• 052350 - SYSTEM IDENTIFICATION AND PREDICTION

The general goal of the course is to enable students to extract (“learn”) from measured data useful information for automation,  systems and control applications. The course covers the fundamentals of data-driven learning of dynamical systems, with a focus on black-box system identification. Both linear and non-linear systems are considered. Prediction and forecasting are emphasized in time-series analysis and modelling as important applications of system identification. Each technique is treated both theoretically and practically through application examples.

Through theoretical lectures and numerical-exercises sessions, the students are expected to:

• Understand the fundamental problems of statistical learning for dynamical systems, that can be encountered while extracting information from a finite set of observations taken from an unknown system.
• Learn the main tools of dynamical system identification.
• Be able to formulate identification problems corresponding to different applications.
• Understand a range of system identification and prediction algorithms along with their strengths and weaknesses.
• Be able to apply algorithms to solve application problems.
• Be able to read current research papers and understand the issues raised by current research in the field.

The program of the course is as follows.

• Discrete-time linear dynamical systems: definition and analysis of model classes for Time Series and Input/Output models (Box-Jenkins models, and sub-classes like ARX and ARMAX)
• Linear optimal prediction
• Black-box identification from measured data-sets of Input/Output models (algorithm, analysis, validation)
• Black-box identification from measured data-sets of state-space models
• Gray-box system-identification using Extended Kalman Filter
• Extension to non-linear dynamical systems (N-ARX and N-ARMAX models) of black-box system-identification

• Familiarity with basic concepts of dynamical systems theory and computer science (algorithms and complexity).
• Maturity in linear algebra and probability theory.

The exam will be a written test in one of the official available dates. The exam will consist of both theoretical questions and simple (i.e., no computer-aided) exercises. The final marks will be awarded based on correctness of the answers, appropriateness of technical terminology and clarity of exposition. Specifically, the students will be asked to:

• show their understanding of the main problems (and the corresponding countermeasures) in the field of data-driven modeling and learning in general;
• select and describe the most appropriate tools for a given application;
• use analytical methods to solve problems of moderate complexity.