System Identification

SYSTEM IDENTIFICATION

Academic Year 2025-2026

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 2022-23):

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

Marco Casini

Office hours: upon request via e-mail (room 227)

Class schedule

Monday, 9:00-11:00 - Classroom 145
Wednesday, 9:00-13:00 - Classroom 101

News

Schedule of oral exams available here: Oral Schedule 2026-01.pdf

Thesis

Thesis and research opportunities

Homework dates

Dates of the system identification homework of the winter session.

Assignment date	Due date	Delivery site	Registration deadline	Registration site	Notes
December 12, 2025	December 19, 2025	closed	December 8, 2025	closed	Results
January 30, 2026	February 2, 2026	https://forms.gle/TA3nt55RBAn6o7oRA	January 26, 2026	closed	-

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: input-output representations; transfer function; Z-transform (discrete-time 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 well-documented 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, take care of the homework dates reported in this page.
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, Discrete-time Stochastic Systems, Springer London Ltd, 2nd ed., 2002. Library code: 247 - 247a.
L. Ljung, System Identification: Theory for the user, 2nd ed., Prentice-Hall, 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]

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, 2.1-2.4].
Material: Notes_random_variables
Estimation theory. Parametric estimation. Properties of estimators. Maximum likelihood estimators. Least squares and Gauss-Markov estimators.
Ref.: [Soderstrom, 5.1-5.3].
Material: Notes_estimation
Stochastic processes and time-series prediction. Distributions, mean and covariance function. Stationary processes. Frequency domain representation. Stochastic dynamic systems. Time-series models: AR, MA, ARMA. Time-series prediction.
Ref.: [Soderstrom, 3.1-3.4; 4.1-4.3; 7.1-7.2].
Material: Notes_timeseries
Lab session: Lab_session_time_series; Solution (m-file)
Homework: Homework_time_series; Solution (pdf-file); Solution (m-file)
System identification theory. Identification of linear systems: prediction error methods. Input-output models: ARX, ARMAX, OE, BJ. Least squares estimator for linear regression models. Recursive system identification. Model validation.
Ref.: [Ljung, 1.1-1.4; 3.1-3.2; 4.1-4.2; 7.1-7.3; 10.1-10.2; 11.1-11.2; 16.1-16.6].
Material: Notes_system_identification; Simple examples
Practical system identification. Use of software tools for system identification.
Ref.: [Ljung, 17.1-17.4].
Lab session #1: Lab session on system identification #1;  Solution (m-file).
Lab session #2: Lab session on system identification #2;  Data (mat-file);  Solution (m-file).
Lab session #3: Lab session on system identification #3;  Data (mat-file);  Solution (m-file).
Lab session #4: Lab session on system identification #4;  Data (mat-file);  Solution (m-file).
Cart dataset: cart.mat;  Solution (m-file).

All-in-one pdf notes (union of the previous notes): SYSID_full_notes.

Useful stuff

LaTeX tutorial (includes Installation, Quick Start, Commands, etc.)
Overleaf (online LaTeX editor that anyone can use)
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)