92991 - Learning and Estimation of Dynamical Systems M

Learning outcomes

The course will provide students with the main data-driven approaches for learning mathematical models of dynamic sytems. The learned models can then be used for automation, control and systems engineering applications. The course covers system identification and machine learning techniques like linear regression, logistic regression, prediction error method, instrumental variable, maximum likelihood, support vector machine. The basics of estimation theory are also covered and the Kalman filter is presented as a tool for estimating the state of a dynamic system from input-output data. At the end of the course students are able to apply the main system identification and machine learning algorithms to solve application problems and to evaluate the quality of the learned models.

Course contents

Introduction
Systems and models. Mathematical models. Physical modeling and black-box (data-driven) modeling: system identification and machine learning.

Brief review of stochastic processes

Stochastic models
Static models and dynamic models. Equation error models.

The estimation problem
Definition of the estimation problem. Parameter estimation and model complexity estimation. Classification and regression.

Linear regression
The linear regression form. The least squares (LS) method and its properties. Least squares identification of dynamic equation error models. Identifiability properties of LS estimates: persistency of excitation (PE) of input signals. Recursive least squares (RLS) identification.

Estimation of the model complexity and model validation

Nonlinear regression
The prediction error method. The instrumental variable method.

Maximum likelihood
Maximum likelihood estimation. The Cramer-Rao lower bound.

Classification
Logistic regression. Linear discriminant analysis. Support vector machine.

Optimal estimation of signals
The fundamental theorem of estimation theory. Stochastic state space models. Kalman filtering.

Readings/Bibliography

T. Söderström and P. Stoica, System Identification, Prentice Hall, Englewood Cliffs, N.J., 1989. This book is now out of print and can be downloaded here [http://user.it.uu.se/~ts/sysidbook.pdf] .

R. Guidorzi, Multivariable System Identification: From Observations to Models, Bononia University Press, Bologna, 2003.

S. Bittanti, Model Identification and Data Analysis, John Wiley & Sons, 2019.

G. James, D. Witten, T. Hastie and R. Tibshirani, An Introduction to Statistical Learning, Springer, 2013. This book can be downloaded here [https://faculty.marshall.usc.edu/gareth-james/ISL/ISLR%20Seventh%20Printing.pdf]

 

Teaching methods

Traditional lectures.

Assessment methods

The final evaluation is based on a written exam and a project.

Teaching tools

Video projector, blackboard.

Office hours

See the website of Roberto Diversi