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7-11 avr. 2025 Aussois (France)
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Title and Abstract- Frédéric Boyer (LS2N, Nantes). Abstract: The objective of this mini-course is to give an example of modelling of infinite-dimensional physical systems. The example chosen will be the deformable body of continuum mechanics. We will start from the geometrical premises of this discipline, to establish the partial differential equations (p.d.e.) of a three-dimensional deformable body. We then introduce the theory of Cosserat beams and establish their p.d.e. on the Lie group SE(3). The talk will end with some examples llustrating the application of this model to continuous robotics.
- Sébastien Fueyo (GIPSA-lab, Grenoble) Title: Algebraic Methods for the Controllability of Some One-Dimensional Hyperbolic PDEs and Delay Systems
Abstract: In this mini-course, we will present algebraic methods, namely working within convolution algebras, to derive frequency-domain controllability criteria of the Hautus type for one-dimensional hyperbolic partial differential equations and delay systems. The approach relies on interpreting the controlled system as an abstract input-output system, whose controllability is characterized using a Bézout identity. Ordinary differential equations will be used as examples to introduce the abstract concepts. - Pierre Lissy (Ecole des Ponts, Paris). Title: TBA Abstract: TBA - Christophe Prieur (GIPSA-lab, Grenoble) Title: Nonlinear boundary stabilization of partial differential equations. Abstract: The goal of this course is to introduce the constructive design methods of stabilizing controllers for infinite-dimensional systems as those modelled by partial differential equations (PDEs). The considered approaches include the possible amplitude constraints on the input controls (as those coming from the presence of a saturation map in the control). The numerically computed controls render the origin of the (possibly) nonlinear PDEs an asymptotically stable equilibrium. Different classes of PDEs will be studied as the reaction-diffusion equations, and some hyperbolic equations, exhibiting a large scope of possible results from local asymptotic stability of the equilibrium to a global exponential stability. Numerical algorithms will be also discussed in this course. - Marius Tucsnak (Université de Bordeaux) Title : TBA
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| Personnes connectées : 2 | Vie privée | Accessibilité |
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