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ARF-013
Automation, robotics, sensors - 2022

Complex linear dynamical systems

OBJECTIVE :

This trainee is tailored to engineers wishing to enhance their complex linear dynamical systems knowledge. A specific accent is given on their property structure, analysis, with a strong emphasis on model reduction, approximation and identification.

The objective is (i) to give a global, up to date, view of the different dynamical systems cla

 

sses (properties and specificities), (ii) to describe and provide some numerical tools allowing to treat these systems in a context of very large-scale and infinite dimensional models, and (iii) to allow the dynamical model construction on the basis of experimental data only.

More specifically, the following points will be detailed along the trainee:

  • Go into details of different linear model structures : ODE, DAE, rational and irrational transfer functions (e.g. delayed systems).
  • Get in touch with high dimensional models and inherent complexity.
  • Understand how to construct simple dynamical models from data collected on a simulator or in experiments.
  • Learn how to reduce and approximate large-scale dynamical models.

The presented concepts will be applied on a class chosen use-case or even, a participant problem (if any). An important part of the course is dedicated to the practical application of the concepts through tools developed in MATLAB. The theoretical issues will be present only if participant are interested. This trainee can be viewed as a basis prior any analysis and control lecture.

COURSE DURATION AND TIMETABLE :

The trainee represents 21h over 3 days. It is balanced 50%-50% between theory and methodology but adaptation can be done according to the audience.

GENERAL APPROACH :

The theoretical and methodological support being provided to the audience, the spirit of the trainee is to go though the application of these notions, by using a dedicated MATLAB toolbox.

PREREQUISITE :

Trainee level : basis / improvement
This trainee is accessible to all engineers, but basic knowledge on Laplace transform, linear algebra a plus.

COURSE DIRECTOR(S) :

Charles POUSSOT-VASSAL

HDR, Ph.D., ONERA

Pierre VUILLEMIN

Ph.D., ONERA

CONTENT :

Introduction

  • Linear dynamical systems (different forms)
  • Time-domain representation (ODE an DAE)
  • Frequency-domain representation
  • Representations, identification an approximation
  • Link between all the different structures
  • Linear dynamical systems fundamental properties

Systems complexity

  • Finite dimension (large, very large)
    • Stability, norms and performances
    • Numerical limitations an solutions
  • Infinite dimension
    • Stability, norms and performances
    • Numerical limitations an solutions
  • Linear algebra in the high dimensional setup

Linear dynamical model approximation and reduction

  • Model based reduction methods
  • Large-scale model reduction
  • Infinite dimensional model approximation
  • Data-driven model approximation
  • Simulator-driven model approximation
  • Approximation from experimental data (and identification)

Use-case and numerical tool presentation

  • Use-case selection (academic / industrial)
  • Problem analysis (properties, limitations, approximation / reduction)
  • Control design application and validation
  • Presentation of the MOR toolbox
  • Optional : audience use-case

WHEN AND WHERE :

Scheduled in French :

TOULOUSE : April, 4 to 6, 2022

COURSE FEES :

€1 580 excluding tax (20% VAT)

See general terms

 

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