Model Reduction of Discrete-Time Interval Type-2 T-S Fuzzy Systems
This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems, which represent the discrete-time nonlinear systems subject to uncertainty. With the use of IT2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured...
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| Published in | IEEE transactions on fuzzy systems Vol. 26; no. 6; pp. 3545 - 3554 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.12.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Online Access | Get full text |
| ISSN | 1063-6706 1941-0034 |
| DOI | 10.1109/TFUZZ.2018.2836353 |
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| Abstract | This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems, which represent the discrete-time nonlinear systems subject to uncertainty. With the use of IT2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured by the lower and upper membership functions. For a given high-order discrete-time IT2 T-S fuzzy system, the purpose is to find a lower dimensional system to approximate the original system. To achieve the approximation performance, an <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_\infty</tex-math></inline-formula> norm is used to suppress the error between the original system and its simplified system. By introducing a membership-functions-dependent technique and applying a convex linearization method, a membership-functions-dependent condition, which takes the information of membership functions into account, is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system. All the obtained theorems are represented as in the form of linear matrix inequalities. Finally, simulation results are demonstrated to show the effectiveness of the derived results. |
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| AbstractList | This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy systems, which represent the discrete-time nonlinear systems subject to uncertainty. With the use of IT2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured by the lower and upper membership functions. For a given high-order discrete-time IT2 T–S fuzzy system, the purpose is to find a lower dimensional system to approximate the original system. To achieve the approximation performance, an [Formula Omitted] norm is used to suppress the error between the original system and its simplified system. By introducing a membership-functions-dependent technique and applying a convex linearization method, a membership-functions-dependent condition, which takes the information of membership functions into account, is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system. All the obtained theorems are represented as in the form of linear matrix inequalities. Finally, simulation results are demonstrated to show the effectiveness of the derived results. This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems, which represent the discrete-time nonlinear systems subject to uncertainty. With the use of IT2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured by the lower and upper membership functions. For a given high-order discrete-time IT2 T-S fuzzy system, the purpose is to find a lower dimensional system to approximate the original system. To achieve the approximation performance, an <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_\infty</tex-math></inline-formula> norm is used to suppress the error between the original system and its simplified system. By introducing a membership-functions-dependent technique and applying a convex linearization method, a membership-functions-dependent condition, which takes the information of membership functions into account, is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system. All the obtained theorems are represented as in the form of linear matrix inequalities. Finally, simulation results are demonstrated to show the effectiveness of the derived results. |
| Author | Zeng, Yi Lam, Hak-Keung Wu, Ligang |
| Author_xml | – sequence: 1 givenname: Yi orcidid: 0000-0002-7708-7146 surname: Zeng fullname: Zeng, Yi email: yi-zeng1991@outlook.com organization: Department of Informatics, King's College London, London, U.K – sequence: 2 givenname: Hak-Keung orcidid: 0000-0002-6572-7265 surname: Lam fullname: Lam, Hak-Keung email: hak-keung.lam@kcl.ac.uk organization: Department of Informatics, King's College London, London, U.K – sequence: 3 givenname: Ligang orcidid: 0000-0001-8198-5267 surname: Wu fullname: Wu, Ligang email: ligangwu@hit.edu.cn organization: Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, China |
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| Snippet | This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems, which represent the discrete-time... This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy systems, which represent the discrete-time... |
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| SubjectTerms | Computer simulation Convex linearization method Discrete time systems discrete-time interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy system Fuzzy sets Fuzzy systems Linear matrix inequalities Linearization Mathematical analysis Mathematical models Matrix methods membership-functions-dependent technique Model reduction Nonlinear systems Reduced order systems Symmetric matrices Uncertainty |
| Title | Model Reduction of Discrete-Time Interval Type-2 T-S Fuzzy Systems |
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