Abstract
This chapter introduces some fundamental concepts and definitions used throughout of the book. It shows that all concepts and methodologies developed for TP models in this book can readily be applied in qLPV and LMI based control theories and TS fuzzy model based concepts. This chapter also discusses the HOSVD and the quasi-HOSVD based canonical form of TP functions that will be used as a basic steps in various frameworks proposed in later chapters.
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References
P. Baranyi, Output feedback control of two-dimensional aeroelastic system. J. Guid. Control. Dyn. 29(3), 762–767 (2006)
P. Baranyi, The generalized TP model transformation for TS fuzzy model manipulation and generalized stability verification. IEEE Trans. Fuzzy Syst. 22(4), 934–948 (2014)
P. Baranyi, L. Szeidl, P. Várlaki, Y. Yam, Definition of the HOSVD based canonical form of polytopic dynamic models, in Proceedings of the 2006 IEEE International Conference on Mechatronics, Budapest, 3–5 July 2006, pp. 660–665
P. Baranyi, Y. Yam, P. Varlaki, Tensor Product Model Transformation in Polytopic Model-Based Control (CRC/Taylor & Francis Group, Boca Raton/London, 2013)
L. De Lathauwer, B. De Moor, J. Vandewalle, Dimensionality reduction in higher-order-only ICA, in Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, 1997, Banff, Alberta (1997), pp. 316–320
L. De Lathauwer, B. De Moor, J. Vandewalle, A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)
M. Ishteva, L. De Lathauwer, P. Absil, S. Van Huffel, Dimensionality reduction for higher-order tensors: algorithms and applications. Int. J. Pure Appl. Math. 42(3), 337 (2008)
L. Szeidl, P. Várlaki, HOSVD based canonical form for polytopic models of dynamic systems. J. Adv. Comput. Intell. Intell. Inf. 13(1), 52–60 (2009)
K. Tanaka, H.O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (Wiley-Interscience, New York, 2001)
D. Tikk, P. Baranyi, R.J. Patton, Approximation properties of TP model forms and its consequences to TPDC design framework. Asian J. Control 9(3), 221–231 (2007)
P. Várkonyi, D. Tikk, P. Korondi, P. Baranyi, A new algorithm for RNO-INO type tensor product model representation, in Proceedings of the IEEE 9th International Conference on Intelligent Engineering Systems (2005), pp. 263–266
Y. Yam, Fuzzy approximation via grid point sampling and singular value decomposition. IEEE Trans. Syst. Man Cybern. B Cybern. 27(6), 933–951 (1997)
Y. Yam, P. Baranyi, C.T. Yang, Reduction of fuzzy rule base via singular value decomposition. IEEE Trans. Fuzzy Syst. 7(2), 120–132 (1999)
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Baranyi, P. (2016). Basic Concepts. In: TP-Model Transformation-Based-Control Design Frameworks. Springer, Cham. https://doi.org/10.1007/978-3-319-19605-3_1
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DOI: https://doi.org/10.1007/978-3-319-19605-3_1
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