| Hamecmopsys | |
Presentation/Project scope
| Goals |
The
control of infinite-dimensional dynamical systems,
represented by systems of coupled Partial Differential
Equations, is subject to a recently growing interest due
to two major impulses. Firstly recent technological
progress in material sciences induce an increased use of
complex and heterogeneous materials for sensing, actuation
and new energy sources. One may cite for instance the use
of Ionic Polymer Metal Composite or Memory Shape Alloys
for robotics applications, fuel cells in transport
applications or emergence of intensified chemical
processes. Secondly, increased computer power allows for
the use of extremely high order models, which become
structurally very closed to infinite dimensional dynamical
systems. The control and system-theoretic properties of
infinite-dimensional dynamical systems is the object of
long-ongoing researches and the reader is referred to
recent monographs for details on the results and the
references. The theoretical tools are very diverse, as in
the case of finite-dimensional systems, ranging from
functional analysis, to algebra and operator theory.
Although the general problem of the control of a system of
coupled nonlinear Partial Differential Equations is in
general intractable, major progresses have been achieved
by restricting the class of infinite-dimensional systems
to systems arising from physical models. In the same way
as for finite-dimensional control system, it reveals to be
essential to use balance equations, in general the energy
balance equation, in order to derive stabilizing
controllers for instance. For linear infinite-dimensional
systems a rich theory has been build up which uses
so-called passivity properties, for instance the energy
balance equations including energy flows with the
environment of the system, in order to derive basic
stability and stabilizability. For nonlinear
infinite-dimensional systems, the results are scattered on
case studies of different types for which control Lyapunov
functionals are constructed. Recently a particular class
of systems (called boundary port Hamiltonian systems) has
been suggested which generalizes systems of conservation
laws to different classes of boundary control systems. For
port-Hamiltonian systems defined on one-dimensional
spatial domains from differential-geometric structure,
called Dirac structure, the precize relation with boundary
control systems, some stabilizing controllers and
passivity-based controllers have been investigated. Dirac
structure are mainly used for the analysis of invariants
and symmetries of infinite-dimensional systems and their
use for the formulation and control of distributed
parameter systems with boundary external (input and
output) variables and their control is quite in the
beginning. Indeed, the results on the control of these
systems, have mostly concerned distributed parameter
systems defined on one-dimensional spatial domains and
systems stemming from two coupled conservation laws. The aim of the project is to bundle the efforts of control and applied mathematics laboratories (from both theoretical and experimental point of view) dealing with the structural properties and control of systems pertaining to different physical areas (acoustics, structural mechanics, mass and heat transport phenomena, chemical engineering systems, material science) for the development of methods and algorithms for the boundary control of nonlinear and dissipative open multiphysical systems using the formalism of dissipative Hamiltonian systems with boundary port variables. The first kernel topic of the project is to deal with coupled reversible and irreversible phenomena and deal for instance with or coupled convection and diffusive phenomena using the common geometric structure of Stokes-Dirac structures. The second kernel topic is to deal with approximations of infinite- dimensional port Hamiltonian systems obtained by spatial discretization preserving the Dirac structure and develop algorithms robust with respect to this reduction. |
Experimental Setups |
|
Nanotweezeers for DNA manipulation (FEMTO-ST) MSMA Based actuators (FEMTO-ST) Moving boundaries in tween screws extruders (LAGEP)
 Flexible structures (ISAE) Swimming creatures (IECN) |
|
NRA | FEMTO-ST | LAGEP | ISAE | IECN
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