|
|
脉冲控制场下量子系统时变目标函数的有限时间跟踪控制
|
Abstract:
研究一类脉冲控制场作用下封闭量子系统的有限时间跟踪问题。其目的是使量子系统的状态进入有界时变目标函数的轨迹。根据Lyapunov稳定性定理，设计改进的脉冲跟踪控制律，使得误差动态系统在有限时间内收敛到0。而有限时间跟踪意味着最优的收敛时间和更好的抗干扰能力。数值仿真验证了控制律在系统轨迹跟踪上的优越性。
In this paper, a class of finite-time tracking issues for closed quantum systems under the action of impulsive control fields is addressed. The objective is to steer the state of quantum system into the trajectory of bounded time-variant target function. By using the Lyapunov stability theorem, modi-fied impulse tracking controllers are designed such that the error dynamical system convergence to zero in a finite time. While finite-time tracking means the optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.
| [1] | Smith, G. and Yard, J. (2008) Quantum Communication with Zero-Capacity Channels. Science, 321, 1812-1815.
https://doi.org/10.1126/science.1162242 |
| [2] | Knill, E. (2010) Quantum Computing. Nature, 463, 441-443. https://doi.org/10.1038/463441a |
| [3] | Bennett, C.H. and Di Vincenzo, D.P. (2000) Quantum Information and Computation. Nature, 404, 247-255.
https://doi.org/10.1038/35005001 |
| [4] | D’alessandro, D. and Dahleh, M. (2001) Optimal Control of Two-Level Quantum Systems. IEEE Transactions on Automatic Control, 46, 866-876. https://doi.org/10.1109/9.928587 |
| [5] | Zhu, W. and Rabitz, H. (2003) Quantum Control Design via Adaptive Tracking. The Journal of Chemical Physics, 119, 3619-3625. https://doi.org/10.1063/1.1582847 |
| [6] | Mirrahimi, M., Rouchon, P. and Turinici, G. (2005) Lyapunov Control of Bilinear Schr？dinger Equations. Automatica, 41, 1987-1994. https://doi.org/10.1016/j.automatica.2005.05.018 |
| [7] | Shuang, C. and Kuang, S. (2007) Quantum Control Strategy Based on State Distance. Acta Automatica Sinica, 33, 28-31.
https://doi.org/10.1360/aas-007-0028 |
| [8] | Sugawara, M. (2003) General Formulation of Locally Designed Coher-ent Control Theory for Quantum System. The Journal of Chemical Physics, 118, 6784-6800. https://doi.org/10.1063/1.1559680 |
| [9] | Kuang, S. and Cong, S. (2010) Population Control of Equilibrium States of Quantum Systems via Lyapunov Method. Acta Automatica Sinica, 36, 1257-1263. https://doi.org/10.3724/SP.J.1004.2010.01257 |
| [10] | Cong, S., Zhu, Y. and Liu, J. (2012) Dynamical Trajectory Tracking of Quantum Systems with Different Target Functions. Journal of Systems Science and Mathematical Sciences, 32, 719-730. |
| [11] | Liu, J., Cong, S. and Zhu, Y. (2012) Adaptive Trajectory Tracking of Quantum Systems. 12th Inter-national Conference on Control, Automation and Systems, Jeju, 17-21 October 2012, 322-327. |
| [12] | Cong, S. and Liu, J. (2014) Trajectory Tracking Theory of Quantum Systems. Journal of Systems Science and Complexity, 27, 679-693. https://doi.org/10.1007/s11424-014-2013-4 |
| [13] | Yang, X. and Cao, J. (2010) Finite-Time Stochastic Synchroniza-tion of Complex Networks. Applied Mathematical Modelling, 34, 3631-3641. https://doi.org/10.1016/j.apm.2010.03.012 |
