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Complex System Modelling and Control Through Intelligent Soft Computations pp 165–193Cite as

PWARX Model Identification Based on Clustering Approach

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 319))

Abstract

This chapter addresses the problem of clustering based procedure for the identification of PieceWise Auto-Regressive eXogenous (PWARX) models. In order to overcome the main drawbacks of the existing methods such as their sensitivity to poor initializations and the existence of outliers, we propose the use of the Chiu’s clustering algorithm and the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. A comparative study of the two proposed approaches with the k-means method is achieved in simulation. The results of experimental validation are also presented to illustrate the effectiveness of the proposed methods.

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References

  • Bako, L. (2011). Identification of switched linear systems via sparse optimization. Automatica, 47(4), 668–677.

    Article  MATH  MathSciNet  Google Scholar 

  • Bako, L., & Lecoeuche, S. (2013). A sparse optimization approach to state observer design for switched linear systems. Systems and Control Letters, 62(2), 143–151.

    Article  MATH  MathSciNet  Google Scholar 

  • Bemporad, A., Ferrari-Trecate, G., & Morari, M. (2000). Observability and controllability of piecewise affine and hybrid systems. IEEE Transactions on Automatic Control, 45(10), 1864–1876.

    Article  MATH  MathSciNet  Google Scholar 

  • Bemporad, A., Garulli, A., Paoletti, S., & Vicino, A. (2003). A greedy approach to identification of piecewise affine models. In Hybrid systems: Computation and control (pp. 97–112). New York: Springer.

    Google Scholar 

  • Bemporad, A., Garulli, A., Paoletti, S., & Vicino, A. (2005). A bounded-error approach to piecewise affine system identification. IEEE Transactions on Automatic Control, 50(10), 1567–1580.

    Article  MathSciNet  Google Scholar 

  • Boukharouba, K. (2011). Modélisation et classification de comportements dynamiques des systemes hybrides. Ph.D. thesis, Université de Lille, France.

    Google Scholar 

  • Chaitali, C. (2012). Optimizing clustering technique based on partitioning DBSCAN and ant clustering algorithm. International Journal of Engineering and Advanced Technology (IJEAT), 2(2), 212–215.

    Google Scholar 

  • Chiu, S. (1994). Fuzzy model identification based on cluster estimation. Journal of Intelligent and Fuzzy Systems, 2(3), 267–278.

    Google Scholar 

  • Chiu, S. (1997). Extracting fuzzy rules from data for function approximation and pattern classification. In D. Dubois, et al. (Eds.), Chapter 9 in fuzzy information engineering: A guided tour of applications. New York: Wiley.

    Google Scholar 

  • De Schutter, B., & De Moor, B. (1999). The extended linear complementarity problem and the modeling and analysis of hybrid systems. In Hybrid systems V (pp. 70–85). New York: Springer.

    Google Scholar 

  • De Schutter, B., & Van den Boom, T. (2000). On model predictive control for max-min-plus-scaling discrete event systems. Technical report, bds 00-04: Control Systems Engineering, Faculty of Information Technology and Systems, Delft University of Technology, The Netherlands.

    Google Scholar 

  • Doucet, A., Gordon, N., & Krishnamurthy, V. (2001). Particle filters for state estimation of jump markov linear systems. IEEE Transactions on Signal Processing, 49(3), 613–624.

    Article  Google Scholar 

  • Duda, R. O., Hart, P. E., & Stork, D. G. (2001). Pattern classification (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Ferrari-Trecate, G., Muselli, M., Liberati, D., & Morari, M. (2001). A clustering technique for the identification of piecewise affine systems. In Hybrid systems: Computation and control (pp. 218–231). New York: Springer.

    Google Scholar 

  • Ferrari-Trecate, G., Muselli, M., Liberati, D., & Morari, M. (2003). A clustering technique for the identification of piecewise affine systems. Automatica, 39(2), 205–217.

    Article  MATH  MathSciNet  Google Scholar 

  • Heemels, W. P., De Schutter, B., & Bemporad, A. (2001). Equivalence of hybrid dynamical models. Automatica, 37(7), 1085–1091.

    Article  MATH  Google Scholar 

  • Henson, M. A., & Seborg, D. E. (1994). Adaptive nonlinear control of a ph neutralization process. IEEE Transactions on Control Systems Technology, 2(3), 169–182.

    Article  Google Scholar 

  • Juloski, A., Weiland, S., & Heemels, W. (2005). A bayesian approach to identification of hybrid systems. IEEE Transactions on Automatic Control, 50(10), 1520–1533.

    Article  MathSciNet  Google Scholar 

  • Juloski, A. L., Paoletti, S., & Roll, J. (2006). Recent techniques for the identification of piecewise affine and hybrid systems. In Current trends in nonlinear systems and control (pp. 79–99). New York: Springer.

    Google Scholar 

  • Lai, C. Y. (2011). Identification and control of nonlinear systems using multiple models. Ph.D. thesis.

    Google Scholar 

  • Lai, C. Y., Xiang, C., & Lee, T. H. (2010). Identification and control of nonlinear systems via piecewise affine approximation. In The 49th IEEE Conference on Decision and Control (CDC) (pp. 6395–6402).

    Google Scholar 

  • Lassoued, Z., & Abderrahim, K. (2013a). A comparison study of some PWARX system identification methods. In The 17th IEEE International Conference in System Theory, Control and Computing (ICSTCC) (pp. 291–296).

    Google Scholar 

  • Lassoued, Z., & Abderrahim, K. (2013b). A Kohonen neural network based method for PWARX identification. In Adaptation and learning in control and signal processing, IFAC (Vol. 11, pp. 742–747).

    Google Scholar 

  • Lassoued, Z., & Abderrahim, K. (2013c). New approaches to identification of PWARX systems. Mathematical Problems in Engineering. http://dx.doi.org/10.1155/2013/845826.

  • Lassoued, Z., & Abderrahim, K. (2013d). A new clustering technique for the identification of PWARX hybrid models. In The 9th IEEE Asian Control Conference (ASCC) (pp. 1–6).

    Google Scholar 

  • Lassoued, Z., & Abderrahim, K. (2014a). An experimental validation of a novel clustering approach to PWARX identification. Engineering Applications of Artificial Intelligence, 28, 201–209.

    Article  Google Scholar 

  • Lassoued, Z., & Abderrahim, K. (2014b). New results on PWARX model identification based on clustering approach. International Journal of Automation and Computing, 11(2), 180–188.

    Article  Google Scholar 

  • Lin, J., & Unbehauen, R. (1992). Canonical piecewise-linear approximations. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 39(8), 697–699.

    Article  MATH  MathSciNet  Google Scholar 

  • Nakada, H., Takaba, K., & Katayama, T. (2005). Identification of piecewise affine systems based on statistical clustering technique. Automatica, 41(5), 905–913.

    Article  MATH  MathSciNet  Google Scholar 

  • Roll, J., Bemporad, A., & Ljung, L. (2004). Identification of piecewise affine systems via mixed-integer programming. Automatica, 40(1), 37–50.

    Article  MATH  MathSciNet  Google Scholar 

  • Salehi, S., Shahrokhi, M., & Nejati, A. (2009). Adaptive nonlinear control of ph neutralization processes using fuzzy approximators. Control Engineering Practice, 17(11), 1329–1337.

    Article  Google Scholar 

  • Sander, J., Ester, M., Kriegel, H.-P., & Xu, X. (1998). Density-based clustering in spatial databases: The algorithm gdbscan and its applications. Data Mining and Knowledge Discovery, 2(2), 169–194.

    Article  Google Scholar 

  • Talmoudi, S., Abderrahim, K., Abdennour, R. B., & Ksouri, M. (2008). Multimodel approach using neural networks for complex systems modeling and identification. Nonlinear Dynamics and Systems Theory, 8(3), 299–316.

    MATH  MathSciNet  Google Scholar 

  • Vander-Schaft, A. J., & Schumacher, J. M. (1998). Complementarity modeling of hybrid systems. IEEE Transactions on Automatic Control, 43(4), 483–490.

    Article  MathSciNet  Google Scholar 

  • Vidal, R., Chiuso, A., & Soatto, S. (2002). Observability and identifiability of jump linear systems. In Proceedings of the 41st IEEE Conference on Decision and Control (Vol. 4, pp. 3614–3619).

    Google Scholar 

  • Wang, L. (2005). Support vector machines: Theory and applications (Vol. 177). New York: Springer.

    Google Scholar 

  • Wen, C., Wang, S., Jin, X., & Ma, X. (2007). Identification of dynamic systems using piecewise-affine basis function models. Automatica, 43(10), 1824–1831.

    Article  MATH  MathSciNet  Google Scholar 

  • Xiao, C., Xue, A., Peng, D., & Guo, Y. (2014). Modeling of ph neutralization process using fuzzy recurrent neural network and dna based nsga-ii. Journal of the Franklin Institute, 351(7), 3847–3864.

    Article  MATH  Google Scholar 

  • Xu, J., Huang, X., Mu, X., & Wang, S. (2012). Model predictive control based on adaptive hinging hyperplanes model. Journal of Process Control, Elsevier, 22(10), 1821–1831.

    Article  Google Scholar 

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Authors and Affiliations

  1. Numerical Control of Industrial Processes, National School of Engineers of Gabes, University of Gabes, St. Omar Ibn-Khattab, 6029, Gabes, Tunisia

    Zeineb Lassoued & Kamel Abderrahim

Authors
  1. Zeineb Lassoued
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  2. Kamel Abderrahim
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Corresponding author

Correspondence to Kamel Abderrahim .

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Editors and Affiliations

  1. Department of Engineering Design and Mathematics, University of the West of England, Bristol, United Kingdom

    Quanmin Zhu

  2. Faculty of Computers and Information, Benha University, Benha, Egypt

    Ahmad Taher Azar

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Lassoued, Z., Abderrahim, K. (2015). PWARX Model Identification Based on Clustering Approach. In: Zhu, Q., Azar, A. (eds) Complex System Modelling and Control Through Intelligent Soft Computations. Studies in Fuzziness and Soft Computing, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-319-12883-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-12883-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12882-5

  • Online ISBN: 978-3-319-12883-2

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