Abstract
In this paper, a weighted least square support vector machine algorithm for identification is proposed based on the T-S model. The method adopts fuzzy c-means clustering to identify the structure. Based on clustering, the original input/output space is divided into several subspaces and submodels are identified by least square support vector machine (LS-SVM). Then, a regression model is constructed by combining these submodels with a weighted mechanism. Furthermore we adopt the method to identify a class of inverse systems with immeasurable state variables. In the process of identification, an allied inverse system is constructed to obtain enough information for modeling. Simulation experiments show that the proposed method can identify the nonlinear allied inverse system effectively and provides satisfactory accuracy and good generalization.
Similar content being viewed by others
References
Singh S N. Functional reproducibility in nonlinear systems using dynamic compensation. IEEE Trans Automat Contr, 1984, 29(4): 446–450
Hirschorn R M. Invertibility of multivariable nonlinear control systems. IEEE Trans Automat Contr, 1979, 24(8): 855–865
Dai X Z, Liu J, Feng C, et al. Neural network á-th order inverse system method for the control of nonlinear continuous systems. IEE Proc-Control Theor Appl, 1998, 145: 519–523
Dai X Z. Inverse Control Method Based on Neural Networks for Multi-variables Nonlinear System (in Chinese). Beijing: Science Press, 2005. 18–67
Suykens J A K. Nonlinear modelling and support vector machines. In: Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference. Budapest, Hungary: IEEE Press, 2001. 287–294
Vapnik V. An overview of statistical learning theory. IEEE Trans Neural Netw, 1999, 10: 955–999
Suykens J A K, Vandewalle J. Least squares support vector machine classifiers. Neural Proc Lett, 1999, 9: 293–300
Chua K. S. Efficient computations for large least square support vector machine classifiers. Patt Recog Lett, 2003, 24: 75–80
Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern, 1985, 15(1): 116–132
Sun C Y, Mu C X, Liang H. Inverse system identification of nonlinear systems using LSSVM. In: Sun F C, Zhang Y T, Cao J D, et al, eds. Advances in Neural Networks-ISNN2008, LNCS 5263. Berlin: Springer-Verlag, 2008. 682–690
Shawe-Taylor J, Cristianini N. Kernel methods for pattern analysis. England: Cambridge University Press, 2004. 200–240
Rong H N, Zhang G X, Jin W D. Selection of kernel functions and parameters for support vector machines in system identification (in Chinese). J System Simulation, 2006, 18(11): 3204–3208
Sun C Y, Liang H, Li L F, et al. Clustering with a weighted sum validity function using a niching PSO algorithm. In: Proceedings of the 2007 IEEE International Conference on Networking, Sensing and Control. London: IEEE Press, 2007. 368–373
Chuang C C. Fuzzy weighted support vector regression with a fuzzy partition. IEEE Trans Syst Man Cybern B Cybern, 2007, 37(3): 630–640
Dai X Z, Wang W C, Ding Y H, et al. “Assumed inherent sensor” inversion based ANN dynamic soft-sensing method and its application in erythromycin fermentation process. Comput Chem Eng, 2006, 30: 1203–1225
Dai X Z, He D, Zhang T, et al. ANN generalized inversion for the linearization and decoupling control of nonlinear systems. IEE Proc-Control Theor Appl, 2003, 150(3): 267–277
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (Grant No. 60874013) and the Doctoral Project of the Ministry of Education of China (Grant No. 20070286001)
Rights and permissions
About this article
Cite this article
Sun, C., Mu, C. & Li, X. A weighted LS-SVM approach for the identification of a class of nonlinear inverse systems. Sci. China Ser. F-Inf. Sci. 52, 770–779 (2009). https://doi.org/10.1007/s11432-009-0097-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-009-0097-6