Abstract: We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid) dynamics; the coupling occurs at the interface between the regions occupied by the fluid and the solid. We establish several trace regularity results for the fluid component of the system, which are then applied to show well-posedness of the Differential Riccati Equations arising in the optimization problem. This yields the feedback synthesis of the unique optimal control, under a very weak constraint on the observation operator; in particular, the present analysis allows general functionals, such as the integral of the natural energy of the physical system. Furthermore, this work confirms that the theory developed in Acquistapace et al. (Adv Diff Eq, [2]) -- crucially utilized here -- encompasses widely differing PDE problems, from thermoelastic systems to models of acoustic-structure and, now, fluid-structure interactions.
Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions / Bucci, Francesca; Lasiecka, Irena. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 37:(2010), pp. 217-235. [10.1007/s00526-009-0259-9]
Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions
BUCCI, FRANCESCA;
2010
Abstract
Abstract: We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid) dynamics; the coupling occurs at the interface between the regions occupied by the fluid and the solid. We establish several trace regularity results for the fluid component of the system, which are then applied to show well-posedness of the Differential Riccati Equations arising in the optimization problem. This yields the feedback synthesis of the unique optimal control, under a very weak constraint on the observation operator; in particular, the present analysis allows general functionals, such as the integral of the natural energy of the physical system. Furthermore, this work confirms that the theory developed in Acquistapace et al. (Adv Diff Eq, [2]) -- crucially utilized here -- encompasses widely differing PDE problems, from thermoelastic systems to models of acoustic-structure and, now, fluid-structure interactions.File | Dimensione | Formato | |
---|---|---|---|
arXiv-BucciLas-0902.2091_2010.pdf
accesso aperto
Tipologia:
Preprint (Submitted version)
Licenza:
Open Access
Dimensione
259.08 kB
Formato
Adobe PDF
|
259.08 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.