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Analysis and
control of fluids and of fluid-structure interactions. In
this class of problems a system of partial differential
equations modeling a fluid (Laplace, wave, Stokes or
Navier-Stokes) is coupled with the equations describing the
dynamics of a portion of the boundary (either a rigid or an
elastic body). Many difficulties arise, in particular because
of the free-boundary nature of the problem.
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Frequency domain methods
for the analysis and control of systems governed by PDEs and
the study of time-reversal phenomena.
Control: The problem consists in developing and applying
frequency domain or spectral criteria for the study of the
controllability of infinite-dimensional systems.
Time-reversal phenomena: We try to single out, to analyze and
to justify the focusing phenomena by time-reversal for the
acoustic (Helmholtz equation) and electromagnetic waves
(Maxwell equations).
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General observation
and control theory in infinite dimension. We develop an
approach that combines Fourier non-harmonic analysis,
multipliers, Carleman estimates and geometric methods. We
also focus on several convergence problems for the dynamics
of a control system subject to a time and/or space
discretization.
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Systems coupling
ordinary and partial differential equations. Among the
applications motivating the study of such systems, in
addition to fluid-structure interactions, we can mention the
control of a overhead crane, the SCOLE models, the elastic
plate attached to a non-zero mass boundary.
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Control of
nonlinear finite-dimensional systems. This research line
is motivated by different applications (quantum control,
trajectory tracking for controlled mechanical systems,
optimal control strategy for the fuel-cell powered racing
vehicle HydrogESSTINe) that we study by applying geometric
control theory methods.
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Implementation.
This research activity is transversal, since each of the
subjects presented above involves an implementation step.
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