Abstract
Piecewise Bilinear (PB) model is found to be a good general approximator for nonlinear functions. This paper deals with the problem of optimal PB modeling where we apply the least squares method in order to minimize the modeling error.
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References
Khalil, H.K.: Nonlinear systems, vol. 122. Prentice-Hall, Upper Saddle River (2002)
Isidori, A.: Nonlinear control systems, vol. 1. Springer (1995)
Sontag, E.: Nonlinear regulation: The piecewise linear approach. IEEE Transactions on Automatic Control 26(2), 346–358 (1981)
Johansson, M., Rantzer, A.: Computation of piecewise quadratic lyapunov functions for hybrid systems. IEEE Transactions on Automatic Control 43(4), 555–559 (1998)
Grandin, H.: Fundamentals of the finite element method. Macmillan (1986)
Imura, J., Van Der Schaft, A.: Characterization of well-posedness of piecewise-linear systems. IEEE Transactions on Automatic Control 45(9), 1600–1619 (2000)
Sugeno, M.: On stability of fuzzy systems expressed by fuzzy rules with singleton consequents. IEEE Transactions on Fuzzy Systems 7(2), 201–224 (1999)
Tanaka, K., Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy Sets and Systems 45(2), 135–156 (1992)
Lee, C.H., Sugeno, M.: An extension of stability condition for a class of fuzzy systems with singleton consequents and its application to stabilizing control of general nonlinear systems. J. Japan Soc. Fuzzy Theory Syst. 12(2), 266–285 (2000)
Sugeno, M., Taniguchi, T.: On improvement of stability conditions for continuous mamdani-like fuzzy systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(1), 120–131 (2004)
Taniguchi, T., Sugeno, M.: Stabilization of nonlinear systems with piecewise bilinear models derived from fuzzy if-then rules with singletons. In: 2010 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–6. IEEE (2010)
Takagi, T., Sugeno, M.: Fuzzy identification of system and its applications to modelling and control. IEEE Trans. Syst., Man, and Cyber. 1, 5 (1985)
Tanaka, K., Wang, H.: Fuzzy control systems design and analysis: a linear matrix inequality approach. Wiley-Interscience (2001)
Vogt, M., Müller, N., Isermann, R.: On-line adaptation of grid-based look-up tables using a fast linear regression technique. Journal of Dynamic Systems, Measurement, and Control 126, 732 (2004)
Sugeno, M., Hirano, I., Nakamura, S., Kotsu, S.: Development of an intelligent unmanned helicopter. In: Proceedings of 1995 IEEE International Conference on International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium, Fuzzy Systems, vol. 5, pp. 33–34. IEEE (1995)
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Eciolaza, L., Sugeno, M. (2012). Optimal Piecewise Bilinear Modeling of Nonlinear Systems. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances on Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31709-5_10
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DOI: https://doi.org/10.1007/978-3-642-31709-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31708-8
Online ISBN: 978-3-642-31709-5
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