pr\u00e9sentent<\/p>\n\n\n\n
Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 l’Institut Polytechnique de Paris T\u00e9l\u00e9com SudParis en :<\/p>\n\n\n\n
le MERCREDI 8 JUILLET 2026 \u00e0 10h00<\/p>\n\n\n\n
\u00e0<\/p>\n\n\n\n
Amphith\u00e9\u00e2tre 2
T\u00e9l\u00e9com SudParis 19 Place Marguerite Perey, 91120 Palaiseau<\/p>\n\n\n\n
Membres du jury :<\/strong><\/p>\n\n\n\n M. Nel SAMAMA<\/strong>, Full professor, T\u00e9l\u00e9com SudParis, Institut Polytechnique de Paris, FRANCE – Directeur de these R\u00e9sum\u00e9 :<\/strong><\/p>\n\n\n\n Cette th\u00e8se porte sur le probl\u00e8me de l\u2019estimation du domaine d\u2019attraction (DoA) et de la synth\u00e8se d\u2019une loi de commande pour des syst\u00e8mes lin\u00e9aires \u00e0 param\u00e8tres variables (LPV) soumis \u00e0 des contraintes sur l\u2019\u00e9tat et l\u2019entr\u00e9e. Plus pr\u00e9cis\u00e9ment, les travaux abordent : i) Estimation du DoA : d\u00e9terminer l\u2019ensemble des conditions initiales \u00e0 partir desquelles les trajectoires du syst\u00e8me LPV convergent vers un point d\u2019\u00e9quilibre donn\u00e9 tout en respectant les contraintes ; ii) Synth\u00e8se de lois de commande : concevoir des contr\u00f4leurs stabilisants permettant d\u2019atteindre des performances prescrites tout en garantissant le respect des contraintes malgr\u00e9 les variations param\u00e9triques. Dans la premi\u00e8re partie, des conditions sous forme d\u2019in\u00e9galit\u00e9s matricielles lin\u00e9aires (LMI) sont \u00e9tablies afin de calculer des ensembles invariants ellipso\u00efdaux ainsi que des ensembles ellipso\u00efdaux d\u00e9pendant des param\u00e8tres pour des syst\u00e8mes LPV en boucle ferm\u00e9e sous retour d\u2019\u00e9tat \u00e0 gain programm\u00e9. Une contribution majeure r\u00e9side dans la d\u00e9rivation, pour la premi\u00e8re fois, de conditions LMI permettant le calcul d\u2019ellipso\u00efdes invariants par rapport aux param\u00e8tres pour des syst\u00e8mes LPV soumis \u00e0 des contraintes de saturation de l\u2019entr\u00e9e, fournissant ainsi des estimations constructives du DoA en pr\u00e9sence de saturation. La deuxi\u00e8me partie propose deux nouvelles approches de commande pr\u00e9dictive (MPC) pour les syst\u00e8mes LPV contraints : i) un algorithme MPC quasi min\u2013max bas\u00e9 sur une loi de commande par retour d\u2019\u00e9tat \u00e0 param\u00e9trisation non lin\u00e9aire ; ii) un cadre MPC sans double sommation bas\u00e9 sur une fonction de Lyapunov d\u00e9pendant des param\u00e8tres. Enfin, ce dernier cadre est \u00e9tendu pour int\u00e9grer un retour \u00e0 gain programm\u00e9 avec saturation, en tenant explicitement compte des limites des actionneurs afin d\u2019am\u00e9liorer les performances en boucle ferm\u00e9e. La troisi\u00e8me partie traite du probl\u00e8me de la fusion progressive de lois de commande \u00e0 faible et \u00e0 fort gain dans un cadre de gain scheduling. Une strat\u00e9gie syst\u00e9matique de fusion est d\u00e9velopp\u00e9e afin de garantir que la loi de commande r\u00e9sultante : i) est continue ; ii) pr\u00e9serve les performances locales autour du point d\u2019\u00e9quilibre ; iii) assure un large domaine d\u2019attraction. Globalement, cette th\u00e8se propose des outils unifi\u00e9s bas\u00e9s sur les LMI pour le calcul d\u2019ensembles invariants, la conception de MPC \u00e0 conservatisme r\u00e9duit, l\u2019int\u00e9gration du gain scheduling, ainsi que la commande optimale de syst\u00e8mes LPV contraints. This PhD focuses on the problem of estimating the domain of attraction (DoA) and designing a control law for linear parameter-varying (LPV) systems subject to input and state constraints. More specially, the research addresses: i) DoA estimation: determining the set of initial conditions from which the LPV system trajectories converge to a desired quilibrium point while satisfying constraints. ii) Control law design: synthesizing stabilizing controllers that achieve prescribed performance objectives and guarantee constraint satisfaction despite parameter variations. In the first part, linear matrix inequality (LMI) conditions are derived to compute ellipsoidal and parameter-dependent ellipsoidal invariant sets for closed-loop LPV systems under gain-scheduled feedback. A main contribution is the derivation, for the first time, of LMI conditions for computing parameter-invariant ellipsoids for LPV systems subject to saturated input constraints, providing constructive DoA estimates under saturation. The second part proposes two new Model Predictive Control (MPC) schemes for constrained LPV systems: i) a quasi\u2013min\u2013max MPC algorithm based on a nonlinearly parameterized state-feedback control law; ii) a double-sum-free MPC framework based on a parameter-dependent Lyapunov function. Finally, the latter framework is extended to incorporate saturated gain-scheduling feedback, explicitly accounting for actuator saturation to improve the closed loop performance. The third part addresses the problem of smoothly merging low- and high-gain gain-scheduling controllers.. A systematic merging strategy is developed to guarantee that the resulting control law: i) is continuous; ii) preserves local performance around the equilibrium point; iii) achieves a large domain of attraction. Overall, the thesis provides unified LMI-based tools for invariant-set computation, reduced conservatism MPC design, gain-scheduling integration, and optimal control design for constrained LPV systems.<\/p>\n","protected":false},"excerpt":{"rendered":" L’Ecole doctorale : Ecole Doctorale de l’Institut Polytechnique de Paris et le Laboratoire de recherche SAMOVAR – Services r\u00e9partis, Architectures, Mod\u00e9lisation, Validation, Administration des R\u00e9seaux pr\u00e9sentent l\u2019AVIS DE SOUTENANCE de Monsieur Jin YAN Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 l’Institut Polytechnique de Paris 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M. Pedro RODRIGUEZ-AYERBE<\/strong>, Full professor, CentraleSup\u00e9lec, FRANCE – Rapporteur
Mme Isabelle QUEINNEC<\/strong>, Directrice de recherche, LAAS-CNRS, FRANCE – Rapporteure
M. Romain BOURDAIS<\/strong>, Full professor, CentraleSup\u00e9lec, FRANCE – Examinateur
M. Anh-Tu NGUYEN<\/strong>, Associate Professor, INSA Hauts-de-France, Universit\u00e9 Polytechnique Hauts-de-France, FRANCE – Examinateur
M. Hoai-nam NGUYEN<\/strong>, Associate Professor, T\u00e9l\u00e9com SudParis, Institut Polytechnique de Paris, FRANCE – Co-encadrant de these<\/p>\n\n\n\n\u00ab Commande sous contrainte des syst\u00e8mes lin\u00e9aires \u00e0 param\u00e8tres variables \u00bb<\/h2>\n\n\n\n
pr\u00e9sent\u00e9 par Monsieur Jin YAN<\/h2>\n\n\n\n
Abstract :<\/strong><\/p>\n\n\n\n