Control, Optimisation, Calculus of Variations

Course coordinator : E. Trélat

The Control, Optimisation, Calculus of Variations (COCV) course is one of five courses offered by the Mathematical Modeling programme in the second year of the MA in Applied Mathematics.

Presentation slides

This course offers high-level training in the field of Control, Optimization and Calculus of Variations. Control theory analyses properties of controlled systems, i.e. dynamic systems which can be acted upon by means of a control (or command). The aim is to transform the system from an initial state to a particular end-state, respecting, if applicable, certain criteria. Numerous systems are addressed: differential, discrete, noise or delayed systems and partial differential equations. The systems' origins are very diverse: mechanics, electricity, electronics, biology, chemistry, economics, game theory, IT, etc. The aim might be to stabilize the system to make it resistant to certain disruptions or perhaps to determine optimal solutions for a particular optimization criterion (optimal control). Optimization theory generalizes the mathematical calculus theory of variations.

Job prospects are in academia as well as industry. Students of this course can pursue both academic theses or theses in industry (e.g. CIFRE thesis, a partnership between industry and university), and can lead to engineering jobs in specialised fields such as aeronautics or aerospace. In performance-driven modern industries where the aim is to design, build and optimise, or at least improve existing methods. As a consequence there are many other industrial opportunities: Thalès' R&D department, IFPEN, EDF, Dassault, RTE, Airbus and others. This course also attracts considerable interest from other organizations such as the French Alternative Energies and Atomic Energy Commission (CEA) or the National Institute of Agricultural Research (INRA). Finally, there are a number of partnerships with a great many universities in France and abroad, ensuring a wide choice of potential academic theses.

This Master and the MASEF Master ("Mathématiques de la Finance, de l'Economie et de l'Assurance") from Paris Dauphine University have established a convention which allows students from both universities to follow common courses. Theses courses are labelled "MASEF" in the following list.

Course title Lecturer(s) Type Course Code
Control in Finite and Infinite Dimension Emmanuel Trélat Fundamental MU5MAM53
Structured equations in biology Benoit Perthame Fundamental MU5MAM70
Introduction to evolution PDE Katharina Schratz Fundamental MU5MAM12
Elliptic equations Antoine Gloria Fundamental MU5MAM47
Continuous optimisation Antonin Chambolle Fundamental MU5MAM02
Méthodes du premier ordre pour l'optimisation non convexe et non lisse Pauline Tan Fondamental MU5MAM71
Game theory and applications in finance and economics (Master MASEF Dauphine) Miquel Oliu Barton Fundamental MU5MAM17
Approximation et traitement de données en grande dimension Albert Cohen Specialised MU5MAM73
Geometric control theory Mario Sigalotti & Ugo Boscain Specialised MU5MAM80
Fonctionnement des réseaux de neurones: analyse mathématique Delphine Salort Specialised MU5MAM74
Optimisation de formes: aspects géométriques et topologiques Samuel Amstutz Specialised MU5MAM78
Optimal Control of Partial Differential Equations Frédéric Bonnans Specialised MU5MAM77
Tropical algebraic geometry in optimisation and games Stéphane Gaubert Specialised MU5MAM58
Mean field games (Master MASEF Dauphine) Pierre Cardaliaguet Specialised MU5MAM85
Problèmes variationnels et de transport en économie (Master MASEF Dauphine) Guillaume Carlier Specialised
Réseaux de neurones et approximation numérique adaptative Bruno Després Specialised MU5MAM86