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Comparison of Four Procedures for the Identification of Hybrid Systems

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Book cover Hybrid Systems: Computation and Control (HSCC 2005)

Abstract

In this paper we compare four recently proposed procedures for the identification of PieceWise AutoRegressive eXogenous (PWARX) and switched ARX models. We consider the clustering-based procedure, the bounded-error procedure, and the Bayesian procedure which all identify PWARX models. We also study the algebraic procedure, which identifies switched linear models. We introduce quantitative measures for assessing the quality of the obtained models. Specific behaviors of the procedures are pointed out, using suitably constructed one dimensional examples. The methods are also applied to the experimental identification of the electronic component placement process in pick-and-place machines.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Bemporad, A., Garulli, A., Paoletti, S., Vicino, A.: A greedy approach to identification of piecewise affine models. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 97–112. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Bemporad, A., Garulli, A., Paoletti, S., Vicino, A.: Data classification and parameter estimation for the identification of piecewise affine models. In: Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, pp. 20–25 (2004)

    Google Scholar 

  4. Juloski, A., Weiland, S., Heemels, W.: A Bayesian approach to identification of hybrid systems. In: Proceedings of the 43rd Conference on Decision and Control, Paradise Island, Bahamas, pp. 13–19 (2004)

    Google Scholar 

  5. Vidal, R., Soatto, S., Ma, Y., Sastry, S.: An algebraic geometric approach to the identification of a class of linear hybrid systems. In: Proc. of IEEE Conference on Decision and Control (2003)

    Google Scholar 

  6. Vidal, R.: Identification of PWARX hybrid models with unknown and possibly different orders. In: Proc. of IEEE American Control Conference (2004)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Munz, E., Krebs, V.: Identification of hybrid systems using a priori knowledge. In: Preprints of the 15th IFAC world congress, Barcelona, Spain (2002)

    Google Scholar 

  9. Ferrari-Trecate, G., Schinkel, M.: Conditions of optimal classification for piecewise affine regression. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 188–202. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Bennett, K., Mangasarian, O.: Multicategory discrimination via linear programming. Optimization Methods and Software 3, 27–39 (1993)

    Article  Google Scholar 

  11. Milanese, M., Vicino, A.: Optimal estimation theory for dynamic systems with set membership uncertainty: an overview. Automatica 27, 997–1009 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  12. Arulampalam, M., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing 50, 174–188 (2002)

    Article  Google Scholar 

  13. Verriest, E., Moor, B.D.: Multi-mode system identification. In: Proc. of European Conference on Control (1999)

    Google Scholar 

  14. Amaldi, E., Mattavelli, M.: The MIN PFS problem and piecewise linear model estimation. Discrete Applied Mathematics 118, 115–143 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Niessen, H., Juloski, A., Ferrari-Trecate, G., Heemels, W.: Comparison of three procedures for the identification of hybrid systems. In: Proceedings of the Conference on Control Applications, Taipei, Taiwan (2004)

    Google Scholar 

  16. Juloski, A., Heemels, W., Ferrari-Trecate, G.: Data-based hybrid modelling of the component placement process in pick-and-place machines. Control Engineering Practice 12, 1241–1252 (2004)

    Article  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Juloski, A.L., Heemels, W.P.M.H., Ferrari-Trecate, G., Vidal, R., Paoletti, S., Niessen, J.H.G. (2005). Comparison of Four Procedures for the Identification of Hybrid Systems. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_23

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25108-8

  • Online ISBN: 978-3-540-31954-2

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