Ivan Markovsky, "SHORT Course: Numerical methods for direct data-driven systems theory, signal processing, and control"

Tuesday 9 Jun 2026, 09:00 → Friday 12 Jun 2026, 10:30 Europe/Rome

Lecturer
Ivan Markovsky (ICREA, Barcelona)

Timetable and workload
Tuesday 9 MLH, 9-10.30
Wednesday 10 MLH, 10.45 - 12.15, 16-17.30
Thursday 11 MLH,  9-10.30
Friday 12 MLH,  9-10.30

Course content
The course provides an overview of, and hands-on experience with, newly emerged methods for the identification, analysis, and design of discrete-time linear time-invariant dynamical systems. The key idea is to view a dynamical system as a set of trajectories--the behavior--rather than equations--a representation. This representation-free perspective on systems theory, known as the behavioral approach, is naturally suited for dealing with data, that is, trajectories of the system. Moreover, it leads to novel, simple, and effective computational methods. At the core of this approach is a finite-time representation of the system by the image of a Hankel matrix constructed from the raw data. This data-driven, nonparametric representation allows us to use basic linear algebraic operations and leads to numerical methods for problems that are nontrivial to solve using classical transfer function and state-space techniques. Examples presented in the course include missing data estimation, fault detection, and computing distance to uncontrollability.
References:

- I. Markovsky. The Behavioral Toolbox. In Proc. of Machine Learning Research, 242:130--141, 2024. https://proceedings.mlr.press/v242/markovsky24a/markovsky24a.pdf
- I. Markovsky, L. Huang, and F. Dörfler. “Data-driven control based on behavioral approach: From theory to applications in power systems”. In: IEEE Control Systems Magazine, 43:28--68, 2023. https://imarkovs.github.io/tutorial.pdf
- I. Markovsky. Low-Rank Approximation: Algorithms, Implementation, Applications. Springer, 2019. https://imarkovs.github.io/book/book2e-2x1.pdf