Abstract
The tensor product model transformation (TPMT) is an emerging numerical framework of Takagi-Sugeno (T-S) fuzzy (or polytopic) system modeling for LMI-based system control design. A nested TPMT (NTPMT) is proposed in this paper, which merges the dimensions of the tensors and performs the TPMT iteratively. The resultant fuzzy model is in a multi-level nested tensor product (TP) structure. The vertex tensor obtained by NTPMT has less dimensions than the original TPMT results so that the number of vertices or fuzzy rules, which has been the main bottleneck for further application of the TPMT in higher dimensional systems, is expected to decrease manyfold. It is also proved that the NTPMT contains the hierarchical fuzzy logic, which means that the NTPMT is capable of conducting hierarchical fuzzy modeling and reduction. Furthermore, because the inclusion of multiple TPMTs is prone to augment the conservativeness of the resultant fuzzy model, a suboptimal convex hull rectification algorithm for the TPMT is developed based on a newly defined tightness measure and then extended to render the NTPMT as less conservative as possible. Finally, numerical simulations on two real physical systems (2- and 4-parameter-dimension) are verified to demonstrate the performance of the methods.
| Original language | English |
|---|---|
| Article number | 8400489 |
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | IEEE Transactions on Fuzzy Systems |
| Volume | 27 |
| Issue number | 1 |
| Early online date | 29 Jun 2018 |
| DOIs | |
| Publication status | Published - Jan 2019 |
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A Nested Tensor Product Model Transformation. / Yu, Yin; Li, Zhen; Liu, Xiangdong; Hirota, Kaoru; Chen, Xi; Fernando, Tyrone; Iu, Herbert.
In: IEEE Transactions on Fuzzy Systems, Vol. 27, No. 1, 8400489, 01.2019, p. 1-15.Research output: Contribution to journal › Article
TY - JOUR
T1 - A Nested Tensor Product Model Transformation
AU - Yu, Yin
AU - Li, Zhen
AU - Liu, Xiangdong
AU - Hirota, Kaoru
AU - Chen, Xi
AU - Fernando, Tyrone
AU - Iu, Herbert
PY - 2019/1
Y1 - 2019/1
N2 - The tensor product model transformation (TPMT) is an emerging numerical framework of Takagi-Sugeno (T-S) fuzzy (or polytopic) system modeling for LMI-based system control design. A nested TPMT (NTPMT) is proposed in this paper, which merges the dimensions of the tensors and performs the TPMT iteratively. The resultant fuzzy model is in a multi-level nested tensor product (TP) structure. The vertex tensor obtained by NTPMT has less dimensions than the original TPMT results so that the number of vertices or fuzzy rules, which has been the main bottleneck for further application of the TPMT in higher dimensional systems, is expected to decrease manyfold. It is also proved that the NTPMT contains the hierarchical fuzzy logic, which means that the NTPMT is capable of conducting hierarchical fuzzy modeling and reduction. Furthermore, because the inclusion of multiple TPMTs is prone to augment the conservativeness of the resultant fuzzy model, a suboptimal convex hull rectification algorithm for the TPMT is developed based on a newly defined tightness measure and then extended to render the NTPMT as less conservative as possible. Finally, numerical simulations on two real physical systems (2- and 4-parameter-dimension) are verified to demonstrate the performance of the methods.
AB - The tensor product model transformation (TPMT) is an emerging numerical framework of Takagi-Sugeno (T-S) fuzzy (or polytopic) system modeling for LMI-based system control design. A nested TPMT (NTPMT) is proposed in this paper, which merges the dimensions of the tensors and performs the TPMT iteratively. The resultant fuzzy model is in a multi-level nested tensor product (TP) structure. The vertex tensor obtained by NTPMT has less dimensions than the original TPMT results so that the number of vertices or fuzzy rules, which has been the main bottleneck for further application of the TPMT in higher dimensional systems, is expected to decrease manyfold. It is also proved that the NTPMT contains the hierarchical fuzzy logic, which means that the NTPMT is capable of conducting hierarchical fuzzy modeling and reduction. Furthermore, because the inclusion of multiple TPMTs is prone to augment the conservativeness of the resultant fuzzy model, a suboptimal convex hull rectification algorithm for the TPMT is developed based on a newly defined tightness measure and then extended to render the NTPMT as less conservative as possible. Finally, numerical simulations on two real physical systems (2- and 4-parameter-dimension) are verified to demonstrate the performance of the methods.
KW - computational complexity
KW - Computational modeling
KW - conservativeness reduction
KW - Control design
KW - Fuzzy logic
KW - linear matrix inequalities (LMIs)
KW - Mathematical model
KW - Matrix decomposition
KW - Numerical models
KW - Takagi-Sugeno (T-S) model
KW - Tensile stress
KW - Tensor product (TP) model transformation
UR - http://www.scopus.com/inward/record.url?scp=85049328260&partnerID=8YFLogxK
U2 - 10.1109/TFUZZ.2018.2851575
DO - 10.1109/TFUZZ.2018.2851575
M3 - Article
VL - 27
SP - 1
EP - 15
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
SN - 1063-6706
IS - 1
M1 - 8400489
ER -