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Teaching material (C. Poussot-Vassal, P. Vuillemin & I. Pontes Duff)

Teaching material

This page aims at presenting (a part of) the LTI model reduction problem and solutions. It gathers material for lectures (about 14h):

  • Lecture 1, Introduction, motivating examples and model approximation problem(s)
  • Lecture 2, Overview of the approximation methods and linear algebra tools
  • Lecture 3, Gramian, SVD and modal techniques
  • Lecture 4, Moment matching and Krylov subspace techniques
  • Lecture 5, Generalized Krylov subspace, tangential interpolation techniques
  • Lecture 6, $\mathcal H_2$ model approximation : projection point of view
  • Lecture 7, $\mathcal H_2$ model approximation : optimization point of view
  • Lecture 8, The Loewner framework
  • Lecture 9, Application to delay and irrational dynamical models
  • Lecture 10, Applications on industrial and academic use cases (aeronautics, fluid, river, biology...)
  • Lecture 11, Overview of the lecture, tools and discussions


Lectures and seminars

The MORE team also give lectures/seminar around the problem of model approximation

  1. C. Poussot-Vassal, P. Vuillemin and I. Pontes Duff Pereira.
    "Large-scale dynamical model approximation",
    Seminar (20h, including 6h of Lab) given to the Ph.D. students at the PhD School EDSYS, Toulouse, France, April 4-7, 2016.
  2. I. Pontes Duff Pereira, P. Vuillemin, C. Briat, C. Poussot-Vassal and C. Seren
    "Approximate computation of frequency-limited $\mathcal H_2$ and $\mathcal H_\infty$ norms for LTI infinite dimensional systems: application to time delay systems",
    at the 2nd DELSYS Workshop on Networked Control Systems, LAAS-CNRS, Toulouse, France, November 20-22, 2013.
  3. C. Poussot-Vassal and P. Vuillemin,
    "Approximation de modèles de grande dimension",
    Seminar (14h) given to Master, Ph.D. students and Researchers of the GdR MACS (MOSAR), Strasbourg, France, July, 2013.
  4. C. Poussot-Vassal,
    "Modelling of flexible aircraft",
    Seminar (3h) given to Master, Ph.D. students of the Scuole dottorato Italiana, Bertinoro, Italy, July, 2012.
    Kind invitation of Marco Lovera.
  5. C. Poussot-Vassal,
    "Model Reduction (Approximation) of Large-Scale Systems",
    Seminar (15h) given to Master, Ph.D. students and Researchers of the GIPSA-lab, Grenoble, France, January, 2012.
    Kind invitation of Gildas Besançon and Olivier Sename.