Nonlinear system identification using heterogeneous multiple models

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.

[1]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[3]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[4]  Dilwyn Edwards,et al.  Guide to Mathematical Modeling , 1990 .

[5]  Dimitar Filev.  Fuzzy modeling of complex systems , 1991, Int. J. Approx. Reason..

[6]  T. Johansen,et al.  Constructing NARMAX models using ARMAX models , 1993 .

[7]  Stephen A. Billings,et al.  Nonlinear model validation using correlation tests , 1994 .

[8]  Junhong Nie,et al.  A neural approach to fuzzy modeling , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[9]  P. Gawthrop.  Continuous-time local state local model networks , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[10]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[11]  David J. Murray-Smith,et al.  Nonlinear system modelling using output error estimation of a local model network , 1996 .

[12]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[13]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[14]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[15]  Robert Babuska,et al.  Fuzzy Modeling for Control , 1998 .

[16]  John Yen,et al.  Improving the interpretability of TSK fuzzy models by combining global learning and local learning , 1998, IEEE Trans. Fuzzy Syst..

[17]  W. Leithead,et al.  Analytic framework for blended multiple model systems using linear local models , 1999 .

[18]  José Ragot,et al.  Non-linear dynamic system identification: A multi-model approach , 1999 .

[19]  F. Doyle,et al.  Multiple Model Approach for CSTR Control , 1999 .

[20]  J. Abonyi,et al.  Local and global identification and interpretation of parameters in Takagi-Sugeno fuzzy models , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[21]  L. Jain,et al.  Fuzzy sets and their application to clustering and training , 2000 .

[22]  O. Nelles.  Nonlinear System Identification , 2001 .

[23]  Gail D. Baura,et al.  Nonlinear System Identification , 2002 .

[24]  L. Ljung,et al.  Identification of composite local linear state-space models using a projected gradient search , 2002 .

[25]  G. Irwin,et al.  On Velocity‐Based Local Model Networks For Nonlinear Identification , 2003 .

[26]  Tor Arne Johansen,et al.  Multiobjective identification of Takagi-Sugeno fuzzy models , 2003, IEEE Trans. Fuzzy Syst..

[27]  Jonathan R. Partington,et al.  On linear models for nonlinear systems , 2003, Autom..

[28]  Ravindra D. Gudi,et al.  Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space , 2003 .

[29]  K. Burnham,et al.  EXTENDED GLOBAL TOTAL LEAST SQUARE APPROACH TO MULTIPLE-MODEL IDENTIFICATION , 2005 .

[30]  Didier Maquin,et al.  NON-LINEAR SYSTEM IDENTIFICATION USING UNCOUPLED STATE MULTIPLE-MODEL APPROACH , 2006 .

[31]  MULTIPLE MODEL WEIGHT ESTIMATION FOR MODELS WITH NO COMMON STATE , 2006 .

[32]  Marcin Witczak,et al.  A neuro-fuzzy multiple-model observer approach to robust fault diagnosis based on the DAMADICS benchmark problem , 2006 .

[33]  Shuning Wang,et al.  Identification of dynamic systems using Piecewise-Affine basis function models , 2007, Autom..

[34]  Michel Verhaegen,et al.  Multiple Model Weight Estimation for Models With No Common State , 2007 .

[35]  Kiriakos Kiriakidis,et al.  Nonlinear Modeling by Interpolation Between Linear Dynamics and Its Application in Control , 2007 .

[36]  Didier Theilliol,et al.  Fault Tolerant Control Design For Polytopic LPV Systems , 2007, Int. J. Appl. Math. Comput. Sci..

[37]  Gordon Lightbody,et al.  Nonlinear system identification: From multiple-model networks to Gaussian processes , 2008, Eng. Appl. Artif. Intell..

[38]  Didier Maquin,et al.  State estimation for non-linear systems using a decoupled multiple model , 2008, Int. J. Model. Identif. Control..

[39]  B. Marx,et al.  On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy , 2009 .

[40]  Didier Maquin,et al.  New fault tolerant control strategies for nonlinear Takagi-Sugeno systems , 2012, Int. J. Appl. Math. Comput. Sci..

[41]  Peng Shi,et al.  Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model , 2012, Int. J. Appl. Math. Comput. Sci..