Hyperbolicity and curvature in dynamics and control

In this thesis, we will use some techniques developed in the frame of Optimal Control Theory and some tools of Hyperbolic Dynamics to investigate problems of Hamiltonian dynamics and infinite horizon optimal control. The intimate relation between Optimal Control Theory and Hamiltonian Dynamics became clear after the publication of Pontryagin Maximum Principle (PMP) in the 50s ([24]): this result in fact shows that the extremals of an optimal control problem have to be seeked among the solutions of a certain Hamiltonian system associated to the problem..

Controllability of the Schrödinger equation via adiabatic methods and conical intersections of the eigenvalues

Abstract — We present a constructive method to control the bilinear Schrödinger equation by means of two or three controlled external fields. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, with respect to variations of the controls, and if the latter are conical. We provide sharp estimates of the relation between the error and the controllability time. I