基于数值迭代的两能级封闭量子系统最优控制  

The optimal control of two-level closed quantum system based on numerical iteration

作　　者：谢国[1,2] 田冰[1,3] 刘丁[1,2] 

机构地区：[1]西安理工大学自动化与信息工程学院,陕西西安710048 [2]陕西省复杂系统控制与智能信息处理重点实验室,陕西西安710048 [3]中铁第一勘察设计院集团有限公司通号处,陕西西安710043

出　　处：《西安理工大学学报》2016年第1期7-11,共5页Journal of Xi'an University of Technology

基　　金：中国博士后科学基金面上资助项目(2014M552471);陕西省创新团队资助项目(2013KCT-04)

摘　　要：期望的性能指标是实施系统控制的基准。针对现有的量子控制主要集中在基于末态精度最优、时间最优、或者能量最小等单一性能指标的控制,而缺乏对系统综合性能考虑的问题,本文在综合分析两能级封闭量子系统特性的基础上,提出了基于幺正演化和能量最优的复合性能指标,并通过对性能指标变分,得到了满足最优控制量的状态及其拉格朗日乘子的微分方程组。在此基础上,采用差分的方法,设计了基于数值迭代的最优控制量求解策略。最后,仿真分析了参数对控制结果的影响,验证了本文所提最优控制方法和迭代算法的有效性。The expected performance index is the foundation for all of control systems. The research on the control of quantum systems mainly focus on a unique object such as the precision of final state,the minimum of time or energy,which lacks a comprehensive consideration on the actual system. Based on the comprehensive analysis of the characteristic of the two-level closed quantum system,a comprehensive performance index leading to an optimal unitary evolution and energy is proposed in this paper. Then a group of differential equations of state and Lagrange multipliers which satisfies the optimality condition to the performance index is obtained based on the variation of performance index. Further,regarding the group of differential equations,a strategy for the solution of optimal control is designed based on numerical iteration with finite difference methods. Lastly,the influence of parameters to the control results is analyzed based on numerical simulation,and the effectiveness of the optimal control method and the iteration algorithm suggested in this paper is tested.

关 键 词：两能级量子系统 最优控制 性能指标 数值迭代 

分 类 号：TP206.3[自动化与计算机技术—检测技术与自动化装置]