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Exact controllability in fluid – solid structure: The Helmholtz model

Jean-Pierre Raymond, Muthusamy Vanninathan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...

Exact controllability in fluid–solid structure : the Helmholtz model

Jean-Pierre Raymond, Muthusamy Vanninathan (2005)

ESAIM: Control, Optimisation and Calculus of Variations

A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results....

Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions

Scott W. Hansen, Oleg Imanuvilov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood...

Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions

Scott W. Hansen, Oleg Imanuvilov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood...

Exact controllability of a pluridimensional coupled problem.

Serge Nicaise (1992)

Revista Matemática de la Universidad Complutense de Madrid

We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [2,3], with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave equation with...

Exact controllability of an elastic membrane coupled with a potential fluid

Scott Hansen (2001)

International Journal of Applied Mathematics and Computer Science

We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is that if the density of the fluid is sufficiently small, then the coupled system is exactly controllable....

Exact controllability of linear dynamical systems: A geometrical approach

María Isabel García-Planas (2017)

Applications of Mathematics

In recent years there has been growing interest in the descriptive analysis of complex systems, permeating many aspects of daily life, obtaining considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems it is of interest to study the exact controllability; this measure is defined as the minimum set of controls that are needed...

Exact controllability of shells in minimal time

Paola Loreti (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].

Exact controllability of the 1-d wave equation from a moving interior point

Carlos Castro (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.

Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case

Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel (2006)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form ∂ y ∂ n + f ( y ) = 0 . We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one...

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