| 引用本文: | 柳松,匡森.两能级量子系统的固定时间控制及鲁棒性[J].控制理论与应用,2022,39(2):393~400.[点击复制] |
| LIU Song,KUANG Sen.Fixed-time control and robustness of two-level quantum systems[J].Control Theory and Technology,2022,39(2):393~400.[点击复制] |
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| 两能级量子系统的固定时间控制及鲁棒性 |
| Fixed-time control and robustness of two-level quantum systems |
| 摘要点击 1457 全文点击 354 投稿时间：2021-03-21 修订日期：2021-05-12 |
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| DOI编号 10.7641/CTA.2021.10235 |
| 2022,39(2):393-400 |
| 中文关键词 两能级量子系统 固定时间控制 非光滑切换策略 鲁棒性 |
| 英文关键词 two-level quantum systems fixed-time control non-smooth switching strategy robustness |
| 基金项目 国家自然科学基金项目(61873251, 61773370)资助. |
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| 中文摘要 |
| 本文考虑刘维尔方程描述的两能级量子系统对于目标平衡态的固定时间控制问题. 首先通过相干矢量和
复数的指数形式对系统模型及控制目标进行等价变换, 并借助合适的Lyapunov函数设计一个含分数幂的连续非光
滑控制律, 然后利用固定时间稳定性定理给出了系统实现固定时间收敛的条件. 针对某些分数幂取值导致控制性能
较差的情况, 提出了两种非光滑切换策略. 此外, 论文也分析了实际量子系统中可能存在的多种不确定性对固定时
间控制的影响. 最后, 通过数值仿真实验验证了本文方案的有效性, 同时展示了非光滑控制比标准Lyapunov控制具
有更强的鲁棒性. |
| 英文摘要 |
| The problem of fixed-time control is considered for a target equilibrium state of two-level quantum systems
described by the Liouville equation. Equivalent transformations are performed on the system model and the control goal by
the coherence vector representation and the exponential forms of complex numbers. A continuous non-smooth control law
with a fractional power is designed by a candidate Lyapunov function and the fixed-time stability theorem is used to obtain
the conditions for the fixed-time convergence of quantum systems. For the case of bad control performance caused by some
values of the fractional power, two non-smooth switching control strategies are proposed. Besides, the effect of various
uncertainties that may exist in actual quantum systems on fixed-time control is also analyzed. Finally, the effectiveness of
the control scheme in this paper is verified by numerical simulation experiments. At the same time, it is demonstrated that
the fixed-time control has better robustness than the standard Lyapunov control. |