System Identification

linma2875  2020-2021  Louvain-la-Neuve

System Identification
Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 30.0 h
Hendrickx Julien;
Main themes
This class is an introduction to system identification, which consists in finding an appropriate representation of a dynamical system using appropriate measurements. It will cover some of the main parametric and nonparametric methods for identifying dynamical systems, including in closed loop. It will also cover the properties of signals and model classes that are relevant for system identification. A realistic identification project will give students the opportunity to apply and implement the techniques that they will have learned.

At the end of this learning unit, the student is able to :

1 With respect to the L.O. framework, this class contributes to the developpement of the following learning outcomes
  • AA1.1, AA1.2, AA1.3
  • AA2.1, AA2.4
  • AA3.2
  • AA5.3, AA5.5
More precisely, by the end of the class, the student will be able to :
  • recognize a problem of system identificaiton
  • propose and implement solutions to simple identification problems
  • identify a dynamical systems using input-output data
  • validate a model of system that has been identified, and compare different simple models
  • design an experiment to identify a simple system
  • develop a deeper understanding of system identification by him/herself if necessary  in order to solve more complex problems
Transversal learning outcomes :
  • Handling unforeseen technical issues that appear when treating a real-world problem
  • Making reasonable hypothesis for a given problem, and evaluating them a posteriori
  • Taking part to a technical class in English
The following topics will be covered
  • Nonparametric methods: temporal analysis, frequential analysis, including Fourier and spectral analysis
  • Main classes of LTI systems and their properties, including the notions of identifiability and predictors
  • Certain parametric methods: linear regression, instrumental variables, prediction errors, and some statistical methods including the maximum likelihood method
  • The properties of (input) signal, including the notion of information content of the signals and the level of persistence of excitation.
  • The convergence of the method seen
  • Identification techniques for systems controlled in closed loop
Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

  • Regular lectures.
  • Resolutions of simple problems under the supervison of teaching assistant in order to get familiar with new concepts.
The activities above take place in a classroom, but may be organized partly or entirely remotely if required by the sanitary situation or by practical constraints.
  • Problem sets to be solved in small group in order to develop a deeper understanding of the concepts.
  • A complete project of system identification in realistic conditions.
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The grade will be based on
  • An exam at the end of the year. The exam is normally a written exam, but may be replaced by a remote oral exam in case required by sanitary situation or by practical constraints.
  • A project on the identification of a system on the basis of real input/output data. This project may involve an oral discussion.
  • Problem sets during the year.
In case there is a significant difference between the grade obtained for individual activities and group activities, the teaching team may assign a grade reflecting the individual level. A (compulsory) oral exam may be organized for some students to obtain complementary information in case the teaching team has a doubt on the grade to assign.
More precise information will be made available on Moodle.
Other information
The lectures and problem sessions are in English, and all documents are in English. Homework, exams, and project reports can be written in English or French.
Students are expected to be familiar with dynamical systems and transfer functions.
Le cours s'appuie sur un syllabus disponible sur Moodle
Des livres de références sont également proposés :
  1. L. Ljung System Identification - Theory for the user Prentice Hall, 1999. (disponible en bibliothèque)
  2. T. Soderstorm and P Stoica, System Identification (
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