Etude unidimensionnelle des approximations de l’opérateur de Koopman

Abstract

Recent years have witnessed an increasing attention to the Koopman operator approach in nonlinear control theory. A key idea is to dispense with the traditional trajectory-oriented system description and adopt a global functional description turning nonlinear systems into linear (but infinite-dimensional) ones. This approach therefore allows to apply linearalgebraic methods to nonlinear control in a systematic way. Moreover, it lends itself to data-driven techniques that are anticipated in nonlinear control theory. However, the recently proposed control methods relying on the Koopman operator formalism are inherently vitiated by unknown finite-dimensional approximation errors and are usually not supported by any rigorous validation. This thesis aim to obtain bounds on the error of the finite dimensional approximation of the Koopman operator.

Date of Award	21 Jun 2021
Original language	French
Awarding Institution	University of Namur
Supervisor	Alexandre Mauroy (Supervisor)