Modares Mechanical Engineering

Modares Mechanical Engineering

Hybrid adaptive intelligent controller design using quantum wavelet neural networks for trajectory tracking control in finite dimensional closed quantum systems

Authors
Zeinab Sahebi
Majid Yarahmadi
Department of Mathematics and Computer Science, Faculty of Science, Lorestan University, Khorramabad, Iran
Abstract
In this paper, a new hybrid adaptive intelligent controller is introduced to track a dynamic trajectory in finite dimensional closed quantum systems. The problem of inherent singularities in control signals of trajectory tracking in quantum systems leads to a sharp increase in control signal amplitude. As a result, the amplitude of the large signal increases the control cost and control system instability. Consequently, the large control signal amplitude increases the control cost and leads to instability in control system. Firstly, according to the Lyapunov stability theory, an adaptive controller is designed to track the dynamic path. Then, to overcome the singularity drawback, a quantum intelligent controller is designed based on a quantum adaptive wavelet neural network with batch back propagation learning and combined with adaptive controller by a singularity observer. The proposed hybrid adaptive intelligent controller by combining the adaptive and intelligent control signals adjusts the quantum state so that the desired dynamic trajectory is traced effectively and simultaneously eliminates the effects of singularities and reduces the control amplitude. The performance of the hybrid adaptive intelligent controller is checked for step response tracking in a population transfer of a four-level closed quantum system. The simulation results show that the introduced controller reduces the tracking error and significantly decreases the number of singular points. Also, the control cost is reduced by effective adjustment of the control signal’s amplitude.
Keywords
Quantum Adaptive Control
Quantum Wavelet Neural Network
Quantum Intelligent Control
Quantum Trajectory Tracking
Quantum Hybrid Controller
[1] S. Cong, F. Meng, A survey of quantum lyapunov control methods, The Scientific World Journal, Vol. 2013, pp. 1-14, 2013.
[2] F. Albertini, D. D'Alessandro, Time-optimal control of a two level quantum system via interaction with an auxiliary system, IEEE Transactions on Automatic Control, Vol. 59, No. 11, pp. 3026-3032, 2014.
[3] S. Chegini, M. Yarahmadi, Design of an adaptive sliding mode controller based on quantum neural network, Modares Mechanical Engineering, Vol. 17, No. 1, pp. 305-310, 2017. (in Persianفارسی)
[4] J. M. Coron, A. Grigoriu, C. Lefter, G. Turinici, Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling, New Journal of Physics, Vol. 11, No. 10, pp. 105034, 2009.
[5] J. Liu, S. Cong, Y. Zhu, Adaptive trajectory tracking of quantum systems, Proceeding of The 12th International Conference on Control, Automation and Systems, ICC, Jeju Island, Korea, October 17-21, 2012.
[6] M. Mirrahimi, G. Turinici, P. Rouchon, Reference trajectory tracking for locally designed coherent quantum controls, The Journal of Physical Chemistry A, Vol. 109, No. 11, pp. 2631-2637, 2005.
[7] L. M. Vandersypen, I. L. Chuang, NMR techniques for quantum control and computation, Reviews of Modern Physics, Vol. 76, No. 4, pp. 1037, 2005.
[8] A. Arjmandzadeh, M. Yarahmadi, Quantum genetic learning control of quantum ensembles with hamiltonian uncertainties, Entropy, Vol. 19, No. 8, pp. 1-12, 2017.
[9] H. Sedghee Rostami, B. Rezaie, Controlling state of quantum system using fuzzy controller, Modares Mechanical Engineering, Vol. 16, No. 9, pp. 124- 134, 2016. (in Persianفارسی)
[10] A. Borzì, G. Stadler, U. Hohenester, Optimal quantum control in nanostructures: Theory and application to a generic three-level system, Physical Review A, Vol. 66, No. 5, pp. 1-7, 2002.
[11] R. Mathew, C. E. Pryor, M. E. Flatté, K. C. Hall, Optimal quantum control for conditional rotation of exciton qubits in semiconductor quantum dots, Physical Review B, Vol. 84, No. 20, pp. 1-11, 2011.
[12] J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, M. Motzkus, Quantum control of energy flow in light harvesting, Nature, Vol. 417, No. 6888, pp. 533-535, 2002.
[13] M. Shapiro, P. Brumer, Principles of the quantum control of molecular processes, Principles of the Quantum Control of Molecular Processes, Moshe Shapiro, Paul Brumer, pp. 250. Wiley-VCH, 2003.
[14] D. Dong, I. R. Petersen, Quantum control theory and applications: a survey, IET Control Theory & Applications, Vol. 4, No. 12, pp. 2651-2671, 2010.
[15] J. Liu, S. Cong, Trajectory tracking of quantum states based on Lyapunov method, Proceeding of The 9th IEEE International Conference on Control and Automation (ICCA), Santiago, Chile, December 19-21, 2011.
[16] M. Mirrahimi, P. Rouchon, Trajectory tracking for quantum systems: A lyapounov approach, Proceedings of the International Symposium MTNS, pp. 1-6, 2004.
[17] S. Cong, J. Liu, Trajectory tracking theory of quantum systems, Journal of Systems Science and Complexity, Vol. 27, No. 4, pp. 679-693, 2014.
[18] W. Zhu, H. Rabitz, Quantum control design via adaptive tracking, Chemical Physics, Vol. 119, No. 7, pp. 3619-3625, 2003.
[19] S. Cong, Control of Quantum Systems: Theory and Methods, pp. 381-402 John Wiley & Sons, Singapore, 2014.
[20] W. Zhu, M. Smit, H. Rabitz, Managing singular behavior in the tracking control of quantum dynamical observables, Chemical Physics, Vol. 110, No. 4, pp. 1905-1915, 1999.
[21] S .Kak, On quantum neural computing, Information Sciences, Vol. 83, No. 3- 4, pp. 143-160, 1995.
[22] N. Matsui, N. Kouda, H. Nishimura, Neural network based on QBP and its performance, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, IEEE, pp. 247-252, 2000.
[23] L. Panchi, L. Shiyong, Learning algorithm and application of quantum BP neural networks based on universal quantum gates, Journal of Systems Engineering and Electronics, Vol. 19, No. 1, pp. 167-174, 2008.
[24] M. Khosravi, M. Zekri, A review of quantum neural networks, Soft Computing Journal, Vol. 1, No. 1, pp. 46-55, 2013. (in Persianفارسی)
[25] S. S. Mukherjee, R. Chowdhury, S. Bhattacharyya, Image restoration using a multilayered quantum backpropagation neural network, Proceeding of International Conference on Computational Intelligence and Communication Networks, IEEE, pp. 426-430, 2011.
[26] K. Takahashi, M .Kurokawa, M. Hashimoto, Controller application of a multi-layer quantum neural network trained by a conjugate gradient algorithm, Proceeding of 37th Annual Conference on IEEE industrial Electronics Society, IEEE, pp. 2353-2358, 2011.
[27] A. Sagheer, M. Zidan, Autonomous quantum perceptron neural network, arXiv preprint arXiv:1312.4149, 2013.
[28] H. Cao, F. Cao, D. Wang, Quantum artificial neural networks with applications, Information Sciences, Vol. 290, pp. 1-6, 2015.
[29] D. Mu, Z. Guan, H. Zhang, Learning algorithm and application of quantum neural networks with quantum weights, International Journal of Computer Theory and Engineering, Vol. 5, No. 5, pp. 788-792, 2013.
[30] A. J. da Silva, T. B. Ludermir, W. R. de Oliveira, Quantum perceptron over a field and neural network architecture selection in a quantum computer, Neural Networks, Vol. 76, pp. 55-64, 2016.
[31] R. Cheng, Y. Bai, A novel approach to fuzzy wavelet neural network modeling and optimization, International Journal of Electrical Power & Energy Systems, Vol. 64, pp. 671-678, 2015.
[32] J. E. Guillermo, L. J. R. Castellanos, E. N. Sanchez, A. Y. Alanis, Detection of heart murmurs based on radial wavelet neural network with Kalman learning, Neurocomputing, Vol. 164, pp. 307-317, 2015.
[33] H. Z. Hosseinabadi, B. Nazari, R. Amirfattahi, H. R. Mirdamadi, A. R. Sadri, Wavelet network approach for structural damage identification using guided ultrasonic waves, IEEE Transactions on Instrumentation and Measurement, Vol. 63, No. 7, pp. 1680-1692, 2014.
[34] F. Zhou, L. Wang, H. Lin, Z. Lv, High accuracy state-of-charge online estimation of EV/HEV lithium batteries based on Adaptive Wavelet Neural Network, Proceeding of 2013 IEEE ECCE Asia Downunder, IEEE, pp. 513- 517, 2013.
[35] K. Liu, L. Peng, Q. Yang, The algorithm and application of quantum wavelet neural networks, Proceeding of 2010 Chinese Control and Decision Conference (CCDC), IEEE, pp. 2941-2945, 2010.
[36] S. M. Taha, A. K. Nawar, A new quantum radial wavelet neural network model applied to analysis and classification of EEG signals, International Journal of Computer Applications, Vol. 85, No. 7, 2014.
[37] K. Takahashi, Y .Shiotani, M. Hashimoto, Remarks on model reference selftuning PID controller using quantum neural network with qubit neurons, Proceeding of 2013 International Conference of Soft Computing and Pattern Recognition (SoCPaR), IEEE, pp. 253-257, 2013.
[38] D. D'Alessandro, Introduction to Quantum Control and Dynamics, pp. 1-35, Chapman & Hall, London, 2007.
[39] C. Y. Liu, C. Chen, C. T. Chang, L. M. Shih, Single-hidden-layer feedforward quantum neural network based on Grover learning, Neural Networks, Vol. 45, No. Supplement C, pp. 144-150, 2013.
Modares Mechanical Engineering
Volume 18, Issue 2
April 2018
Pages 179-188