Tensor product model transformation: Difference between revisions

Revision as of 11:32, 29 January 2018

Revision as of 17:48, 29 January 2018

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|pages = 387–400

|doi=10.1109/tie.2003.822037

}}</ref><ref>P. Baranyi (2016). "TP-Model Transformation-Based-Control Design Frameworks". P. Baranyi: „TP-Model Transformation-Based-Control Design Frameworks”, Springer International, Publishing Switzerland,p. 258. (eBook 978-3-319-19605-3, 978-3-319-19604-6, doi: 10.1007/978-3-319-19605-3, httphttps://www.springer.com/gp/book/9783319196046)</ref><ref>P. Baranyi: „The Generalized TP Model Transformation for TS Fuzzy Model Manipulation and Generalized Stability Verification” in IEEE Trans. on Fuzzy Systems, August 2014, Vol. 22, No. 4, pp. 934-948. (1063- 6706, doi: 10.1109/TFUZZ.2013.2278982)</ref>

<ref name=compind>{{cite journal

|author = P. Baranyi and D. Tikk and Y. Yam and R. J. Patton

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A free [[MATLAB]] implementation of the TP model transformation can be downloaded at [https://nas.mistems.hu:5001/sharing/6IIIPxmtf] or an old version of the toolbox is aviable at [[MATLAB]] Central [http://www.mathworks.com/matlabcentral/fileexchange/25514-tp-tool]. A key underpinning of the transformation is the [[higher-order singular value decomposition]].<ref name=Lath00 />

Besides being a transformation of functions, the TP model transformation is also a new concept in qLPV based control which plays a central role in the providing a valuable means of bridging between identification and polytopic systems theories. The TP model transformation is uniquely effective in manipulating the convex hull of polytopic forms, and, as a result has revealed and proved the fact that convex hull manipulation is a necessary and crucial step in achieving optimal solutions and decreasing conservativeness<ref>A.Szollosi, and Baranyi, P. (2016). Influence of the Tensor Product model representation of qLPV models on the feasibility of Linear Matrix Inequality. Asian Journal of Control, 18(4), 1328-1342</ref><ref>A. Szöllősi and P. Baranyi: „Improved control performance of the 3‐DoF aeroelastic wing section: a TP model based 2D parametric control performance optimization.” in Asian Journal of Control, 19(2), 450-466. / 2017</ref><ref>P. Baranyi (2016). "TP-Model Transformation-Based-Control Design Frameworks". P. Baranyi: „TP-Model Transformation-Based-Control Design Frameworks”, Springer International, Publishing Switzerland,p. 258. (eBook 978-3-319-19605-3, 978-3-319-19604-6, doi: 10.1007/978-3-319-19605-3, httphttps://www.springer.com/gp/book/9783319196046)</ref> in modern LMI based control theory. Thus, although it is a transformation in a mathematical sense, it has established a conceptually new direction in control theory and has laid the ground for further new approaches towards optimality. Further details on the control theoretical aspects of the TP model transformation can be found here: [[TP model transformation in control theory]].

The TP model transformation motivated the definition of the "HOSVD canonical form of TP functions",<ref name=canon1>{{cite book