Online identification of the bilinear model expansion on Laguerre orthonormal bases

References

• Alireza, R., & Scott, S. (2009). Identification of nonlinear systems using NARMAX model. Nonlinear Analysis Theory, Methods and Applications, 71(12), e1198–e1202.
   Web of Science ®Google Scholar
• Bazaraa, M.S., Sherali, H.D., & Shetty, C.M. (1993). Nonlinear programming: Theory and algorithms (2nd ed.). New York, NY: Wiley.
   Google Scholar
• Berk Hizir, N., Phan Minh, Q., Betti, R., & Longman Richard, W. (2012). Identification of discrete-time bilinear systems through equivalent linear models. Nonlinear Dynamics, 9(4), 2065–2078.
   Google Scholar
• Billings, S.A., & Chen, S. (1989). Extended model set, global data and threshold model identification of severely non-linear systems. International Journal of Control, 50(5), 1897–1923.
   Web of Science ®Google Scholar
• Billings, S.A., & Leontaritis, I.J. (1985). Input– output parametric models for non-linear systems. Part ii: Stochastic non-linear systems. International Journal of Control, 41(2), 329–344.
   Web of Science ®Google Scholar
• Bouzrara, K., Garna, T., Ragot, J., & Messaoud, H. (2012). Decomposition of an ARX model on Laguerre orthonormal bases. ISA Transactions, 51(6), 848–860.
   PubMed Web of Science ®Google Scholar
• Bouzrara, K., Garna, T., Ragot, J., & Messaoud, H. (2013). Online identification of the ARX model expansion on Laguerre orthonormal bases with filters on model input and output. International Journal of Control, 86(3), 369–385.
   Web of Science ®Google Scholar
• Demuth, H., Beale, M., & Hagan, M. (2007). Neural network toolbox 5, user’s guide. Natick, MA: The MathWorks.
   Google Scholar
• Etcheverry, G., Suleiman, W., & Monin, A. (2006). Quadratic system identification by hereditary approach. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vol. 3, pp. III.129–III.132, Toulouse, France.
   Google Scholar
• Favier, G., Kibangou, A.Y., & Khouaja, A. (2004, Septembre). Nonlinear systems modelling by means of Volterra models. Approaches for parametric complexity reduction. Symposium Techniques Avancées et Stratégies Innovantes en Modélisation et Commandes Robustes des Processus Industriels. Martigues.
   Google Scholar
• Foulloy, L., Galichet, S., & Titli, A. (2003). Commande floue ( Vol. 2). Paris: Hermes Science.
   Google Scholar
• Garna, T., Bouzrara, K., Ragot, J., & Hassani, M. (2013). Optimal expansions of discrete-time bilinear models using Laguerre function. IMA Journal of Mathematical Control & Information, doi:10.1093/imamci/dnt013.
   Web of Science ®Google Scholar
• Glass, J.W., & Franchek, M.A. (1999). NARMAX modelling and robust control of internal combustion engines. International Journal of Control, 72(4), 289–304.
   Web of Science ®Google Scholar
• Gomez, J.C., & Baeyens, E. (2000). Identification of multivariable Hammerstein systems using rational orthonormal bases. Proceedings of the 39th IEEE Conference on Decision and Control (CDC) (pp. 2849–2854). Sydney, Australia.
   Google Scholar
• Greblicki, W. (1994). Nonparametric identification of Wiener systems by orthogonal series. IEEE Transaction on Automatic Control, 39(10), 2077–2086.
   Web of Science ®Google Scholar
• Greblicki, W., & Pawlak, M. (2008). Nonparametric system identification. Cambridge: Cambridge University Press.
   Google Scholar
• Guo-Xing, W., & Yan-Jun, L. (2011). Adaptive fuzzy-neural tracking control for uncertain nonlinear discrete-time systems in the NARMAX form. Nonlinear Dynamics, 66(4), 745–753.
   Web of Science ®Google Scholar
• Hacioglu, R., & Williamson, G.A. (2001). Reduced complexity Volterra models for nonlinear system identification. Eurasip Journal on Applied Signal Processing, 2001(4), 257–265.
   Google Scholar
• Malti, R., Ekongolo, S.B., & Ragot, J. (1998). Dynamic SISO and MISO system approximations based on optimal Laguerre models. IEEE Transactions on Automatic Control, 43(9), 1318–1323.
   Web of Science ®Google Scholar
• Mohler, R.R. (1980). An overview of bilinear systems theory and applications. IEEE Transaction on System, Man, Cybernetics (SMC), 10(10), 683–688.
   Web of Science ®Google Scholar
• Oliveira, G.H.C., Amaral, W.C., Favier, G., & Dumont, G.A. (2000). Constrained robust predictive controller for uncertain processes modeled by orthonormal series functions. Automatica, 36(4), 563–571.
   Web of Science ®Google Scholar
• Seborg, D.E., Edger, T.F., & Millichamp, D.A. (2004). Process dynamics and control (2nd ed.). John Wiley and Sons, USA.
   Google Scholar
• Sliwinski, P. (2012). Nonlinear system identification by Haar wavelets. Heidelberg: Springer-Verlag.
   Google Scholar
• Sunil, L.K., Henrietta, L.G., & Robert, E.K. (2004). A bootstrap method for structure detection of NARMAX models. International Journal of Control, 77(2), 132–143.
   Web of Science ®Google Scholar
• Tanguy, N., Morvan, R., Vilbé, P., & Calvez, L.C. (2000). Online optimization of the time scale in adaptive Laguerre-based filters. IEEE Transactions on Signal Processing, 48(4), 1184–1187.
   Web of Science ®Google Scholar
• Van de Wouw, N., Njmeijer, H., & Van Campen, D.H. (2002). A Volterra series approach to the approximation of stochastic nonlinear dynamics. Nonlinear Dynamics, 27(4), 397–409.
   Web of Science ®Google Scholar
• Wahlberg, B. (1991). System identification using Laguerre models. IEEE Transactions on Automatic Control, 36(5), 551–562.
   Web of Science ®Google Scholar