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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.2 P.275-284


Nonlinear decoupling controller design based on least squares support vector regression

Author(s):  Wen Xiang-jun, Zhang Yu-nong, Yan Wei-wu, Xu Xiao-ming

Affiliation(s):  Department of Automatic Control, Shanghai Jiao Tong University, Shanghai 200030, China; more

Corresponding email(s):   wenxiangjun@sjtu.edu.cn, ynzhang@ieee.org, yanwwsjtu@sjtu.edu.cn, xmxu@sjtu.edu.cn

Key Words:  Support Vector Machine (SVM), Decoupling control, Nonlinear system, Generalized inverse system

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Wen Xiang-jun, Zhang Yu-nong, Yan Wei-wu, Xu Xiao-ming. Nonlinear decoupling controller design based on least squares support vector regression[J]. Journal of Zhejiang University Science A, 2006, 7(2): 275-284.

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journal="Journal of Zhejiang University Science A",
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%T Nonlinear decoupling controller design based on least squares support vector regression
%A Wen Xiang-jun
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%A Xu Xiao-ming
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A0275

T1 - Nonlinear decoupling controller design based on least squares support vector regression
A1 - Wen Xiang-jun
A1 - Zhang Yu-nong
A1 - Yan Wei-wu
A1 - Xu Xiao-ming
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A0275

Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control of a general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is unknown or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.

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[1] Chen, F., Liu, C., 1994. Adaptively controlling nonlinear continuous-time systems using multiplayer neural networks. IEEE Transactions on Automatic Control, 39(6):1306-1310.

[2] Dai, X., Zhang, K., Zhang, T., Lu, X., 2004. ANN generalized inversion control of turbo generator governor. IEE Proceedings-Generation, Transmission and Distribution, 151(3):327-333.

[3] Descusse, J., Moog, C., 1985. Decoupling with dynamic compensation for strong invertible affine nonlinear systems. International Journal of Control, 42(6):1387-1398.

[4] Godbole, D.N., Sastry, S.S., 1995. Approximate decoupling and asymptotic tracking for MIMO systems. IEEE Transactions on Automatic Control, 40(3):441-450.

[5] He, D., Dai, X., Wang, Q., 2002. Generalized ANN inverse control method. Control Theory and Applications, 19(1):34-40 (in Chinese).

[6] Hirschorn, R.M., 1979. Invertibility of multivariable nonlinear control systems. IEEE Transactions on Automatic Control, 24(6):855-865.

[7] Kwok, J.T., 2000. The evidence framework applied to Support Vector Machines. IEEE Transaction on Neural Network, 11(5):1162-1173.

[8] Mackay, D.J.C., 1992. Bayesian interpolation. Neural Computing, 4:415-447.

[9] Mackay, D.J.C., 1997. Probable network and plausible predictions-A review of practical Bayesian methods for supervised neural networks. Network Computation in Neural Systems, 6:1222-1267.

[10] Mercer, J., 1909. Functions of positive and negative type and their connection with the theory of integral equations. Transactions of the London Philosophical Society A, 209:415-446.

[11] Nguyen, D.H., Widrow, B., 1990. Neural networks for self-learning control systems. IEEE Control Systems Magazine, 10(3):18-23.

[12] Nijmeijer, H., Schaft, A., 1990. Nonlinear Dynamical Control Systems. Springer-Verlag, New York.

[13] Suykens, J.A.K., 2001. Support vector machines: a nonlinear modelling and control perspective. European Journal of Control, 7(2-3):311-327.

[14] Suykens, J.A.K., Vandewalle, J., 2000. Recurrent least squares support vector machines. IEEE Transactions on Circuits and Systems, Part I, 47(7):1109-1114.

[15] Suykens, J.A.K., Vandewalle, J., de Moor, B., 2001. Optimal control by least squares Support Vector Machines. Neural Networks, 14(1):23-35.

[16] Suykens, J.A.K., Gestel, T., de Brabanter, J., de Moor, B., Vandewalle, J., 2002. Least Squares Support Vector Machines. World Scientific, Singapore.

[17] van Gestel, T., Suykens, J.A.K., Baestaens, D., Lambrechts, A., Lanckriet, G., Vandaele, B., de Moor, B., 2001. Financial time series prediction using least squares support vector machines within the evidence framework. IEEE Transaction on Neural Network, 12(4):809-821.

[18] van Gestel, T., Suykens, J.A.K, Lanckriet, G., Lambrechts, A., de Moor, B., Vandewalle, J., 2002. Bayesian framework for least squares Support Vector Machine classifiers, Gaussian processes and Kernel Fisher discriminant analysis. Neural Computation, 15(5):1115-1148.

[19] Vapnik, V., 1998. The Nature of Statistical Learning Theory. Springer-Verlag, New York.

[20] Walach, E., Widrow, B., 1983. Adaptive Signal Processing for Adaptive Control. IFAC workshop on Adaptive Systems in Control and Signal Processing, San Francisco, CA.

[21] Yan, W., Shao, H., Wang, X., 2004. Soft sensing modelling based on Support Vector Machine and Bayesian model selection. Computers and Chemical Engineering, 28:1489-1498.

[22] Zhang, Y., Wang, J., 2001. Recurrent neural networks for nonlinear output regulation. Automatica, 37:1161-1173.

[23] Zhang, Y., Wang, J., 2002. Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment. IEEE Transactions on Neural Networks, 13(3):633-644.

[24] Zhang, Y., Ge, S.S., 2003. A General Recurrent Neural Network Model for Time-varying Matrix Inversion. The IEEE 42nd IEEE Conference on Decision and Control, p.6169-6174.

[25] Zhang, Y., Jiang, D., Wang, J. 2002. A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Transactions on Neural Networks, 13(5):1053-1063.

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