Nonuniform piecewise membership function approximation methods based robust tracking control design of T‐S fuzzy systems
For the stability analysis issue of a T‐S fuzzy system, improved piecewise membership functions dependent approach is proposed to reduce conservatism. Based on a least‐square method, the nonlinear membership functions are approximated by a series of decoupled polynomial functions. Then the piecewise...
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| Published in | International journal of robust and nonlinear control Vol. 32; no. 8; pp. 4980 - 5001 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Bognor Regis
Wiley Subscription Services, Inc
25.05.2022
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| Abstract | For the stability analysis issue of a T‐S fuzzy system, improved piecewise membership functions dependent approach is proposed to reduce conservatism. Based on a least‐square method, the nonlinear membership functions are approximated by a series of decoupled polynomial functions. Then the piecewise vertices are chosen by a newly proposed derivative‐integral nonuniform division approach. For the robust tracking control task, a series of convex robust stable conditions are obtained. Finally, a mass‐spring‐damper (MSD) simulation example is adopted to illustrate the effectiveness of the designed method. |
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| AbstractList | For the stability analysis issue of a T‐S fuzzy system, improved piecewise membership functions dependent approach is proposed to reduce conservatism. Based on a least‐square method, the nonlinear membership functions are approximated by a series of decoupled polynomial functions. Then the piecewise vertices are chosen by a newly proposed derivative‐integral nonuniform division approach. For the robust tracking control task, a series of convex robust stable conditions are obtained. Finally, a mass‐spring‐damper (MSD) simulation example is adopted to illustrate the effectiveness of the designed method. |
| Author | Xie, Wen‐Bo Zhang, Jian Xu, Bo‐Lin Peng, Chen |
| Author_xml | – sequence: 1 givenname: Wen‐Bo orcidid: 0000-0002-3325-2779 surname: Xie fullname: Xie, Wen‐Bo email: daniel_xwb@163.com organization: Shanghai University – sequence: 2 givenname: Bo‐Lin surname: Xu fullname: Xu, Bo‐Lin organization: Shanghai University – sequence: 3 givenname: Chen surname: Peng fullname: Peng, Chen organization: Shanghai University – sequence: 4 givenname: Jian surname: Zhang fullname: Zhang, Jian organization: Harbin Engineering University |
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| Notes | Funding information the National Natural Science Foundation of China, 61803127; 61803114; 61833011; the Natural Science Foundation in Heilongjiang Province, YQ2019F012; the Fundamental Research Foundation for Universities of Heilongjiang Province, China, 2019‐KYYWF‐0210 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
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| SubjectTerms | Apexes Approximation conservatism Control tasks Derivatives Functions (mathematics) Fuzzy systems Integrals Mathematical analysis Polynomials Robust control Stability analysis Takagi‐Sugeno fuzzy systems Tracking control |
| Title | Nonuniform piecewise membership function approximation methods based robust tracking control design of T‐S fuzzy systems |
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