Détails du cours OROC-OP-OC

Optimal control of ordinary differential equations

Cette page est essentiellement destinée aux enseignants et regroupe toutes les informations nécessaires à la gestion d'un cours ENSTA.

Identité du cours

Sigle : OROC-OP-OC
Titre français : Optimal control of ordinary differential equations
Titre anglais : Optimal control of ordinary differential equations
Méta infos : modifiée le : 06/06/2016   par : pcarpent   Nb de visiteurs : 545   annee : 3A      periode : 1      Rattachement/module : A      ECTS : 1.5      type : unknown     
ouvert : Oui     modif. autorisée : Oui     email auto. au responsable : Oui     à évaluer : Oui     en ligne : Non    
domaine ParisTech : 1,1b    

Equipe pédagogique

Responsable (login) :
Professeur principal :
Professeurs participants : Hasnaa ZIDANI,    Joseph-Frédéric BONNANS,   
Maitres de conférences :

Contenu

Objectifs :

Joint course between ENSTA and M2 Optimization (Paris-Saclay University)

The course will be given in English

Current technologies are increasingly looking for new methods to process complex systems consisting of a large number of parameters related to each other by a well-defined structure. One particular aspect aims at reaching advanced performances (notion of productivity, cost, product quality ...) and optimale performances (go to the moon by consuming minimum fuel, energy management, etc.). The objective of this course is to present theoretical and numerical methods for solving some optimal control problems involving complex systems.

The lecture is accompanied by exercice sessions and numerical simulations during which students implement on a quite concrete case some numerical methods presented in the course

This course is also included in the cursus of the master Optimization of University Paris-Saclay:

  • the first 15 hours of the course and the Friday 14th October lecture correspond to the ENSTA course
  • The remaining 12 hours present further develpement for the Master course
  • the joint exam will take place during the last session (to be fixed).

ENSTA students not enrolled in a double Master program are strongly encouraged to follow the entire course (ENSTA part + M2 part).

Mots clés : Optimal control - Pontryagin Maximum Principle - Shooting method
Objectives :

Joint course between ENSTA and M2 Optimization (Paris-Saclay University)

The course will be given in English

Current technologies are increasingly looking for new methods to process complex systems consisting of a large number of parameters related to each other by a well-defined structure. One particular aspect aims at reaching advanced performances (notion of productivity, cost, product quality ...) and optimale performances (go to the moon by consuming minimum fuel, energy management, etc.). The objective of this course is to present theoretical and numerical methods for solving some optimal control problems involving complex systems.

The lecture is accompanied by exercice sessions and numerical simulations during which students implement on a quite concrete case some numerical methods presented in the course

This course is also included in the cursus of the master Optimization of University Paris-Saclay:

  • the first 15 hours of the course and the Friday 14th October lecture correspond to the ENSTA course
  • The remaining 12 hours present further develpement for the Master course
  • the joint exam will take place during the last session (to be fixed).

ENSTA students not enrolled in a double Master program are strongly encouraged to follow the entire course (ENSTA part + M2 part).

Keywords : Optimal control - Pontryagin Maximum Principle - Shooting method
Supports : polycopié ENSTA fourni aux élèves
Biblio :
Contrôle :

Besoins particuliers et remarques éventuelles

Moyens :
Commentaires :

Séances

mer. 21 sept. 2016   - 16:00 à 18:00 : Bloc de Module (1/2 journée) (MOD)
programme : Prog1: Introduction - Examples, differential calculus in functional spaces
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
ven. 23 sept. 2016   - 09:00 à 12:15 : Bloc de Module (1/2 journée) (MOD)
programme : Prog1: Pontryagin's principle (PMP)
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
mer. 28 sept. 2016   - 16:00 à 18:00 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 1: Applications of the PMP
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
ven. 30 sept. 2016   - 09:00 à 12:15 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 1: Minimal time function, optimal synthesis
besoin : Vidéo,
Intervenants : Hasnaa ZIDANI,
mer. 05 oct. 2016   - 16:00 à 18:00 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 1: Shooting methods
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
ven. 07 oct. 2016   - 09:00 à 12:15 : TD en salle info (TD)
programme : Prog 1: Shooting method (numerical simulations)
besoin : Vidéo,
Intervenants : Hasnaa ZIDANI,
mer. 12 oct. 2016   - 16:00 à 18:00 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 2: State constraints (PMP) - Beginning of the Master part of the course
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
ven. 14 oct. 2016   - 09:00 à 12:15 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 1: Set of controlled trajectories: Compacity and other regularity properties - End of the ENSTA part of the course
besoin : Vidéo,
Intervenants : Hasnaa ZIDANI,
mer. 19 oct. 2016   - 16:00 à 18:00 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 2: State constraints and shooting
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
ven. 21 oct. 2016   - 09:00 à 12:15 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 2: HJB approach HJB for optimal control. Value function, dynamic principle
besoin : Vidéo,
Intervenants : Hasnaa ZIDANI,
mer. 02 nov. 2016   - 16:00 à 18:00 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 2: Singular arcs
besoin : Vidéo,
Intervenants : Joseph-Frédéric BONNANS,
ven. 04 nov. 2016   - 09:00 à 12:15 : Bloc de Module (1/2 journée) (MOD)
programme : Prog 2: HJB equations, verification theorem
besoin : Vidéo,
Intervenants : Hasnaa ZIDANI,
mer. 16 nov. 2016   - 14:00 à 17:00 : Contrôle (CC)
programme : Exam
besoin :
Intervenants : Hasnaa ZIDANI, Joseph-Frédéric BONNANS,