学习辨识:最小二乘算法及其重复一致性

孙明轩; 毕宏博

doi:10.3724/SP.J.1004.2012.00698

学习辨识:最小二乘算法及其重复一致性

doi: 10.3724/SP.J.1004.2012.00698

1.
浙江工业大学信息工程学院杭州 310023

详细信息

通讯作者:
孙明轩, 浙江工业大学信息工程学院教授. 主要研究方向为学习辨识与控制.

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- 被引次数: 0
出版历程
- 收稿日期: 2011-08-26
- 修回日期: 2011-12-19
- 刊出日期: 2012-05-20

Learning Identification: Least Squares Algorithms and Their Repetitive Consistency

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023

摘要

摘要: 针对重复时变系统, 提出学习辨识方法用于估计系统的时变参数. 讨论了有限时间作业区间上重复运行的时变系统以及周期时变系统两种情形. 文中给出最小二乘学习算法的推导过程, 并分析了所提算法的收敛性. 结果表明, 当重复持续激励条件成立时, 提出的学习算法具有重复一致性, 能够给出时变参数的完全估计. 通过数值算例进一步验证了学习算法的有效性.
- 学习辨识 /
- 最小二乘法 /
- 随机时变系统 /
- 重复一致性
Abstract: This paper presents a learning identification method for stochastic systems with time-varying parametric uncertainties. The systems undertaken perform tasks repetitively over a pre-specified finite-time interval, and a least squares learning algorithm is derived on the basis of the repetitive operations. The learning identification method applies to periodically time-varying systems. It is shown that the estimates converge to the time-varying values of the parameters, and the complete estimation can be achieved under repetitive persistent excitation condition, a sufficient condition for establishing repetitive consistency of the learning algorithms. Numerical results are presented to demonstrate the effectiveness of the proposed learning algorithms.
- Learning identification /
- least squares /
- stochastic time-varying systems /
- repetitive consistency

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参考文献(1)

[1]

Richards J A. Analysis of Periodically Time-Varying Systems. New York: Springer-Verlag, 1983[2] Tsakalis K S, Ioannou P A. Linear Time-Varying Systems: Control and Adaptation. Upper Saddle River, NJ: Prentice- Hall, 1993[3] Goodwin G C, Sin K S. Adaptive Filtering, Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984[4] Chen H F, Guo L. Identification and Stochastic Adaptive Control. Boston, MA: Birkhuser, 1991[5] Guo Lei. Time-Varying Stochastic Systems: Stability, Estimation and Control. Changchun: Jilin Science and Technology Press, 1993 (郭雷. 随机时变系统: 稳定性、估计与控制. 长春: 吉林科学技术出版社, 1993)[6] Sternby J. On consistency for the method of least squares using martingale theory. IEEE Transactions on Automatic Control, 1977, 22(3): 346-352[7] Moore J B. On strong consistency of least squares identification algorithms. Automatica, 1978, 14(5): 505-509[8] Solo V. The convergence of AML. IEEE Transactions on Automatic Control, 1979, 24(6): 958-962[9] Lai T, Wei C Z. Extended least squares and their applications to adaptive control and prediction in linear systems. IEEE Transactions on Automatic Control, 1986, 31(10): 898-906[10] Ding F, Shi Y, Chen T W. Performance analysis of estimation algorithms of nonstationary ARMA processes. IEEE Transactions on Signal Processing, 2006, 54(3): 1041-1053[11] Mareels I, Polderman J W. Adaptive Systems: an Introduction. Boston, MA: Birkhuser, 1996[12] Niedzwiecki M. Identification of Time-Varying Processes. New York: John Wiley and Sons, 2000[13] Arimoto S. Control Theory of Non-Linear Mechanical Systems: a Passivity-Based and Circuit-Theoretic Approach. Oxford UK: Oxford University Press, 1996[14] Sun Ming-Xuan, Huang Bao-Jian. Iterative Learning Control. Beijing: National Defence Industry Press, 1999 (孙明轩, 黄宝健. 迭代学习控制. 北京: 国防工业出版社, 1999)[15] Sun M X, He X X. Iterative learning identification and control of discrete time-varying systems. In: Proceedings of the 26th Chinese Control Conference. Zhangjiajie, China: IEEE, 2007. 520-524[16] Sun M X. Iterative learning neurocomputing. In: Proceedings of the 2009 International Conference on Wireless Networks and Information Systems. Shanghai, China: IEEE, 2009. 158-161[17] Wu P J, Sun M X. Two iterative learning identification algorithms for discrete time-varying systems. In: Proceedings of the 27th Chinese Control Conference. Kunming, China: IEEE, 2008. 91-95[18] Yan W L, Sun M X. Identification of discrete-time varying nonlinear systems using time-varying neural networks. In: Proceedings of the 8th World Congress on Intelligent Control and Automation. Ji'nan, China: IEEE, 2010. 301-306[19] Hua G F, Sun M X. Learning identification and control of a class of discrete periodic systems. In: Proceedings of the 4th IEEE International Conference on Industrial Electronics and Applications. Xi'an, China: IEEE, 2009. 6-11

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