Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

0546799 - MÚ 2022 RIV GB eng J - Journal Article
Mitra, D. - Roy, Arnab - Takahashi, T.
Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body.
Mathematics of Control Signals and Systems. Roč. 33, č. 4 (2021), s. 637-667. ISSN 0932-4194. E-ISSN 1435-568X
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : controllability * finite-dimensional controls * fluid-structure interaction systems * stabilizability * viscoelastic fluids
OECD category: Pure mathematics
Impact factor: 1.600, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s00498-021-00295-x

We study control properties of a linearized fluid–structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that as in the case without structure, the system is not exactly null-controllable in finite time.
Permanent Link: http://hdl.handle.net/11104/0323178