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.

提出了一种基于李雅普诺夫的封闭量子系统统一控制方法，用于将状态从任意初始状态转换为期望的目标状态。特别地，在系统的自由哈密顿量不是很强规则，并且（或）控制哈密顿量没有完全连通的情况下，可以使用所提出的控制方法。基于隐式Lyapunov控制理论，同时提出了三种控制律，其中设计了两个隐函数和一个具有虚拟机械量的Lyapunov函数。研究了量子控制系统的最大不变集，并证明了所设计控制系统的收敛性。详细地进行了数值模拟，以指导设计过程并证明所提出的控制方法的有效性。