CAJ | 학술논문

已有研究结果表明，在封闭量子系统中，当被控系统满足强正则条件以及内部哈密顿量所有不同于目标态的本征态和目标态直接连接时，能够根据基于状态偏差的李雅普诺夫控制方法设计控制律使控制系统渐近稳定，但当被控系统不满足强正则或至少有一个本征态不和目标态连接时，被称为退化情况，情况将变的复杂。首先提出基于状态偏差的隐李雅普诺夫控制方法来解决这两种退化情况的收敛控制问题，将目标态从本征态拓展到了任意纯态。并且，所提出的方法也可以被用于控制退化情况下的多控制哈密顿量子系统。其次，研究了基于状态偏差和状态距离的隐李雅普诺夫控制方法的关系。最后，通过进行控制系统的数值仿真实验来验证提出的控制方法的正确性和有效性，并对基于状态偏差和状态距离的隐李雅普诺夫控制方法的控制效果进行对比。
이유연구결과표명，재봉폐양자계통중，당피공계통만족강정칙조건이급내부합밀돈량소유불동우목표태적본정태화목표태직접련접시，능구근거기우상태편차적리아보낙부공제방법설계공제률사공제계통점근은정，단당피공계통불만족강정칙혹지소유일개본정태불화목표태련접시，피칭위퇴화정황，정황장변적복잡。수선제출기우상태편차적은리아보낙부공제방법래해결저량충퇴화정황적수렴공제문제，장목표태종본정태탁전도료임의순태。병차，소제출적방법야가이피용우공제퇴화정황하적다공제합밀돈양자계통。기차，연구료기우상태편차화상태거리적은리아보낙부공제방법적관계。최후，통과진행공제계통적수치방진실험래험증제출적공제방법적정학성화유효성，병대기우상태편차화상태거리적은리아보낙부공제방법적공제효과진행대비。
In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.