Trajectory generation for quantum systems based on lyapounov techniques

Abstract: The convergence of a Lyapounov based control of the Schrödinger equation (finite dimensional) is analyzed via Lasalle invariance principle. When the linear tangent approximation around the goal eigen-state is controllable, such a feedback ensures global asymptotic convergence. When this linear tangent system is not controllable, the stability of the closed-loop system is not asymptotic. To overcome such lack of convergence we propose a modification based on adiabatic invariance. Simulations illustrate the simplicity and also the interest of these Lyapounov based controls for trajectory generation. Such control methods can also be adapted to tracking