## Lecturers

**Alexandre Mauroy,** University of Namur (UNamur)

Contact

Webpage

**Igor Mezic**, University of California, Santa Barbara, USA

Contact

Webpage

**Schedule and place**

This 15-hour course will take place in August 2021 and in September 2021 at** University of Namur (UNamur) **

Bâtiment des sciences: Building 09 (room S09) - Rue de Bruxelles, 61 - 5000 Namur see map here

**Schedule**: including a 15-minute coffee break in each session

- Lectures by Igor Mezic : August 18, 19 and 20: from 9:30 to 12:15
- Lectures by Alexandre Mauroy: September 1, 2 and 3: from 9:30 to 12:15

**Teaching method**: Face-to-face

**Description**

Classical approach to dynamical systems relies on the pointwise description of a set of trajectories in the state space. In contrast, an alternative global description of nonlinear dynamical systems is provided by operator-theoretic methods. The so-called Koopman operator describes the evolution of “observables-functions” of the state space and turns a nonlinear system into a linear (but infinite-dimensional) system. This approach enables the use of spectral analysis for studying nonlinear systems, a method which mirrors the classical spectral approach to linear systems. More generally, the

approach yields systematic and efficient linear techniques to solve nonlinear problems. Recent years have also witnessed increasing interest to the Koopman operator framework, in particular in the context of nonlinear control theory (e.g. stability analysis, observability, controllability, optimal control, model predictive control, and identification, to list a few).

The course will provide a broad overview of the current state-of-the-art in Koopman operator theory. In the first part, basic concepts will be reviewed in the context of dynamical systems theory. The second part will focus on numerical (data-driven) methods that allow to obtain finite-dimensional approximations of the operator. Recent developments of the Koopman operator approach in the context of control theory will be presented in the third part of the course.

**Course material**

The Koopman Operator Theory in Systems and Control: Concepts, Methodologies, and Applications. Eds.: A. Mauroy, I. Mezic, and Y. Susuki. Lectures Notes in Control and Information Sciences, Springer, 2020.

**Evaluation**

To be determined.