理想条件下混合态量子系统的Lyapunov稳定化策略

Lyapunov stabilization strategy of mixed-state quantum systems with ideal conditions

在假定被控系统满足非退化、没有退化跃迁和完全连通的理想条件下,借助于带有附加自由度的Lyapunov函数研究了混合态量子系统的稳定化问题.基于LaSalle原理推导了闭环系统的最大不变集和任一初始态下的收敛状态集,给出了系统对最大不变集中任一平衡态渐近稳定化的自由度的构造原则.最后通过一个两能级系统的数值仿真,验证了所得理论结果的正确性.

Under the ideal conditions that the controlled systems are non-degenerate,transitionally non-degenerate,and fully connected,the stabilization problem of mixed-state quantum systems is studied by using a Lyapunov function with free degrees. Based on the LaSalle＇s principle,the largest invariant set of the closed-loop systems and the convergent state set associated with any initial state are deduced,and the construction principles of free degrees that ensure the system can be asymptotically stabilized in any equilibrium state contained in the largest invariant set are given. A numerical simulation experiment on a two-level system shows the rationality of the obtained theoretical results.