'Stabilization methods for nonlinear dynamical systems with partial measurements and constrained inputs'

Directeur de thèse :     Christophe PRIEUR

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (EEATS)

Spécialité : Automatique et productique

Structure de rattachement : CNRS

Établissement d'origine : ENS Cachan

Financement(s) : Contrat doctoral ; contrat à durée déterminée

Date d'entrée en thèse : 01/09/2014

Date de soutenance : 20/09/2017

Composition du jury :
Sophie TARBOURIECH, Rapporteur Directeur de recherche, LAAS-CNRS
Fabian WIRTH, Rapporteur Professeur, Université de Passau
Yacine CHITOUR, Examinateur Professeur, Université Paris-Sud
Jean-Michel CORON, Examinateur Professeur, Université Pierre et Marie Curie
Emmanuelle CRÉPEAU, Examinateur Maître de conférences, Université de Versailles
Christophe PRIEUR, Directeur de thèse Directeur de recherche, GIPSA-lab CNRS
Vincent ANDRIEU, Co-directeur de thèse Chargé de recherche, LAGEP CNRS
Eduardo CERPA, Invité Professeur associé, Universidad Técnica Federico Santa María

Résumé : This thesis provides contributions on stabilization methods for nonlinear dynamical systems. In particular, it focuses on two main subjects: the analysis of infinite-dimensional systems subject to saturated inputs and the design of output feedback laws for either infinite-dimensional or finite-dimensional systems. The presentation will focus on the first subject. In the first part, we will introduce a more general class of saturations than the one already known for finite-dimensional systems. When bounding a linear stabilizing feedback law with such nonlinearity, a well-posedness result together with an attractivity result will be stated for systems whose open-loop is defined by operators generating strongly continuous semigroup of contractions. The attractivity result will be proved by using the LaSalle's Invariance Principle together with some compactness properties. In the second part, a particular nonlinear partial differential equation is studied, namely the Korteweg-de Vries equation, which models long waves in water of relatively shallow depth. A control actuating on a small part of the channel will be considered. This control will be modified with two different types of saturations. The attractivity result will be proved by using Lyapunov argument and a contradiction argument. Finally, the results will be illustrated with some numerical simulations.