In this study, a comprehensive quality measure criterion is developed to evaluate the performance of the identified models for nonlinear hybrid systems using support vector regression-based techniques. The proposed quality measure criterion includes all the factors that affect the quality of the identified models, namely identification error, quality of the switching signal, and model complexity. Using the proposed criterion, the resulting models of hybrid systems identification can be efficiently compared and the best model with acceptable complexity, tolerable identification error, and desirable switching signal quality will be selected. This quality measure criterion prevents selecting the complex models relying on the Occam’s Razor theorem. Besides, it provides the possibility of comparing the effects of different kernel functions on the identified models considering the aforementioned factors.

Type of Article: Research paper |
Subject:
Special

Received: 2021/04/18 | Accepted: 2021/06/22 | ePublished ahead of print: 2021/06/23 | Published: 2022/05/31

Received: 2021/04/18 | Accepted: 2021/06/22 | ePublished ahead of print: 2021/06/23 | Published: 2022/05/31

1. [1] G. Ferrari-Trecate, M. Muselli, D. Liberati, M. Morari, "A clustering technique for the identification of piecewise affine systems," Automatica, vol. 39, no. 2, pp. 205-217, 2003. [DOI:10.1016/S0005-1098(02)00224-8]

2. [2] H. Nakada, K. Takaba, T. Katayama, "Identification of piecewise affine systems based on statistical clustering technique," Automatica, vol. 41,no. 5, pp. 905-913, 2005. [DOI:10.1016/j.automatica.2004.12.005]

3. [3] A.L. Juloski, S. Weiland, W.P.M.H Heemels, "A Bayesian approach to identification of hybrid systems," IEEE Transactions on Automatic Control, vol. 50, no. 10, pp. 1520-1533, 2005. [DOI:10.1109/TAC.2005.856649]

4. [4] Y. Lu, S. Khatibisepehr, B. Huang, "A variational Bayesian approach to identification of switched ARX models," in IEEE 53rd Annual Conference on Decision and Control(CDC), 2014, pp.2542-2547. [DOI:10.1109/CDC.2014.7039777]

5. [5] J. Roll, A. Bemporad, L. Ljung, "Identification of piecewise affine systems via mixed-integer programming," Automatica, vol. 40, no. 1,pp. 37-50, 2004. [DOI:10.1016/j.automatica.2003.08.006]

6. [6] A. Bemporad, J. Roll, L. Ljung, "Identification of hybrid systems via mixed-integer programming," in Proceedings of the 40th IEEE Conference on Decision and Control, 2001, pp.786-792.

7. [7] A. Bemporad, A. Garulli, S. Paoletti, A. Vicino, "A bounded-error approach to piecewise affine system identification," IEEE Transactions on Automatic Control, vol. 50, no. 10, pp. 1567-1580, 2005. [DOI:10.1109/TAC.2005.856667]

8. [8] A. Bemporad, A. Garulli, S. Paoletti, A. Vicino, "A greedy approach to identification of piecewise affine models," in International Workshop on Hybrid Systems: Computation and Control, 2003, pp.97-112. [DOI:10.1007/3-540-36580-X_10]

9. [9] Y. Ma, R. Vidal, "Identification of deterministic switched ARX systems via identification of algebraic varieties," in International Workshop on Hybrid Systems: Computation and Control, 2005, pp.449-465. [DOI:10.1007/978-3-540-31954-2_29]

10. [10] R. Vidal, S. Soatto, Y. Ma, S. Sastry, "An algebraic geometric approach to the identification of a class of linear hybrid systems," in 42nd IEEE Conference on Decision and Control, 2003, pp.167-172.

11. [11] F. Lauer, "From support vector machines to hybrid system identification," Ph.D. dissertation, Université Henri Poincaré-Nancy I, 2008.

12. [12] A. Hartmann, J. M. Lemos, R. S. Costa, J. Xavier, S. Vinga, "Identification of switched ARX models via convex optimization and expectation maximization," Journal of Process Control, vol. 28, pp. 9-16, 2015. [DOI:10.1016/j.jprocont.2015.02.003]

13. [13] G. Pillonetto, "A new kernel-based approach to hybrid system identification,"Automatica, vol. 70, pp. 21-31, 2016. [DOI:10.1016/j.automatica.2016.03.011]

14. [14] A. L. J. Juloski, S. Paoletti, J. Roll, "Recent techniques for the identification of piecewise affine and hybrid systems," in Current trends in nonlinear systems and control, Springer, 2006, pp. 79-99. [DOI:10.1007/0-8176-4470-9_5]

15. [15] S. Paoletti, A. L. J. Juloski, G. Ferrari-Trecate, R. Vidal, "Identification of hybrid systems: A tutorial," European journal of control, vol. 13, no.2, pp. 242-260, 2007. [DOI:10.3166/ejc.13.242-260]

16. [16] A. Garulli, S. Paoletti, A. Vicino, "A survey on switched and piece-wise affine system identification," IFAC Proceedings Volumes, vol. 45, no.16, pp. 344-355, 2012. [DOI:10.3182/20120711-3-BE-2027.00332]

17. [17] F. Lauer, G. Bloch, "Switched and piecewise nonlinear hybrid sys-tem identification," in International Workshop on Hybrid Systems: Computation and Control, Berlin., 2008, pp.330-343. [DOI:10.1007/978-3-540-78929-1_24]

18. [18] G. Bloch and F. Lauer, "Reduced-size kernel models for nonlinear hybrid system identification," IEEE Transactions on Neural Networks, vol. 22,no. 12, pp. 2398-2405, 2011. [DOI:10.1109/TNN.2011.2171361]

19. [19] F. Lauer, G. Bloch, R. Vidal, "Nonlinear hybrid system identification with kernel models," in49thIEEEConferenceonDecisionandControl,CDC2010, 2010, pp.696-701. [DOI:10.1109/CDC.2010.5718011]

20. [20] L. Bako, K. Boukharouba, S. Lecoeuche, "Anℓ0-ℓ1norm based optimization procedure for the identification of switched nonlinear systems," in 49th IEEE Conference on Decision and Control (CDC), 2010,pp.4467-4472.

21. [21] V. L. Le, F. Lauer, L. Bako, G. Bloch, "Learning nonlinear hybridsystems: from sparse optimization to support vector regression," in Proceedings of the 16th international conference on Hybrid systems: computation and control, 2013, pp.33-42.

22. [22] F. Bianchi, M. Prandini, L. Piroddi, "A randomized approach to switched nonlinear systems identification," IFAC Papers On Line, vol. 51, no. 15,pp. 281-286, 2018. [DOI:10.1016/j.ifacol.2018.09.148]

23. [23] A. Scampicchio, A. Giaretta, G. Pillonetto, "Nonlinear Hybrid Systems Identification using Kernel-Based Techniques," IFAC Papers On Line, vol.51, no. 15, pp. 269-274, 2018. [DOI:10.1016/j.ifacol.2018.09.146]

24. [24] A. Brusaferri, M. Matteucci, A. Spinelli,"Estimation of Switched Markov Polynomial NARX models, "arXivpreprintarXiv: 2009.14073,2020.

25. [25] F. Bianchi, M. Prandini, L. Piroddi, "A randomized two-stage iterative method for switched nonlinear systems identification," Nonlinear Analysis: Hybrid Systems, vol. 35, pp. 100818, 2020. [DOI:10.1016/j.nahs.2019.100818]

26. [26] C. Xiujun, H. Hongwei, W. Lin, X. Zhengqing, "Identification of switched nonlinear systems based on EM algorithm," In 39th Chinese Control Conference (CCC), pp.1337-1342, 2020. [DOI:10.23919/CCC50068.2020.9188381]

27. [27] J. Lunze, F. Lamnabhi-Lagarrigue, Handbook of hybrid systems control: Theory, tools, applications, Cambridge University Press, 2009. [DOI:10.1017/CBO9780511807930]

28. [28] David. JC. MacKay, "Bayesian interpolation," Neural computation, vol.4, no. 3, pp. 415-447, 1992. [DOI:10.1162/neco.1992.4.3.415]

29. [29] L. Ljung, System identification, in: Signal analysis and prediction, Springer, 1998, pp. 163-173. [DOI:10.1007/978-1-4612-1768-8_11]

30. [30] S. S. Keerthi, C.-J. Lin, Asymptotic behaviors of support vector machines with Gaussian kernel, Neural computation 15 (7) (2003) 1667-1689. [DOI:10.1162/089976603321891855]

31. [31] D. J. MacKay, Probable networks and plausible predictions: a review of practical Bayesian methods for supervised neural networks, Network: computation in neural systems 6 (3) (1995) 469-505. [DOI:10.1088/0954-898X_6_3_011]

32. [32] M. E. Tipping, Bayesian inference: An introduction to principles and practice in machine learning, in: Advanced lectures on machine Learning, Springer, 2004, pp. 41-62. [DOI:10.1007/978-3-540-28650-9_3]

33. [33] T. V. Gestel, J. A. Suykens, G. Lanckriet, A. Lambrechts, B. D. Moor,J. Vandewalle, Bayesian framework for least-squares support vector machine classifiers, Gaussian processes, and kernel Fisher discriminant analysis, Neural computation 14 (5) (2002) 1115-1147. [DOI:10.1162/089976602753633411]

34. [34] P. Grünwald, A tutorial introduction to the minimum description length principle, Advances in minimum description length: Theory and applications (2005) 3-81. [DOI:10.7551/mitpress/1114.001.0001]

35. [35] F. Lauer, R. Vidal, G. Bloch, A product-of-errors framework for linear hybrid system identification, in: Proc. of the 15th IFAC Symp. on System Identification (SYSID), Saint-Malo, France, 2009. [DOI:10.3182/20090706-3-FR-2004.00093]

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