Koopman Operator Theory in Systems and Control
18, 19 & 20 August 2021
+ 1,2 & 3 September 2021
SOCN, Graduate School in Systems, Optimization, Control and Networks
Discover the state of the art in Koopman operator theory. The basic concepts will be reviewed by Alexandre Mauroy (University of Namur). Following, Igor Mezic (University of California) will focus on numerical (data-driven) methods that allow to obtain finite-dimensional approximations of the operator. The course finishes with recent developments.
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.
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.
- Igor Mezic
- 18, 19 & 20 August 2021
- Alexandre Mauroy
- 1, 2 & 3 September 2021
- Location: University of Namur
Building 63 (room BN01), Rempart de la vierge, 5000 Namur
- Language: English
- Target audience: students & researchers
- Registration period: before 12 August 2021
- Price: €500
(employees of academical institutions: €50 and of partner institutions: €0)