SYSTEM IDENTIFICATION
Academic Year 20232024
6 CFU
Degree Courses
 M.S. in Artificial Intelligence and Automation Engineering (Curriculum Robotics and Automation) (first module of System Identification and Data Analysis)
 M.S. in Engineering Management
 M.S. in Applied Mathematics (first module of Data and Financial Analysis)
Instructions for students from previous academic years (until 202223):
 Students who have to take the 6 CFU exam, must take this exam.
 Students who have to take the 9 CFU exam, must refer to the old version of the course, whose details are provided here.
Instructors
Office hours: upon request via email (room 227)
News
Homework dates
In the following, dates regarding the system identification homework are reported.
Assignment date  Due date  Delivery site  Registration deadline  Registration site  Notes 
June 14, 2024  June 17, 2024  closed  June 10, 2024  closed  Results 
July 8, 2024  July 11, 2024  closed  July 4, 2024  closed  Results 
How the exam works: things you must know about the exam organization
Prerequisites
What do I need to know before starting?
 Linear algebra and calculus.
 Basics of probability theory and random variables (though there will be a very short review).
 Basics of dynamic systems theory: inputoutput representations; transfer function; Ztransform (discretetime systems).
 Basics of Matlab language.
How to pass the exam
In order to pass the exam, you have to perform two steps:
 (A) the homework;
 (B) the oral exam.
Step (A) must be done before step (B). Details and schedule of step (A) will be communicated by the instructors during the course. The dates of the oral exams are usually published in the News section above (they may not coincide with those in segreteriaonline).
The oral exam involves the discussion of the homework and questions about all the topics treated during the course.
How to do the homework
The homework will require to write a report explaining the adopted methodologies and the obtained results in a welldocumented and concise fashion. Such report must be written in LaTeX (a LaTeX tutorial is available here).
A LaTeX template for the report is provided here.
Additional information will be provided during the course.
Golden rules
 Rule 1: the right time to do the exam is at the end of the course, during the winter exam session. You are strongly encouraged to do that!
In case you need to do the exam in subsequent sessions, you have to ask for the homework well in advance, in order to deliver the report at least 7 days before the oral exam.

Rule 2: do the homework by yourself and report it carefully. During the oral exam you will have to explain and motivate the homework solution.
Bibliography
 A. Papoulis, S.U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed., 2002. Library code: 130  130a.
 T. Soderstrom, Discretetime Stochastic Systems, Springer London Ltd, 2nd ed., 2002. Library code: 247  247a.
 L. Ljung, System Identification: Theory for the user, 2nd ed., PrenticeHall, 1999. Library code: 71  71a  71b.
 L. Ljung. System Identification Toolbox: Getting started, The Mathworks, 2001. [download]
 L. Ljung. System Identification Toolbox: User's guide, The Mathworks, 2001. Library code: 152. [download]
Contents
 Course introduction.
Material: Slides_introduction

Random variables (recap). Probability distributions. Mean and covariance. Conditional probability. Gaussian variables.
Ref.: [Papoulis, 1,2,3,4,5,6,7] [Soderstrom, 2.12.4].
Material:
Notes_random_variables

Estimation theory. Parametric estimation. Properties of
estimators. Maximum likelihood estimators. Least squares and
GaussMarkov estimators.
Ref.: [Soderstrom, 5.15.3].
Material:
Notes_estimation

Stochastic processes and timeseries prediction.
Distributions, mean and covariance function.
Stationary processes.
Frequency domain representation.
Stochastic dynamic systems.
Timeseries models: AR, MA, ARMA.
Timeseries prediction.
Ref.: [Soderstrom, 3.13.4; 4.14.3; 7.17.2].
Material:
Notes_timeseries
Lab session: Lab_session_time_series; Solution (mfile)
Homework: Homework_time_series;
Solution (pdffile);
Solution (mfile)

System identification theory.
Identification of linear systems: prediction error methods.
Inputoutput models: ARX, ARMAX, OE, BJ.
Least squares estimator for linear regression models.
Recursive system identification.
Model validation.
Ref.: [Ljung, 1.11.4; 3.13.2; 4.14.2; 7.17.3; 10.110.2; 11.111.2; 16.116.6].
Material:
Notes_system_identification
Lab session #1: Lab session on system identification #1; Solution (mfile).
Lab session #2: Lab session on system identification #2; Data (matfile); Solution (mfile).
Lab session #3: Lab session on system identification #3; Data (matfile); Solution (mfile).
Lab session #4: Lab session on system identification #4; Data (matfile); Solution (mfile).

Practical system identification. Use of software tools for system identification.
Ref.: [Ljung, 17.117.4].
Cart dataset: cart.mat
Allinone pdf notes (union of the previous notes): SYSID_full_notes.
Useful stuff
 LaTeX tutorial (includes Installation, Quick Start, Commands, etc.)
 Matlab download site (create an account using your Unisi email address. Be sure to install the Control Systems Toolbox, the System Identification Toolbox and the Signal Processing Toolbox)