Beauchard, Karine Koenig, Armand Le Balc'h, Kévin

Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the previous results. We consider constant coefficients heat-transport systems with coupling of order zero and one, ...

Brivadis, Lucas Gauthier, Jean-Paul Sacchelli, Ludovic Serres, Ulysse

Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback s...

Brivadis, Lucas Gauthier, Jean-Paul Sacchelli, Ludovic Serres, Ulysse

Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback s...

Bergounioux, Maïtine Bretin, Elie Privat, Yannick

Thermo-acoustic tomography is a non-invasive medical imaging technique: the object to be reconstructed is excited by an impulse, inducing inhomogeneous heating and thus tissue expansion. This creates an acoustic wave pressure that can be measured by sensors. The reconstruction of internal heterogeneities can then be achieved by solving an inverse p...

Bergounioux, Maïtine Bretin, Elie Privat, Yannick

Thermo-acoustic tomography is a non-invasive medical imaging technique: the object to be reconstructed is excited by an impulse, inducing inhomogeneous heating and thus tissue expansion. This creates an acoustic wave pressure that can be measured by sensors. The reconstruction of internal heterogeneities can then be achieved by solving an inverse p...

Tsinias, John Kitsos, Constantinos

We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by means of a sequence of functionals approximating the unknown state of the system on a given bounded time interv...

Tsinias, John Kitsos, Constantinos

We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by means of a sequence of functionals approximating the unknown state of the system on a given bounded time interv...

Boyer, Franck Hernández-Santamaría, Víctor

In this paper, we prove a Carleman estimate for a time-discrete parabolic equation in which the large parameter is connected to the time step of the discretization scheme. This estimate is then used to obtain a relaxed observability estimate that yields some controllability results for linear and semi-linear time-discrete parabolic equations. We al...

Boyer, Franck Hernández-Santamaría, Víctor

In this paper, we prove a Carleman estimate for a time-discrete parabolic equation in which the large parameter is connected to the time step of the discretization scheme. This estimate is then used to obtain a relaxed observability estimate that yields some controllability results for linear and semi-linear time-discrete parabolic equations. We al...

Boyer, Franck Hernández-Santamaría, Víctor

In this paper, we prove a Carleman estimate for a time-discrete parabolic equation in which the large parameter is connected to the time step of the discretization scheme. This estimate is then used to obtain a relaxed observability estimate that yields some controllability results for linear and semi-linear time-discrete parabolic equations. We al...