Abstract
Fuzzy modeling of dynamical systems can be viewed as an interpolation of a collection of linear models where the interpolation coefficients depend on set membership functions. The fuzzy interference applies only when the membership functions intersect otherwise only one model is valid. The approach presented in this paper models the intersections with an uncertainty measure reducing the overall fuzzy model to Piecewise Affine (PWA) description, over-approximating the original fuzzy model. Once such an approximation is calculated, existing algorithms can be applied which yield controllers guaranteeing closed-loop stability. Since the PWA model over-approximates a given fuzzy model, if such a controller is calculated, it guarantees stability of the original fuzzy model as well.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Vasičkaninová, A., Bakošová, M.: Fuzzy modelling and identification of the chemical technological processes. In: Krejčí, S. (ed.) Proc. 7. Int. Scientific-Tehnical Conf. Process Control 2006 (June 13-16 2006)
Allgöwer, F., Zheng, A. (eds.): Nonlinear Model Predictive Control. Birkhäuser (2000)
Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35(3), 407–427 (1999)
Clarke, D.W., Mohtadi, C., Tuffs, P.S.: Generalized predictive control – Parts I-II. Automatica, 23(2) (1987)
Cutler, C.R., Ramaker, B.L: Dynamic matrix control – a computer control algorithm. In: Proceedings, Joint American Control Conference, San Francisco, California (1980)
Espinosa, J.J., Hadjili, M., Wertz, V., Vandewalle, J.: Predictive Control Using Fuzzy Models-Comparative Study. In: Proc. of the European Control Conference, Karlsruhe, Germany (August, September 1999)
Grieder, P., Kvasnica, M., Baotic, M., Morari, M.: Stabilizing low complexity feedback control of constrained piecewise affine systems. Automatica 41(10), 1683–1694 (2005)
He, M., Cai, W.-J., Li, S.-Y.: Multiple fuzzy model-based temperature predictive control for HVAC systems. Information Sciences 169(1-2), 155–174 (2005)
Khaber, F., Zehar, K., Hamzaoui, A.: State Feedback Controller Design via Takagi-Sugeno Fuzzy Model: LMI Approach. International Journal of Computational Intelligence, 2(3) (2005)
Kosko, B.: Fuzzy systems as universal approximators. In: Proceedings FUZZ’IEEE’92, San Diego, California, pp. 1153–1162 (1992)
Kouvaritakis, B., Cannon, M. (eds.): Nonlinear predictive control: theory and practice. IEE Control Engineering series (2001)
Li, J., Wang, H.O., Bushnell, L., Hong, Y.: A Fuzzy Logic Approach to Optimal Controlof Nonlinear Systems. International Journal of Fuzzy Systems 2(3), 153–163 (2000)
Li, N., Li, S.-Y., Xi, Y.-G.: Multi-model predictive control based on the Takagi-Sugeno fuzzy models: a case study. Information Sciences 165(3-4), 247–263 (2004)
Maciejowski, J.M.: Predictive Control with Constraints. Prentice-Hall, Englewood Cliffs (2002)
Prett, D.M., Garcia, C.E.: Fundamental Process Control. Butterworths, Boston (1988)
Raković, S.V., Grieder, P., Kvasnica, M., Mayne, D.Q., Morari, M.: Computation of Invariant Sets for Piecewise Affine Discrete Time Systems subject to Bounded Disturbances. In: Proceeding of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, December 2004, pp. 1418–1423 (2004)
Suard, R., Löfberg, J., Grieder, P., Kvasnica, M., Morari, M.: Efficient Computation of Controller Partitions in Multi-Parametric Programming. In: IEEE Conference on Decision and Control, Bahamas, December 2004, IEEE Computer Society Press, Los Alamitos (2004)
Takagi, T., Sugeno, M.: Fuzzy identications of fuzzy systems and its applications to modelling and control. IEEE Trans. Systems Man and Cybernetics 15, 116–132 (1985)
Yoneyama, J.: Robust stability and stabilization for uncertain Takagi-Sugeno fuzzy time-delay systems. Fuzzy Sets and Systems 158(2), 115–134 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Herceg, M., Kvasnica, M., Fikar, M. (2007). Transformation of Fuzzy Takagi-Sugeno Models into Piecewise Affine Models. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds) Rough Sets and Intelligent Systems Paradigms. RSEISP 2007. Lecture Notes in Computer Science(), vol 4585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73451-2_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-73451-2_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73450-5
Online ISBN: 978-3-540-73451-2
eBook Packages: Computer ScienceComputer Science (R0)