Presentation/Project scope

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)