System Identification

Graduate Course (taught yearly during the 2nd semester), MEC2015 - SYSTEM IDENTIFICATION, 2018

Learn how to build your own data-driven models using classical and machine learning based methods.


To acquire skills for

  • Identification of models for systems with unknown structure based on measured input-output data
  • Estimate the state of dynamic systems from input-output measurements


Introduction to system identification and state estimation

  • classes of models
  • applications
  • linear and nonlinear methods

Practical system identification

  • design of excitation signals
  • residual-based validation: metrics and correlation methods
  • model structure selection

Linear system identification

  • batch and
  • recursive least squares

Nonlinear system identification

  • benchmark problems
  • polinomial NARMAX and
  • machine learning based approaches

State estimation

  • Kalman filtering
  • Receding-horizon methods for linear, nonlinear and hybrid systems


  • Introduction: motivation, application, computational platforms, evaluation criteria;
  • Review of signals and systems: continuous and discrete-time;
  • Linear system identification: least squares methods;
  • Design of excitation signals and model validation methods;
  • Adaptive system identification;
  • Introduction to state estimation: Kalman filter applied to system identification and state estimation, moving-horizon state estimation;
  • Nonlinear system identification: higher-order polynomials and machine learning methods;
  • Practical hands-on sessions assisted by the lecturer.


Computational exercises, oral exams, and final project.

Final Project

At the end of the course the students should choose a challenging problem and solve it using the methods learned throughout the course.

I think this is a good opportunity to get in touch with system identification in a controlled environment and also publicize your own work, besides participating in congresses and symposia.

Such evaluation exercises also important aspects of research methodology, meanwhile applying fundamental concepts of estimation and identification.

I strongly encourage students to then submit their work for peer review with my help. Below I list published works that were recently developed by former students:


AGUIRRE, L. A. Introdução à identificação de sistemas – técnicas lineares e não-lineares aplicadas a sistemas reais. 4th ed. Belo Horizonte, Brazil: Editora UFMG, 2015 [in Portuguese].

BAR-SHALOM, Y.; LI, X. R.; KIRUBARAJAN, T. Estimation with applications to tracking and navigation: theory algorithms and software. John Wiley & Sons, 2004.

BILLINGS, S. A. Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. West Sussex, United Kingdom: John Wiley & Sons Ltd., 2013.

LJUNG, L. System identification: theory for the user. 2nd. ed. Upper Saddle River, NJ: PTR Prentice Hall, 1999.

PINTELON, R.; SCHOUKENS, J. System identification: a frequency domain approach. 2nd ed. Hoboken, NJ: John Wiley & Sons, 2012.

RAWLINGS, J. B.; MAYNE, D. Q.; DIEHL, M. Model Predictive Control: Theory, Computation, and Design. Madison, WI: Nob Hill Publishing, 2017.

SCHOUKENS, J.; PINTELON, R.; ROLAIN, Y. Mastering system identification in 100 exercises. John Wiley & Sons, 2012.