Lyapunov-based unified control method for closed quantum systems

摘要

A Lyapunov-based unified control method for closed quantum systems is proposed in this paper for the state transfers from an arbitrary initial state to a desired target state. Especially, the proposed control method can be used in the cases that the free Hamiltonian of the system is not strongly regular, and (or) the control Hamiltonian is not fully connected. Three types of control laws are proposed simultaneously based on the implicit Lyapunov control theory, in which two implicit functions and one Lyapunov function with virtual mechanical quantity are well-designed. The largest invariant set of the quantum control system is investigated, and the convergence of the control system designed is proved. A numerical simulation is implemented in detail to instruct the design procedure and demonstrate the effectiveness of the control method proposed. (C) 2020 Published by Elsevier Ltd on behalf of The Franklin Institute.