On the approximation properties of TP model forms

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

The tensor product (TP) based models have been applied widely in approximation theory and approximation techniques. Recently, a controller design framework working on dynamic systems has also been established based on TP model transformation combined with Linear Matrix Inequalities (LMI) within Parallel Distributed Compensation (PDC) framework. The effectiveness of the control design framework strongly depends on the approximation property of the TP model used. Therefore, the primary aim of this paper is to investigate the approximation capabilities of dynamic TP model. It is shown that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. This drawback necessitates the application of trade-off techniques between accuracy and complexity of TP form. Such requirements are very difficult to consider in the analytical framework, but TP model transformation offers an easy way to deal with them.

Original languageEnglish
Title of host publicationIEEE International Conference on Fuzzy Systems
Pages1069-1074
Number of pages6
Volume2
Publication statusPublished - 2004
Event2004 IEEE International Conference on Fuzzy Systems - Proceedings - Budapest, Hungary
Duration: Jul 25 2004Jul 29 2004

Other

Other2004 IEEE International Conference on Fuzzy Systems - Proceedings
CountryHungary
CityBudapest
Period7/25/047/29/04

Fingerprint

Tensors
Approximation theory
Linear matrix inequalities
Dynamical systems
Controllers

ASJC Scopus subject areas

  • Software
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

Cite this

Tikk, D., Baranyi, P., & Patton, R. J. (2004). On the approximation properties of TP model forms. In IEEE International Conference on Fuzzy Systems (Vol. 2, pp. 1069-1074)

On the approximation properties of TP model forms. / Tikk, D.; Baranyi, P.; Patton, Ron J.

IEEE International Conference on Fuzzy Systems. Vol. 2 2004. p. 1069-1074.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tikk, D, Baranyi, P & Patton, RJ 2004, On the approximation properties of TP model forms. in IEEE International Conference on Fuzzy Systems. vol. 2, pp. 1069-1074, 2004 IEEE International Conference on Fuzzy Systems - Proceedings, Budapest, Hungary, 7/25/04.
Tikk D, Baranyi P, Patton RJ. On the approximation properties of TP model forms. In IEEE International Conference on Fuzzy Systems. Vol. 2. 2004. p. 1069-1074
Tikk, D. ; Baranyi, P. ; Patton, Ron J. / On the approximation properties of TP model forms. IEEE International Conference on Fuzzy Systems. Vol. 2 2004. pp. 1069-1074
@inproceedings{5543701f385048ca89956df0a20cd7bd,
title = "On the approximation properties of TP model forms",
abstract = "The tensor product (TP) based models have been applied widely in approximation theory and approximation techniques. Recently, a controller design framework working on dynamic systems has also been established based on TP model transformation combined with Linear Matrix Inequalities (LMI) within Parallel Distributed Compensation (PDC) framework. The effectiveness of the control design framework strongly depends on the approximation property of the TP model used. Therefore, the primary aim of this paper is to investigate the approximation capabilities of dynamic TP model. It is shown that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. This drawback necessitates the application of trade-off techniques between accuracy and complexity of TP form. Such requirements are very difficult to consider in the analytical framework, but TP model transformation offers an easy way to deal with them.",
author = "D. Tikk and P. Baranyi and Patton, {Ron J.}",
year = "2004",
language = "English",
volume = "2",
pages = "1069--1074",
booktitle = "IEEE International Conference on Fuzzy Systems",

}

TY - GEN

T1 - On the approximation properties of TP model forms

AU - Tikk, D.

AU - Baranyi, P.

AU - Patton, Ron J.

PY - 2004

Y1 - 2004

N2 - The tensor product (TP) based models have been applied widely in approximation theory and approximation techniques. Recently, a controller design framework working on dynamic systems has also been established based on TP model transformation combined with Linear Matrix Inequalities (LMI) within Parallel Distributed Compensation (PDC) framework. The effectiveness of the control design framework strongly depends on the approximation property of the TP model used. Therefore, the primary aim of this paper is to investigate the approximation capabilities of dynamic TP model. It is shown that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. This drawback necessitates the application of trade-off techniques between accuracy and complexity of TP form. Such requirements are very difficult to consider in the analytical framework, but TP model transformation offers an easy way to deal with them.

AB - The tensor product (TP) based models have been applied widely in approximation theory and approximation techniques. Recently, a controller design framework working on dynamic systems has also been established based on TP model transformation combined with Linear Matrix Inequalities (LMI) within Parallel Distributed Compensation (PDC) framework. The effectiveness of the control design framework strongly depends on the approximation property of the TP model used. Therefore, the primary aim of this paper is to investigate the approximation capabilities of dynamic TP model. It is shown that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. This drawback necessitates the application of trade-off techniques between accuracy and complexity of TP form. Such requirements are very difficult to consider in the analytical framework, but TP model transformation offers an easy way to deal with them.

UR - http://www.scopus.com/inward/record.url?scp=11144269737&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11144269737&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:11144269737

VL - 2

SP - 1069

EP - 1074

BT - IEEE International Conference on Fuzzy Systems

ER -