show that the space of controllable initial data depends on the regularity of the control function and the location of the actuator. Two different spaces of control function, $L^2(0,T)$ and $(H^1(0,T))'$, correspond to two different controllability, $L^2$-controllability and $(H^1)'$-controllability. The approach to prove controllability results is based on Hilbert Uniqueness Method. Some non-controllability results are also obtained. In particular, non-controllability in short control time is studied by using Riesz basis property of exponential family in $L^2(0,T)$. Due to this non-controllability result, minimal time for the exact controllability is obtained.

### Dates and versions

hal-03964846 , version 1 (31-01-2023)

### Identifiers

• HAL Id : hal-03964846 , version 1

### Cite

Yubo Bai, Christophe Prieur, Zhiqiang Wang. Exact controllability for a Rayleigh beam with piezoelectric actuator. Fudan University; Gipsa-Lab. 2023. ⟨hal-03964846⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

0 View