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以随时间变化的二次函数为目标函数,对采用薛定谔方程的量子系统进行轨迹跟踪研究.根据Lyapunov稳定性定理,选择误差的平方作为Lyapunov函数设计控制律,实现系统从任意初始状态到目标函数的跟踪.在Matlab环境下对不同初始状态进行了系统仿真及性能对比研究,分析了系统初始值以及控制中观测量对跟踪性能的影响,验证了控制律在跟踪目标函数上的优越性.
Taking the quadratic function changing with time as the objective function, the trajectory tracking of the quantum system based on Schrödinger equation is studied.According to the Lyapunov stability theorem, the square of the error is selected as the Lyapunov function to design the control law, and the system is transformed from any initial state to the objective function The system simulation and performance comparison of different initial states are carried out under the Matlab environment, the influence of the system initial value and the observed quantity on the tracking performance in the control is analyzed, and the superiority of the control law in tracking the objective function is verified.