Lecture 9. Identification of Linear Dynamical Systems

Learning Goals: You should be able to describe the four model structures BJ, OE, ARX, and ARMAX and how they describe linear dynamical systems of the for LaTeX: y(t) = G(q,\theta) u(t) + H(q,\theta) e(t)y(t)=G(q,θ)u(t)+H(q,θ)e(t). You should be able to describe how the models produces output predictions LaTeX: \widehat{y}(t|t-1,\theta)ˆy(t|t−1,θ). You should be able to describe how algorithms for estimation of parameters LaTeX: \thetaθ work. You should be able to use the matlab system identification GUI for doing simple model identification.

Reading: Parameter Estimation in Linear Models,  Ch 12.1-12.3 in Ljung+Glad+Hansson, version 2 of the book. (Or Ch. 11.1-11.3 in version 1, the old blue book by Ljung+Glad)

 

Lecture Slides: (Updated from 2020 to 2021 by correcting two typos, on slide 9 and 32)

Download Lecture9_Sysidpart1.pdf

 

 

 

 

 

also available on Youtube here: https://youtu.be/_d-aUe1Zk14 Links to an external site.

Watch also this video by Lennart Ljung (LiU):

Introduction to System Identification Links to an external site.Introduction to System Identification

 

Matlab code used on Lecture 9: