Displaying similar documents to “Single input controllability of a simplified fluid-structure interaction model”

Exact controllability in fluid – solid structure: The Helmholtz model

Jean-Pierre Raymond, Muthusamy Vanninathan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations

Jean-Michel Coron (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

Local null controllability of a fluid-solid interaction problem in dimension 3

Muriel Boulakia, Sergio Guerrero (2013)

Journal of the European Mathematical Society

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We are interested by the three-dimensional coupling between an incompressible fluid and a rigid body. The fluid is modeled by the Navier-Stokes equations, while the solid satisfies the Newton's laws. In the main result of the paper we prove that, with the help of a distributed control, we can drive the fluid and structure velocities to zero and the solid to a reference position provided that the initial velocities are small enough and the initial position of the structure is close to...

Control of underwater vehicles in inviscid fluids

Rodrigo Lecaros, Lionel Rosier (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local...

Approximate controllability for a linear model of fluid structure interaction

Axel Osses, Jean-Pierre Puel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in...