Artículos de revistas
An Introduction To Models Based On Laguerre, Kautz And Other Related Orthonormal Functions - Part Ii: Non-linear Models
Registro en:
International Journal Of Modelling, Identification And Control. , v. 16, n. 1, p. 1 - 14, 2012.
17466172
10.1504/IJMIC.2012.046691
2-s2.0-84860779184
Autor
Oliveira G.H.C.
Da Rosa A.
Campello R.J.G.B.
MacHado J.B.
Amaral W.C.
Institución
Resumen
This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and limitations are discussed within the contexts of non-linear system identification. The discussions comprise a broad bibliographical survey of the subject and a comparative analysis involving some specific model realisations, namely, Volterra, fuzzy, and neural models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these non-linear models are presented and illustrated by means of two case studies. Copyright © 2012 Inderscience Enterprises Ltd. 16 1 1 14 Alataris, K., Berger, T.W., Marmarelis, V.Z., A novel network for nonlinear modeling of neural systems with arbitrary point-process inputs (2000) Neural Networks, 13 (2), pp. 255-266. , DOI 10.1016/S0893-6080(99)00092-1, PII S0893608099000921 Arto, V., Hannu, P., Halme, A., Modeling of chromatographic separation process with Wiener-MLP representation (2001) Journal of Process Control, 11 (5), pp. 443-458. , DOI 10.1016/S0959-1524(00)00053-6, PII S0959152400000536 Babuška, R., (1998) Fuzzy Modeling for Control, , Kluwer Academic Publishers, Massachusetts, USA Babuška, R., Verbruggen, H.B., Fuzzy set methods for local modelling and identification (1997) Multiple Model Approaches to Modelling and Control, , Murray-Smith, R. and Johansen, T.A. (Eds.) Taylor and Francis, London, Chap. 2 Back, A.D., Tsoi, A.C., Nonlinear system identification using discrete Laguerre functions (1996) Journal of Systems Engineering, 6 (3), pp. 194-207 Balestrino, A., Caiti, A., Zanobini, G., Identification of Wiener-type nonlinear systems by Laguerre filters and neural networks (1999) Proc. 14th IFAC World Congress, pp. 433-438. , Beijing/China Billings, S.A., Identification of nonlinear systems - A survey (1980) IEE Proc. Pt D, 127 (6), pp. 272-285 Boyd, S., Chua Leon, O., Fading memory and the problem of approximating nonlinear operators with volterra series (1985) IEEE transactions on circuits and systems, CAS-32 (11), pp. 1150-1161 Broome, P.W., Discrete orthonormal sequences (1965) Journal of the Association for Computing Machinery, 12 (2), pp. 151-168 Broomhead, D.S., Lowe, D., Multivariate functional interpolation and adaptive networks (1988) Complex Systems, 2 (3), pp. 321-355 Campello, R.J.G.B., (2002) New Architectures and Methodologies for Modeling and Control of Complex Systems Combining Classical and Modern Tools, , PhD thesis, School of Electrical and Computer Engineering of the State University of Campinas (FEEC/UNICAMP), Campinas-SP, Brazil (in Portuguese) Campello, R.J.G.B., Amaral, W.C., Takagi-Sugeno fuzzy models within orthonormal basis function framework and their application to process control (2002) IEEE International Conference on Plasma Science, 2, pp. 1399-1404 Campello, R.J.G.B., Oliveira, G.H.C., Modelos não lineares (2007) Enciclopédia de Automática, 3. , L.A. Aguirre, A.P. Alves da Silva, M.F.M. Campos and W.C. Amaral (Eds.) (Cap. 4), Edgard Blücher (in Portuguese) Campello, R.J.G.B., Meleiro, L.A.C., Amaral, W.C., Control of a bioprocess using orthonormal basis function fuzzy models (2004) IEEE International Conference on Fuzzy Systems, 2, pp. 801-806. , 2004 IEEE International Conference on Fuzzy Systems - Proceedings Campello, R.J.G.B., Von Zuben, F.J., Amaral, W.C., Meleiro, L.A.C., Maciel Filho, R., Hierarchical fuzzy models within the framework of orthonormal basis functions and their application to bioprocess control (2003) Chemical Engineering Science, 58 (18), pp. 4259-4270. , DOI 10.1016/S0009-2509(03)00309-9 Chen, S., Billings, S., Grant, P., Recursive hybrid algorithm for non-linear system identification using radial basis function networks (1992) Int. J. Control, 55 (5), pp. 1051-1070 Cho, K.B., Wang, B.H., Radial basis function based adaptive fuzzy systems and their applications to system identification and prediction (1996) Fuzzy Sets and Systems, 83 (3), pp. 325-339 Da Rosa, A., (2005) Expansion of discrete-time Volterra models using Kautz functions, , MSc thesis, School of Electrical and Computer Engineering of the State University of Campinas (FEEC/UNICAMP), Campinas- SP, Brazil (in Portuguese) Da Rosa, A., Campello, R.J.G.B., Amaral, W.C., An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension (2008) International Journal of Control, 81 (6), pp. 962-975 Da Rosa, A., Campello, R.J.G.B., Amaral, W.C., Exact search directions for optimization of linear and nonlinear models based on generalized orthonormal functions (2009) IEEE Transactions on Automatic Control, 54 (12), pp. 2757-2772 Doyle Iii, F.J., Ogunnaike, B.A., Pearson, R.K., Nonlinear model-based control using second-order Volterra models (1995) Automatica, 31 (5), pp. 697-714 Doyle Iii, F.J., Pearson, R.K., Ogunnaike, B.A., (2002) Identification and Control Using Volterra Models, , Springer-Verlag, London, UK Dumont, G.A., Fu, Y., Non-linear adaptive control via Laguerre expansion of Volterra kernels (1993) Int. J. Adaptive Control and Signal Processing, 7 (5), pp. 367-382 (1999) Manual for Model 730 - Magnetic Levitation System, , Educational Control Products (ECP), California, USA Espinosa, J., Vandewalle, J., Wertz, V., (2004) Fuzzy Logic, Identification and Predictive Control, , Springer-Verlag, London, UK Eykhoff, P., (1974) System Identification: Parameter and State Estimation, , John Wiley & Sons, UK Fu, Y., Dumont, G.A., Optimum time scale for discrete Laguerre network (1993) IEEE Transactions on Automatic Control, 38 (6), pp. 934-938. , DOI 10.1109/9.222305 Gustafson, D.E., Kessel, W.C., Fuzzy clustering with a fuzzy covariance matrix (1979) Proc. IEEE CDC, pp. 761-766. , San Diego, CA Haykin, S., (1999) Neural Networks: A Comprehensive Foundation, , 2nd ed., Prentice Hall, Upper Saddle River, NJ, USA Heuberger, P.S.C., Van Den Hof, P.M.J., Bosgra, O.H., A generalized orthonormal basis for linear dynamical systems (1995) IEEE Trans. on Automatic Control, 40 (3), pp. 451-465 Heuberger, P.S.C., Van Den Hof, P.M.J., Wahlberg, B., (2005) Modelling and Identification with Rational Orthogonal Basis Functions, , Springer-Verlag, London, UK Hunt, K.J., Haas, R., Murray-Smith, R., Extending the functional equivalence of radial basis function networks and fuzzy inference systems (1996) IEEE Transactions on Neural Networks, 7 (3), pp. 776-781. , PII S1045922796012398 Kosko, B., (1992) Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, , Prentice Hall, Upper Saddle River, NJ, USA Kosko, B., (1997) Fuzzy Engineering, , Prentice Hall, Upper Saddle River, NJ, USA Leontaritis, I., Billings, S.A., Input-output parametric models for nonlinear systems - Parts i and II (1985) Int. Journal of Control, 41 (6), pp. 303-344 Ljung, L., (1999) System Identification: Theory for the User, , 2nd ed., Prentice Hall, Upper Saddle River, NJ, USA MacHado, J.B., Design of OBF-TS fuzzy models based on multiple clustering validity criteria (2007) Proc. IEEE Int. Conf. on Tools with Artificial Intelligence, (2), pp. 336-339. , Patras/Greece Mäkilä, P.M., Approximation of stable systems by Laguerre filters (1990) Automatica, 26 (2), pp. 333-345 Maner, B.R., Doyle III, F.J., Ogunnaike, B.A., Pearson, R.K., Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models (1996) Automatica, 32 (9), pp. 1285-1301. , DOI 10.1016/0005-1098(96)00086-6, PII S0005109896000866 Medeiros, A.V., Amaral, W.C., Campello, R.J.G.B., GA optimization of generalized OBF-TS fuzzy models with global and local estimation approaches (2006) Proc. 15th IEEE Internat. Conference on Fuzzy Systems, pp. 8494-8501. , Vancouver/Canada Narendra, K., Parthasarathy, K., Identification and control of dynamical systems using neural networks (1990) IEEE Trans. Neural Networks, 1 (1), pp. 4-26 Nelles, O., (2001) Nonlinear System Identification, , Springer-Verlag, London, UK Ninness, B., Gustafsson, F., A unifying construction of orthonormal bases for system identification (1997) IEEE Transactions on Automatic Control, 42 (4), pp. 515-521. , PII S0018928697028080 Oliveira, G.H.C., Amaral, W.C., Latawiec, K., CRHPC using Volterra models and orthonormal basis functions: An application to CSTR plants (2003) Proc. IEEE Conference on Control Applications, pp. 718-723. , Istanbul/Turkey Oliveira, G.H.C., Campello, R.J.G.B., Amaral, W.C., Fuzzy models within orthonormal basis function framework (1999) Proc. 8th IEEE Internat. Conference on Fuzzy Systems, pp. 957-962. , Seoul/Korea Oliveira, G.H.C., Da Rosa, A., Campello, R.J.G.B., MacHado, J.M., Amaral, W.C., An introduction to models based on Laguerre, Kautz and other related orthonormal functions - Part I: Linear and uncertain models (2011) International Journal of Modelling, Identification and Control, 14 (1-2) Passino, K.M., Yurkovich, S., (1997) Fuzzy Control, , Addison-Wesley Longman Inc., USA Pearson, R.K., (1999) Discrete-Time Dynamic Models, , Oxford University Press, New York, USA Pottmann, M., Seborg, D., Identification of non-linear process using reciprocal multiquadric functions (1992) Journal of Process Control, 2 (4), pp. 189-203 Rugh, W.J., (1981) Nonlinear System Theory: The Volterra/Wiener Approach, , The Johns Hopkins University Press, Baltimore, USA Rumelhart, D., McClelland, J., (1986) Parallel Distributed Processing, 1. , PDP Research Group MIT Press, Cambridge, MA, USA Saraswati, S., Chand, S., Neural network models for multi-step ahead prediction of air-fuel ratio in SI engines (2009) International Journal of Modelling, Identification and Control, 7 (3), pp. 263-274 Schetzen, M., (1980) The Volterra and Wiener Theories of Nonlinear Systems, , Krieger Publishing Company, Malabar, Florida, USA Sentoni, G., Agamennoni, O., Desages, A., Romagnoli, J., Approximate models for nonlinear process control (1996) AIChE Journal, 42 (8), pp. 2240-2250 Sentoni, G.B., Biegler, L.T., Guiver, J.B., Zhao, H., State-space nonlinear process modeling: Identification and universality (1998) AIChE Journal, 44 (10), pp. 2229-2239 Sjöberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P.-Y., Hjalmarsson, H., Juditsky, A., Nonlinear black-box modeling in system identification: A unified overview (1995) Automatica, 31 (12), pp. 1691-1724 Su, H.-T., McAvoy, T., Integration of multilayer perceptron networks and linear dynamic models: A Hammerstein modeling approach (1993) Ind. Eng. Chem. Res., 32 (9), pp. 1927-1936 Sugeno, M., Kang, G.T., Fuzzy modelling and control of multilayer incinerator (1986) Fuzzy Sets and Systems, 18 (3), pp. 329-346 Sugeno, M., Kang, G.T., Structure identification of fuzzy model (1988) Fuzzy Sets and Systems, 28 (1), pp. 15-33 Sugeno, M., Tanaka, K., Successive identification of a fuzzy model and its applications to prediction of a complex system (1991) Fuzzy Sets and Systems, 42 (3), pp. 315-334 Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control (1985) IEEE Trans. Systems, Man and Cybernetics, SMC-15, pp. 116-132 Takenaka, S., On the orthogonal functions and a new formula of interpolation (1925) Japanese Journal of Mathematics, 2, pp. 129-145 Van Den Hof, P.M.J., Heuberger, P.S.C., Bokor, J., System identification with generalized orthonormal basis functions (1995) Automatica, 31 (12), pp. 1821-1834 Abrahantes Vazquez, M.A., Agamennoni, O.E., Approximate models for nonlinear dynamical systems and their generalization properties (2001) Mathematical and Computer Modelling, 33 (8-9), pp. 965-986. , DOI 10.1016/S0895-7177(00)00293-4, PII S0895717700002934 Wang, L.-X., Mendel, J.M., Fuzzy basis functions, universal approximation and orthogonal least squares learning (1992) IEEE Trans. Neural Networks, 3 (5), pp. 807-814 Wiener, N., (1958) Nonlinear Problems in Random Theory, , MIT Press, Cambridge, MA, USA Yager, R.R., Filev, D.P., (1994) Essentials of Fuzzy Modeling and Control, , John Wiley & Sons, USA Zeng, X.-J., Singh, M.G., Approximation theory of fuzzy systems - SISO case (1994) IEEE Trans. Fuzzy Systems, 2 (2), pp. 162-176 Zeng, X.-J., Singh, M.G., Approximation theory of fuzzy systems - MIMO case (1995) IEEE Trans. Fuzzy Systems, 3 (2), pp. 219-235 Ziaei, K., Wang, D.W.L., Application of orthonormal basis functions for identification of flexible-link manipulators (2006) Control Engineering Practice, 14 (2), pp. 99-106. , DOI 10.1016/j.conengprac.2004.11.020, PII S0967066105000365