Polytopic and TS models are nowhere dense in the approximation model space

D. Tikk, P. Baranyi, Ron J. Patton

Research output: Conference contribution

26 Citations (Scopus)

Abstract

We show in this paper that the set of functions, consisting of polytopic or TS models constructed from finite number of components, is nowhere dense in the approximation model space, if that is defined as a subset of continuous functions. This topological notion means that the given set of functions lies "almost discretely" in the space of approximated functions. As a consequence, by means of the mentioned models we cannot approximate in general continuous functions arbitrarily well, if the number of components are restricted. Thus, only functions satisfying certain conditions can be approximated by such models, or alternatively, we need unbounded number of components. The possible solutions are outlined in the paper.

Original languageEnglish
Title of host publicationProceedings of the IEEE International Conference on Systems, Man and Cybernetics
EditorsA. El Kamel, K. Mellouli, P. Borne
Pages150-153
Number of pages4
Volume7
Publication statusPublished - 2002
Event2002 IEEE International Conference on Systems, Man and Cybernetics - Yasmine Hammamet, Tunisia
Duration: okt. 6 2002okt. 9 2002

Other

Other2002 IEEE International Conference on Systems, Man and Cybernetics
CountryTunisia
CityYasmine Hammamet
Period10/6/0210/9/02

Fingerprint

Set theory

ASJC Scopus subject areas

  • Hardware and Architecture
  • Control and Systems Engineering

Cite this

Tikk, D., Baranyi, P., & Patton, R. J. (2002). Polytopic and TS models are nowhere dense in the approximation model space. In A. El Kamel, K. Mellouli, & P. Borne (Eds.), Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (Vol. 7, pp. 150-153)

Polytopic and TS models are nowhere dense in the approximation model space. / Tikk, D.; Baranyi, P.; Patton, Ron J.

Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. ed. / A. El Kamel; K. Mellouli; P. Borne. Vol. 7 2002. p. 150-153.

Research output: Conference contribution

Tikk, D, Baranyi, P & Patton, RJ 2002, Polytopic and TS models are nowhere dense in the approximation model space. in A El Kamel, K Mellouli & P Borne (eds), Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. vol. 7, pp. 150-153, 2002 IEEE International Conference on Systems, Man and Cybernetics, Yasmine Hammamet, Tunisia, 10/6/02.
Tikk D, Baranyi P, Patton RJ. Polytopic and TS models are nowhere dense in the approximation model space. In El Kamel A, Mellouli K, Borne P, editors, Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. Vol. 7. 2002. p. 150-153
Tikk, D. ; Baranyi, P. ; Patton, Ron J. / Polytopic and TS models are nowhere dense in the approximation model space. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. editor / A. El Kamel ; K. Mellouli ; P. Borne. Vol. 7 2002. pp. 150-153
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