Control, Optimisation, Calculus of Variations

Course coordinator : E. Trélat

The Control, Optimisation, Calculus of Variations (COCV) course is one of the 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.

Course title Lecturer(s) Type Course Code
Control in Finite and Infinite Dimension Emmanuel Trélat Fundamental MU5MAM53
Structured equations in biology Delphine Salort Fundamental MU5MAM70
Introduction to evolution PDE Katharina Schratz Fundamental MU5MAM12
Elliptic equations Hoai-Minh Nguyen Fundamental MU5MAM47
Méthodes du premier ordre pour l'optimisation non convexe et non lisse Pauline Tan Fondamental MU5MAM71
Analyse théorique et numérique des équations hyperboliques Amaury Hayat, Alexandre Ern Fundamental MU5MAM41
Optimisation sous contraintes d’EDP Beniamin Bogosel Fundamental MU5MAM94
Geometric control theory Mario Sigalotti, Ugo Boscain Specialised MU5MAM80
Tropical algebraic geometry in optimisation and games Stéphane Gaubert Specialised MU5MAM58
Réseaux de neurones et approximation numérique adaptative Bruno Després Specialised MU5MAM91
Jeux à champ moyen Charles Bertucci Specialised MU5MAM88