Variable structure control of uncontrollable quantum systems

This paper formulates and solves a variable structure control problem for the state control of quantum systems. Following the concept of wavefunction controllability, we first present a specific quantum system which is wavefunction uncontrollable under the action of any one of two controllers with different fixed structures. However, we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers. An extension and the potential applications of the proposed control strategy are briefly discussed and the general steps of variable structure control design for this class of quantum systems are also presented. The variable structure control scheme provides an alternative quantum engineering approach for the manipulation of quantum systems.