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Conformal mapping and inverse conductivity problem with one measurement

Marc Dambrine, Djalil Kateb (2007)

ESAIM: Control, Optimisation and Calculus of Variations

This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series...

Construction of sampling and interpolating sequences for multi-band signals. the two-band case

Sergei Avdonin, Anna Bulanova, William Moran (2007)

International Journal of Applied Mathematics and Computer Science

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.

Control Norms for Large Control Times

Sergei Ivanov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A control system of the second order in time with control u = u ( t ) ∈ L 2 ( [ 0 , T ] ; U ) is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as 1 / T while the L 1 ( [ 0 , T ] ; U ) –norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.

Control of a clamped-free beam by a piezoelectric actuator

Emmanuelle Crépeau, Christophe Prieur (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.

Control of networks of Euler-Bernoulli beams

Bertrand Dekoninck, Serge Nicaise (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.

Control of the continuity equation with a non local flow

Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...

Control of the continuity equation with a non local flow

Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...

Control of the surface of a fluid by a wavemaker

Lionel Rosier (2004)

ESAIM: Control, Optimisation and Calculus of Variations

The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.

Control of the surface of a fluid by a wavemaker

Lionel Rosier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in Lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.

Control of the wave equation by time-dependent coefficient

Antonin Chambolle, Fadil Santosa (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior...

Control of the Wave Equation by Time-Dependent Coefficient

Antonin Chambolle, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior of...

Control of transonic shock positions

Olivier Pironneau (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Control of Transonic Shock Positions

Olivier Pironneau (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Control structure in optimization problems of bar systems

Leszek Mikulski (2004)

International Journal of Applied Mathematics and Computer Science

Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides...

Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité.

Amar Heminna (2001)

Revista Matemática Complutense

In this work, we examine the exact controllability of the solution of a linear elasticity system, with evolutive Ventcel's conditions, (see [3]), in a bounded domain of R3. We use the Hilbert uniqueness methode, (H.U.M), of J.L.Lions, (see [9]); some multipliers are defined on the boundary; the curvature tensor (see [6]), appears when computing some boundary integrals. This work can be inserted in the framework of the study of the exact controllability and stabilisation of various problems with...

Currently displaying 81 – 100 of 441