Tracking control of single spin-1/2 quantum ensembles

This paper is concerned with the tracking control problem for the closed single spin-1/2 quantum ensembles. Based on the Liouville-von Neumann equation, mathematical model of dynamics for single spin-1/2 quantum ensembles are formulated as a bilinear form with states evolving on Bloch sphere. An associated matrix Lie group equation describing transfers from the initial state being an identity matrix is naturally introduced. The tracking problem for the system in question is transformed to a stabilization problem such that the control techniques are able to be used. In order to deal with the tracking problem, the Lyapunov-based feedback design method is employed to obtain the control such that the dynamics of system can converge to the reference trajectory.