Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid–structure interaction

Lasiecka, Irena; Tuffaha, Amjad

doi:10.1016/j.sysconle.2009.02.010

Cited by 35 publications

(55 citation statements)

References 28 publications

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“…For the fluid-structure interaction under investigation, which comprises a parabolic and a hyperbolic PDE, it was shown in [26] that a singular estimate (for the corresponding abstract evolution) is satisfied in the finite energy space, as long as the penalization in the quadratic functional does not involve the mechanical energy at a truly energy level. More precisely, the study in [26] established specific singular estimates and hence well-posedness of the Riccati equations in the special case of penalization of the mechanical variables below the energy level (say, sub-critical penalization), yet allowing full penalization of the fluid variable.…”

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confidence: 99%

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Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Bucci

Lasiecka

2009

Calc. Var.

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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.

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confidence: 99%

“…More precisely, the study in [26] established specific singular estimates and hence well-posedness of the Riccati equations in the special case of penalization of the mechanical variables below the energy level (say, sub-critical penalization), yet allowing full penalization of the fluid variable.…”

mentioning

confidence: 99%

Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Bucci

Lasiecka

2009

Calc. Var.

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“…> 0 , does not require any smoothing property imposed on the observation operator R. In fact, one can also consider unbounded observation (eg first order differential operator in the Neumann case). This is in contrast with other treatments where such smoothing was required [25,35,36].…”

Section: Remark 54mentioning

confidence: 80%

“…s . The second approach, instead, is variational: it was presented in [33][34][35][36]. We shall use this approach here.…”

Section: Specialization Of Abstract Model To the Fluidstructure Intermentioning

confidence: 99%

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Min-max Game Theory for Elastic and Visco-Elastic Fluid Structure Interactions

Lasiecka¹

2013

TOAMJ

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Abstract:We present the salient features of a min-max game theory developed in the context of coupled PDE's with an interface. Canonical applications include linear fluid-structure interaction problem modeled by Oseen's equations coupled with elastic waves. We shall consider two models for the structures: elastic and visco-elastic. Control and disturbance are allowed to act at the interface between the two media. The sought-after saddle solutions are expressed in a pointwise feedback form, which involves a Riccati operator; that is, an operator satisfying a suitable non-standard Riccati differential equation. Motivations, applications as well as a brief historical account are also provided.

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Exponential Decay Properties of a Mathematical Model for a Certain Fluid-Structure Interaction

Avalos

Bucci

2014

Springer INdAM Series

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In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a boundary interface with a two-dimensional mechanical plate equation. In the case that the PDE plate component is rotational inertia-free, one will have that solutions of this fluid-structure PDE system exhibit an exponential rate of decay. By way of proving this decay, an estimate is obtained for the resolvent of the associated semigroup generator, an estimate which is uniform for frequency domain values along iR. Subsequently, we proceed to discuss relevant point control and boundary control scenarios for this fluid-structure PDE model, with an ultimate view to optimal control studies on both finite and infinite horizon. (Because of said exponential stability result, optimal control of the PDE on time interval (0, ∞) becomes a reasonable problem for contemplation.)

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Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid–structure interaction

Cited by 35 publications

References 28 publications

Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Min-max Game Theory for Elastic and Visco-Elastic Fluid Structure Interactions

Exponential Decay Properties of a Mathematical Model for a Certain Fluid-Structure Interaction

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