This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors. In this paper, the specific control laws under the three forms are given. Stability is analyzed by the LaSalle invariance principle and the numerical simulation is carried out in a 2D test system. The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm. Finally, a unified form of the control laws under the three forms is given.

中文翻译：

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基于三种形式李亚普诺夫函数的量子控制

介绍了基于状态距离、虚数均值和状态误差的李亚普诺夫函数的量子控制。本文给出了三种形式下的具体控制规律。采用拉萨尔不变原理进行稳定性分析，并在二维测试系统中进行数值模拟。 Lyapunov函数的计算过程基于虚拟力学量的平均值、粒子群算法和模拟退火算法的组合。最后给出了三种形式下控制律的统一形式。