Nonlinear system identification using heterogeneous multiple models

Rodolfo Orjuela; Benoît Marx; José Ragot; Didier Maquin

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 1, page 103-115
  • ISSN: 1641-876X

Abstract

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Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.

How to cite

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Rodolfo Orjuela, et al. "Nonlinear system identification using heterogeneous multiple models." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 103-115. <http://eudml.org/doc/251337>.

@article{RodolfoOrjuela2013,
abstract = {Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.},
author = {Rodolfo Orjuela, Benoît Marx, José Ragot, Didier Maquin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear system identification; multiple models; heterogeneous submodels},
language = {eng},
number = {1},
pages = {103-115},
title = {Nonlinear system identification using heterogeneous multiple models},
url = {http://eudml.org/doc/251337},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Rodolfo Orjuela
AU - Benoît Marx
AU - José Ragot
AU - Didier Maquin
TI - Nonlinear system identification using heterogeneous multiple models
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 1
SP - 103
EP - 115
AB - Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.
LA - eng
KW - nonlinear system identification; multiple models; heterogeneous submodels
UR - http://eudml.org/doc/251337
ER -

References

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  1. Abonyi, J. and Babuška, R. (2000). Local and global identification and interpretation of parameters in Takagi-Sugeno fuzzy models, 9th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE, San Antonio, CA, USA, pp. 835-840. 
  2. Babuška, R. (1998). Fuzzy Modeling for Control, Kluwer Academic Publishers, London. 
  3. Billings, S.A. and Zhu, Q.M. (1994). Nonlinear model validation using correlation test, International Journal of Control 60(6): 1107-1120. Zbl0813.93012
  4. Boukhris, A., Mourot, G. and Ragot, J. (1999). Non-linear dynamic system identification: A multiple-model approach, International Journal of Control 72(7/8): 591-604. Zbl0938.93512
  5. Dumitrescu, D., Lazzerini, B. and Jain, L.C. (2000). Fuzzy Sets and Their Application to Clustering and Training, CRC Press Taylor & Francis, Boca Raton, FL. 
  6. Edwards, D. and Hamson, M. (2001). Guide to Mathematical Modelling, 2nd Edn., Basingstoke, Palgrave, Chapter 1, p. 3. Zbl0825.00022
  7. Filev, D. (1991). Fuzzy modeling of complex systems, International Journal of Approximate Reasoning 5(3): 281-290. Zbl0738.93048
  8. Gatzke, E.P. and Doyle III, F.J. (1999). Multiple model approach for CSTR control, 14th IFAC World Congress, Beijing, China, pp. 343-348. 
  9. Gawthrop, P.J. (1995). Continuous-time local state local model networks, 1995 IEEE Conference on Systems, Man and Cybernetics, Vancouver, Canada, pp. 852-857. 
  10. Gray, G.J., Murray-Smith, D.J., Li, Y. and Sharman, K.C. (1996). Nonlinear system modelling using output error estimation of a local model network, Technical Report CSC-96005, Centre for Systems and Control, Glasgow University, Glasgow. 
  11. Gregorčič, G. and Lightbody, G. (2000). Control of highly nonlinear processes using self-tuning control and multiple/local model approaches, 2000 IEEE International Conference on Intelligent Engineering Systems, INES 2000, Portoroz, Slovenia, pp. 167-171. 
  12. Gregorčič, G. and Lightbody, G. (2008). Nonlinear system identification: From multiple-model networks to Gaussian processes, Engineering Applications of Artificial Intelligence 21(7): 1035-1055. 
  13. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2012). New fault tolerant control strategies for nonlinear Takagi-Sugeno systems, International Journal of Applied Mathematics and Computer Science 22(1): 197-210, DOI: 10.2478/v10006-012-0015-8. Zbl1273.93102
  14. Johansen, T.A. and Babuška, R. (2003). Multi-objective identification of Takagi-Sugeno fuzzy models, IEEE Transactions on Fuzzy Systems 11(6): 847-860. 
  15. Johansen, T.A. and Foss, A.B. (1993). Constructing NARMAX using ARMAX models, International Journal of Control 58(5): 1125-1153. Zbl0787.93004
  16. Kanev, S. and Verhaegen, M. (2006). Multiple model weight estimation for models with no common state, 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS, Beijing, China, pp. 637-642. 
  17. Kiriakidis, K. (2007). Nonlinear modelling by interpolation between linear dynamics and its application in control, Journal of Dynamics Systems, Measurement and Control 129(6): 813-824. 
  18. Leith, D.J. and Leithead, W.E. (1999). Analytic framework for blended multiple model systems using linear local models, International Journal of Control 72(7): 605-619. Zbl0938.93501
  19. Ljung, L. (1999). System Identification: Theory for the User, 2nd Edn., Prentice Hall PTR, London. Zbl0615.93004
  20. Mäkilä, P.M. and Partington, J.R. (2003). On linear models for nonlinear systems, Automatica 39(1): 1-13. Zbl1017.93023
  21. McLoone, S. and Irwin, G.W. (2003). On velocity-based local model networks for nonlinear identification, Asian Journal of Control 5(2): 309-315. 
  22. Murray-Smith, R. and Johansen, T.A. (1997). Multiple Model Approaches to Modelling and Control, Taylor & Francis, London. 
  23. Narendra, K.S. and Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks 1(1): 4-27. 
  24. Nelles, O. (2001). Nonlinear System Identification, Springer-Verlag, Berlin/Heidelberg. Zbl0963.93001
  25. Nie, J. (1994). A neural approach to fuzzy modeling, American Control Conference, ACC, Baltimore, MD, USA, pp. 2139-2143. 
  26. Orjuela, R., Maquin, D. and Ragot, J. (2006). Nonlinear system identification using uncoupled state multiple-model approach, Workshop on Advanced Control and Diagnosis, ACD'2006, Nancy, France. 
  27. Orjuela, R., Marx, B., Ragot, J. and Maquin, D. (2008). State estimation for nonlinear systems using a decoupled multiple mode, International Journal of Modelling Identification and Control 4(1): 59-67. 
  28. Orjuela, R., Marx, B., Ragot, J. and Maquin, D. (2009). On the simultaneous state and unknown inputs estimation of complex systems via a multiple model strategy, IET Control Theory & Applications 3(7): 877-890. 
  29. Rodrigues, M., Theilliol, D., Aberkane, S. and Sauter, D. (2007). Fault tolerant control design for polytopic LPV systems, International Journal of Applied Mathematics and Computer Science 17(1): 27-37, DOI: 10.2478/v10006-007-0004-5. Zbl1122.93073
  30. Sjöberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P., Hjalmarsson, H. and Juditsky, A. (1995). Nonlinear black-box modeling in system identification: A unified overview, Automatica 31(12): 1691-1724. Zbl0846.93018
  31. Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to model and control, IEEE Transactions on Systems, Man, and Cybernetics 15(1): 116-132. Zbl0576.93021
  32. Uppal, F.J., Patton, R.J. and Witczak, M. (2006). A neuro-fuzzy multiple-model observer approach to robust fault diagnosis based on the DAMADICS benchmark problem, Control Engineering Practice 14(6): 699-717. 
  33. Venkat, A.N., Vijaysai, P. and Gudi, R.D. (2003). Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space, Journal of Process Control 13(6): 473-488. 
  34. Verdult, V., Ljung, L. and Verhaegen, M. (2002). Identification of composite local linear state-space models using a projected gradient search, International Journal of Control 75(16/17): 1385-1398. Zbl1022.93012
  35. Vinsonneau, B., Goodall, D. and Burnham, K. (2005). Extended global total least square approach to multiple-model identification, 16th IFAC World Congress, Prague, Czech Republic, p. 143. 
  36. Walter, E. and Pronzato, L. (1997). Identification of Parametric Models: From Experimental Data, Springer-Verlag, Berlin. Zbl0864.93014
  37. Wen, C., Wang, S., Jin, X. and Ma, X. (2007). Identification of dynamic systems using piecewise-affine basis function models, Automatica 43(10): 1824-1831. Zbl1119.93026
  38. Xu, D., Jiang, B. and Shi, P. (2012). Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model, International Journal of Applied Mathematics and Computer Science 22(1): 183-196, DOI: 10.2478/v10006-012-0014-9. Zbl1273.93105
  39. Yen, J., Wang, L. and Gillespie, C.W. (1998). Improving the interpretability of Takagi-Sugeno fuzzy models by combining global learning and local learning, IEEE Transactions on Fuzzy Systems 6(4): 530-537. 

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