Nonlinear system identification using heterogeneous multiple models

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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.

Abonyi, J. and Babuška, R. (2000). Local and global identification and interpretation of parameters in Takagi-Sugeno fuzzy models, 9th IEEE InternationalConference on Fuzzy Systems, FUZZ-IEEE, San Antonio,CA, USA, pp. 835-840.

Babuška, R. (1998). Fuzzy Modeling for Control, Kluwer Academic Publishers, London.

Billings, S.A. and Zhu, Q.M. (1994). Nonlinear model validation using correlation test, International Journal of Control60(6): 1107-1120.

Boukhris, A., Mourot, G. and Ragot, J. (1999). Non-linear dynamic system identification: A multiple-model approach, International Journal of Control72(7/8): 591-604.

Dumitrescu, D., Lazzerini, B. and Jain, L.C. (2000). Fuzzy Setsand Their Application to Clustering and Training, CRC Press Taylor & Francis, Boca Raton, FL.

Edwards, D. and Hamson, M. (2001). Guide to MathematicalModelling, 2nd Edn., Basingstoke, Palgrave, Chapter 1, p. 3.

Filev, D. (1991). Fuzzy modeling of complex systems, InternationalJournal of Approximate Reasoning 5(3): 281-290.

Gatzke, E.P. and Doyle III, F.J. (1999). Multiple model approach for CSTR control, 14th IFAC World Congress, Beijing,China, pp. 343-348.

Gawthrop, P.J. (1995). Continuous-time local state local model networks, 1995 IEEE Conference on Systems, Man and Cybernetics,Vancouver, Canada, pp. 852-857.

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 ReportCSC-96005, Centre for Systems and Control, Glasgow University, Glasgow.

Gregorčič, G. and Lightbody, G. (2000). Control of highly nonlinear processes using self-tuning control and multiple/local model approaches, 2000 IEEE InternationalConference on Intelligent Engineering Systems, INES2000, Portoroz, Slovenia, pp. 167-171.

Gregorčič, G. and Lightbody, G. (2008). Nonlinear system identification: From multiple-model networks to Gaussian processes, Engineering Applications of Artificial Intelligence21(7): 1035-1055.

Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2012). New fault tolerant control strategies for nonlinear Takagi-Sugeno systems, International Journal of AppliedMathematics and Computer Science 22(1): 197-210, DOI: 10.2478/v10006-012-0015-8.

Johansen, T.A. and Babuška, R. (2003). Multi-objective identification of Takagi-Sugeno fuzzy models, IEEETransactions on Fuzzy Systems 11(6): 847-860.

Johansen, T.A. and Foss, A.B. (1993). Constructing NARMAX using ARMAX models, International Journal of Control58(5): 1125-1153.

Kanev, S. and Verhaegen, M. (2006). Multiple model weight estimation for models with no common state, 6th IFACSymposium on Fault Detection, Supervision and Safetyof Technical Processes, SAFEPROCESS, Beijing, China, pp. 637-642.

Kiriakidis, K. (2007). Nonlinear modelling by interpolation between linear dynamics and its application in control, Journal of Dynamics Systems, Measurement and Control129(6): 813-824.

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.

Ljung, L. (1999). System Identification: Theory for the User, 2nd Edn., Prentice Hall PTR, London.

Mäkilä, P.M. and Partington, J.R. (2003). On linear models for nonlinear systems, Automatica 39(1): 1-13.

McLoone, S. and Irwin, G.W. (2003). On velocity-based local model networks for nonlinear identification, Asian Journalof Control 5(2): 309-315.

Murray-Smith, R. and Johansen, T.A. (1997). Multiple ModelApproaches to Modelling and Control, Taylor & Francis, London.

Narendra, K.S. and Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks, IEEETransactions on Neural Networks 1(1): 4-27.

Nelles, O. (2001). Nonlinear System Identification, Springer-Verlag, Berlin/Heidelberg.

Nie, J. (1994). A neural approach to fuzzy modeling, AmericanControl Conference, ACC, Baltimore, MD, USA, pp. 2139-2143.

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.

Orjuela, R., Marx, B., Ragot, J. and Maquin, D. (2008). State estimation for nonlinear systems using a decoupled multiple mode, International Journal of Modelling Identificationand Control 4(1): 59-67.

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 ControlTheory & Applications 3(7): 877-890.

Rodrigues, M., Theilliol, D., Aberkane, S. and Sauter, D. (2007). Fault tolerant control design for polytopic LPV systems, International Journal of Applied Mathematicsand Computer Science 17(1): 27-37, DOI: 10.2478/v10006-007-0004-5.

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.

Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to model and control, IEEE Transactions on Systems, Man, and Cybernetics15(1): 116-132.

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, ControlEngineering Practice 14(6): 699-717.

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 ofProcess Control 13(6): 473-488.

Verdult, V., Ljung, L. and Verhaegen, M. (2002). Identification of composite local linear state-space models using a projected gradient search, International Journal of Control75(16/17): 1385-1398.

Vinsonneau, B., Goodall, D. and Burnham, K. (2005). Extended global total least square approach to multiple-model identification, 16th IFAC World Congress, Prague, CzechRepublic, p. 143.

Walter, E. and Pronzato, L. (1997). Identification of ParametricModels: From Experimental Data, Springer-Verlag, Berlin.

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.

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 AppliedMathematics and Computer Science 22(1): 183-196, DOI: 10.2478/v10006-012-0014-9.

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 Transactionson Fuzzy Systems 6(4): 530-537.

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