Displaying similar documents to “The cost of controlling unstable systems: time irreversible systems.”

Sensors and boundary state reconstruction of hyperbolic systems

El Hassan Zerrik, Hamid Bourray, Samir Ben Hadid (2010)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained...

Exact controllability of a pluridimensional coupled problem.

Serge Nicaise (1992)

Revista Matemática de la Universidad Complutense de Madrid

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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...

Controllability of analytic functions for a wave equation coupled with a beam.

Brice Allibert, Sorin Micu (1999)

Revista Matemática Iberoamericana

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We consider the controllability and observation problem for a simple model describing the interaction between a fluid and a beam. For this model, microlocal propagation of singularities proves that the space of controlled functions is smaller that the energy space. We use spectral properties and an explicit construction of biorthogonal sequences to show that analytic functions can be controlled within finite time. We also give an estimate for this time, related to the amount of analyticity...

Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation

George Avalos, Irena Lasiecka (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function ℰ min ( T ) , as terminal time T ↓ 0 . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator 𝒜 , as well as of the explicit characterization of its domain of definition. We ultimately find that the...

An output controllability problem for semilinear distributed hyperbolic systems

E. Zerrik, R. Larhrissi, H. Bourray (2007)

International Journal of Applied Mathematics and Computer Science

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The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated...

Exact Neumann boundary controllability for second order hyperbolic equations

Weijiu Liu, Graham Williams (1998)

Colloquium Mathematicae

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Using HUM, we study the problem of exact controllability with Neumann boundary conditions for second order hyperbolic equations. We prove that these systems are exactly controllable for all initial states in L 2 ( Ω ) × ( H 1 ( Ω ) ) ' and we derive estimates for the control time T.