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Project scope
This project aims at developing theoretical and applied results in the fields of Control Theory and
Identification. More generally, the project develops and coordinates research in this domain in
applied mathematics and in engineering sciences. Indeed it combines the research activities of
researchers from Applied Math and from Systems Theory and Automatic Control departments. The project contributes towards the organization of the French,
Brazilian and Chilean mathematical and control theory community and to its integration within the international community.
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Abstract
In this project the focus will be in both control and identification problems.
Concerning control theory, we plan to work in two main research lines: controllability
of coupled systems of partial differential equations (PDE) and stability of networked control
systems under concurrent communication constraints. The interest in the study of control properties
of coupled systems is rather recent but very active. There are a number of control results for
single PDE but new phenomena appear when dealing with coupled systems. We intend to address this
issue for both dispersive and hyperbolic coupled systems. On the other hand, for control systems where
communication takes place over non-transparent communication links (networked control systems) we aim at
addressing optimal control problems subject to concurrent communication constraints that include delays
and/or are subject to asynchronous sampling.
Regarding identification problems, we address the recovering of heterogeneous medium properties
(for instance conductivity, elasticity, charge density or transmission velocity) by means of indirect
measurements. We look for stability properties and reconstruction algorithms. Very useful tools are the
Carleman estimates, which in fact are useful as well to deal with control properties of PDE. In this
proposal we plan to develop new Carleman estimates at both the continuous level (including limiting
Carleman weights) and the discrete one in order to address some identification problems.
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Project Goals
Besides the main goal of creating/consolidating scientific connections within South America and
with France, we have the following scientific goals:
Study of the control properties of some coupled systems describing the evolution of plates
(Mindlin-Timoshenko systems), the interactions between short-wave and long-wave (Schrodinger-KdV systems),
and the propagation of surface and internal waves (Boussinesq systems).
Characterization, for control systems where communication takes place over non- transparent
communication links, of the interplay between optimal performance and concurrent communication
constraints that includes delays.
Study of the problem of identification of medium properties by using external measurements in the
framework of electro-seismic prospection, semiconductor material and transmission phenomena for beams or plates.