Studying controllability of infinite-dimensional non-linear systems by Lie algebraic methods

Institut de mathématiques de Bourgogne, salle Baire, jeudi 9 juin à 16:30

Geometric control theory studies the properties of non-linear control systems in terms of the Lie algebra generated by the vector fields which constitute the system. Over the last decade there was a number of attempts to generalize Lie algebraic methods in order to study controllability properties for different classes of infinite-dimensional non-linear control systems. We survey some results, achieved for Euler and Navier-Stokes equations of fluid dynamics and for the cubic Schrödinger equation, controlled by a finite-dimensional control, and detail some recent results on the controllability of continual ensembles of nonlinear systems.