Alban Quadrat

• Thèmes de recherches:

1. Systèmes d'équations aux dérivées partielles, D-modules et analyse algébrique effective
2. Méthodes algébriques et géométriques pour l'automatique

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• Publications:

1. Équations aux dérivées partielles, analyse algébrique effective, D-modules et systèmes multidimensionnels
2. Stabilisation des systèmes linéaires de dimension infinie
3. Autres

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• OreModules:

  OreModules is a Maple implementation of algorithms which compute free resolutions, extension modules, left/right/generalized inverses and other algebraic objects for linear systems of differential equations (ODE, PDE), differential time-delay systems, discrete systems etc.

  The algebraic framework for OreModules is module theory and homological algebra over Ore algebras of functional operators (e.g., differential, shift, time-delay operators). Within this algebraic unified framework, OreModules handles:

  • ordinary differential equations,
  • partial differential equations,
  • multidimensional discrete systems,
  • differential time-delay systems,
  • multidimensional convolutional codes, etc.
  These systems may be with constant, polynomial or rational coefficients.

  In the context of linear control systems, the main features of OreModules are the following:

  • Decide controllability and parametrizability.
  • Construct (minimal, injective) parametrizations.
  • Compute a family of generators for the autonomous elements.
  • Compute Bezout identities (left/right/generalized inverses).
  • Decide flatness (also pi-freeness).

  The package OreModules is developed by F. Chyzak, A. Quadrat, and D. Robertz.

  The OreModules package Stafford , developed by D. Robertz and A. Quadrat, is also available. This package computes two generators for left ideals over the Weyl algebras and bases of free left modules over the Weyl algebras.

  The OreModules package OreMorphisms: A homological algebraic package for factoring, reducing and decomposing linear functional systems , developed by T. Cluzeau and A. Quadrat, is available. A second release will be soon available with a larger library of examples.

  An OreModules version of the package QuillenSuslin (implementation of the Quillen Suslin theorem and its applications to mathematical systems theory) is in development.

  The package PurityFiltration2D built upon OreModules will be soon available. This package computes the purity filtration for 2-dimensional linear systems and gives new representations of these systems which are better suitable for their integrations and the study of their structural properties ("normal forms" for 2-dimensional linear systems). This package is developed by A. Quadrat.

  The package Serre handles Serre reduction of linear multidimensional systems. This package, built upon OreModules and implemented by T. Cluzeau and A. Quadrat, is in development.

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• Activités éditoriales: Multidimensional Systems and Signal Processing (Springer).

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• Projet SADDLES

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• Encadrements

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• Cours

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• Conférences:

1. Sage Days 24 at RISC (Autriche) (17-22/07/10)
2. Journées Nationales de Calcul Formel, Luminy, CIRM (France) (03-07/05/10)
3. IFAC Workshop on Control of Distributed Parameter Systems, Toulouse (France) (20-24/07/09)
4. AACA: Algebraic Analysis and Computer Algebra - New Perspective for Applications, lectures, RISC-Linz (Austria) (13-17/07/09)
5. Advances in the Theory of Control, Signals, and Systems, with Physical Modeling, Bernouilli Center, Swiss Federal Institute of Technology (EDPL), Lausanne (Switzerland) (15-17/04/09)
6. The Netherlands Congress of Mathematicians, Groningen (The Netherlands) (14-15/04/09)
7. Colloque international "Calcul algébrique et équations différentielles", Limoges (France) (24-25/03/09)
8. Summer School and Conference, Mathematics, Algorithms and Proofs (MAP), The Abdus Salam International Centre for Theoretical Physics (25-29/08/08), Trieste (Italy)
9. Eighteenth International symposium on Mathematical Theory of Networks and Systems (MTNS2008), Virginia Tech (USA) (28/07-01/08/08)
10. Conférence internationale en mémoire de Manuel Bronstein, INRIA Sophia Antipolis (France) (13/07/06)

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