Perturbation theory for quantum control with weak input

Perturbation theory, an important method in both classical control theory and quantum mechanics, is used to quantum control theory. Perturbation model of quantum control system with weak control input is introduced when the Hamiltonian of control system can be written into two parts: the free Hamiltonian of unperturbed system and the interaction Hamiltonian between the controlled system and its external control. As an example, the quantum control problem of oscillator control system with weak input is analyzed and its second-order approximate quantum control input is found by perturbation method.