Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems

In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a Takagi-Sugeno (T-S) fuzzy PDS is first proposed to model an NPDS. Then, the T-S fuzzy PDS can be represented by a finite-dimensional T-...

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Published inIEEE transactions on fuzzy systems Vol. 17; no. 5; pp. 1025 - 1043
Main Authors Chen, Bor-Sen, Chang, Yu-Te
Format Journal Article
LanguageEnglish
Published New York IEEE 01.10.2009
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Asymptotic properties
Attenuation measurement
Control design
Design engineering
Fuzzy
Fuzzy approach
Fuzzy control
Fuzzy logic
fuzzy partial differential systems (PDSs)
Fuzzy set theory
Fuzzy systems
Mathematical model
Mathematical models
Matlab
Moment methods
Noise measurement
Noise robustness
nonlinear partial differential systems (NPDSs)
Nonlinearity
Robust control
robust H_{\infty } control
robust stabilization
robust Takagi-Sugeno (T-S) fuzzy observer-based controller
Studies
Takagi-Sugeno model
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Abstract In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a Takagi-Sugeno (T-S) fuzzy PDS is first proposed to model an NPDS. Then, the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy subsystem in residual mode. Therefore, the NPDS can be partitioned into a finite-dimensional T-S fuzzy slow state-space subsystem to be controlled and a coupled infinite-dimensional fast residual subsystem to be tolerated. Based on the small-gain theorem, a robust fuzzy observer-based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the NPDS. Furthermore, based on the dissipative theory, an Hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of NPDSs. The MATLAB linear matrix inequality toolbox can be employed to efficiently solve the optimal Hinfin fuzzy observer-based control design problem of NPDSs. Finally, a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer-based control method for the perturbative NPDSs.
AbstractList In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a Takagi-Sugeno (T-S) fuzzy PDS is first proposed to model an NPDS. Then, the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy subsystem in residual mode. Therefore, the NPDS can be partitioned into a finite-dimensional T-S fuzzy slow state-space subsystem to be controlled and a coupled infinite-dimensional fast residual subsystem to be tolerated. Based on the small-gain theorem, a robust fuzzy observer-based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the NPDS. Furthermore, based on the dissipative theory, an Hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of NPDSs. The MATLAB linear matrix inequality toolbox can be employed to efficiently solve the optimal Hinfin fuzzy observer-based control design problem of NPDSs. Finally, a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer-based control method for the perturbative NPDSs.
[...] the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy subsystem in residual mode. [...] the NPDS can be partitioned into a finite-dimensional T-S fuzzy slow state-space subsystem to be controlled and a coupled infinite-dimensional fast residual subsystem to be tolerated.
Author Yu-Te Chang
Bor-Sen Chen
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Snippet In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a...
[...] the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Publisher
StartPage 1025
SubjectTerms Asymptotic properties
Attenuation measurement
Control design
Design engineering
Fuzzy
Fuzzy approach
Fuzzy control
Fuzzy logic
fuzzy partial differential systems (PDSs)
Fuzzy set theory
Fuzzy systems
Mathematical model
Mathematical models
Matlab
Moment methods
Noise measurement
Noise robustness
nonlinear partial differential systems (NPDSs)
Nonlinearity
Robust control
robust H_{\infty } control
robust stabilization
robust Takagi-Sugeno (T-S) fuzzy observer-based controller
Studies
Takagi-Sugeno model
Title Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems
URI https://ieeexplore.ieee.org/document/4812065
https://www.proquest.com/docview/912379332
https://search.proquest.com/docview/875083697
Volume 17
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