H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems

Xiaojie SU; Ligang WU; Peng SHI; Yong-Duan SONG

doi:10.1109/TSMCB.2012.2195723

H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems

Xiaojie SU^*
, Ligang WU
, Peng SHI
, Yong-Duan SONG^*

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

180 Citations (Scopus)

Abstract

This paper is concerned with the problem of H∞ model reduction for Takagi–Sugeno (T–S) fuzzy stochastic systems. For a given mean-square stable T–S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H∞ performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Original language	English
Article number	6202714
Pages (from-to)	1574-1585
Number of pages	12
Journal	IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume	42
Issue number	6
Early online date	23 May 2012
DOIs	https://doi.org/10.1109/TSMCB.2012.2195723
Publication status	Published - Dec 2012
Externally published	Yes

Bibliographical note

This paper was recommended by Editor E. Santos, Jr.

Funding

This work was supported in part by the National Key Basic Research Program under Grant 2012CB215202, by the 111 Project under Grant B12018, by the National Natural Science Foundation of China under Grants 61174126 and 61174058, by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61021002, by the Natural Science Foundation of Heilongjiang Province of China under Grants QC2009C58 and F201002, by the Program for New Century Excellent Talents in University under Grant NCET-09-0063, and by the Fundamental Research Funds for the Central Universities under Grant HIT.BRET2.2010011.

Keywords

Cone complementary linearization
H ∞ model reduction
stochastic systems
Takagi-Sugeno (T-S) fuzzy systems

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10.1109/TSMCB.2012.2195723

Cite this

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title = "H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems",

abstract = "This paper is concerned with the problem of H∞ model reduction for Takagi–Sugeno (T–S) fuzzy stochastic systems. For a given mean-square stable T–S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H∞ performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.",

keywords = "Cone complementary linearization, H ∞ model reduction, stochastic systems, Takagi-Sugeno (T-S) fuzzy systems",

author = "Xiaojie SU and Ligang WU and Peng SHI and Yong-Duan SONG",

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AU - SHI, Peng

AU - SONG, Yong-Duan

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N2 - This paper is concerned with the problem of H∞ model reduction for Takagi–Sugeno (T–S) fuzzy stochastic systems. For a given mean-square stable T–S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H∞ performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

AB - This paper is concerned with the problem of H∞ model reduction for Takagi–Sugeno (T–S) fuzzy stochastic systems. For a given mean-square stable T–S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H∞ performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

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H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems

Abstract

Bibliographical note

Funding

Keywords

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