A Lyapunov-based Shaking Function for a Class of Non-bilinear Quantum Systems
A Lyapunov-based Shaking Function for a Class of Non-bilinear Quantum Systems
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DOI：
10.23919/acc53348.2022.9867736
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Jieqiu Shao;M. Nicotra
中科院分区：
文献类型：
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作者：
Jieqiu Shao;M. Nicotra
本文介绍了一种基于李雅普诺夫反馈定律的量子系统，通过移动光束的相位控制。我们的目标是驱动系统的标称哈密顿量的目标本征态（即相位等于零），通过设计一个振动函数，使得希尔伯特-施密特距离单调递减。在确定的控制律，最大化的下降率，两种可能的调整策略，提出了解决有界输入的要求。所提出的控制器的收敛性示出使用Krasovskiii-LaSalle原则下通常发现的双线性量子系统的相同条件。数值模拟表明了所提出的振动函数的有效性。
This paper introduces a Lyapunov-based feedback law for quantum systems that are controlled by shifting the phase of an optical beam. The objective is to drive the system to a target eigenstate of the nominal Hamiltonian (i.e. phase equal zero) by designing a shaking function such that the Hilbert-Schmidt distance is monotonically decreasing. After identifying the control law that maximises the descent rate, two possible tuning strategies are proposed to address bounded input requirements. Convergence of the proposed controller is shown using the Krasovskii-LaSalle principle under the same conditions commonly found for bilinear quantum systems. Numerical simulations showcase the effectiveness of the proposed shaking function.