Paolo Mason

Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field

In this paper we consider the minimum time population transfer problem for the z component of the spin of a (spin 1/2) particle, driven by a magnetic field, that is constant along the z axis and controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e., after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on two-dimensional (2-D) manifolds. Let (−E,E) be the two energy levels, and ∣Ω(t)∣≤M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level −E, and we provide the explicit expression of the time optimal trajectories, steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M∕E≪1, every time optimal trajectory is bang-bang and, in particular, the corresponding control is periodic with frequency of the order of the resonance frequency ωR=2E. On the other side, for M∕E>1, the time optimal ...

Controllability of the discrete-spectrum Schrödinger equation driven by an external field

We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials.

Common Polynomial Lyapunov Functions for Linear Switched Systems

In this paper, we consider linear switched systems

A note on stability conditions for planar switched systems

\dot x(t)=A_{u(t)} x(t)

Time Optimal Swing-Up of the Planar Pendulum

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Generic Controllability Properties for the Bilinear Schrödinger Equation

x\in\R^n

On the marginal instability of linear switched systems

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Adiabatic Control of the Schrödinger Equation via Conical Intersections of the Eigenvalues

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Optimal Control Models of Goal-oriented Human Locomotion

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On stability analysis of linear discrete-time switched systems using quadratic Lyapunov functions

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