Static Output-Feedback Tracking Control for Positive Polynomial Fuzzy Systems

Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this article, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transformin...

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Published inIEEE transactions on fuzzy systems Vol. 30; no. 6; pp. 1722 - 1733
Main Authors Fu, Lining, Lam, H. K., Liu, Fucai, Xiao, Bo, Zhong, Zhixiong
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
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Analytical models
Control systems
Convexity
Design improvements
Fuzzy control
Fuzzy systems
imperfectly matched premises
membership-function-dependent stability analysis
Model-based systems
Nonlinear control
Nonlinear systems
Observers
Output feedback
Polynomials
positive polynomial fuzzy-model-based (PPFMB)
scalar implantation transformation (SIT)
Stability analysis
static output-feedback tracking control
Systems analysis
Tracking control
Online AccessGet full text
ISSN1063-6706
1941-0034
DOI10.1109/TFUZZ.2021.3065521

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Abstract Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this article, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transforming the nonconvexity conditions when both positive and stability conditions exist into convexity conditions that can be solved by the convex programming techniques. This article focuses on the static output-feedback tracking control issue of positive polynomial fuzzy-model-based systems. The purpose of the tracking control is to design an appropriate static output feedback polynomial fuzzy controller which can drive the system states of the nonlinear plant to follow those of a stable reference model subject to an <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> performance. The concept of imperfectly matched premises is employed to enhance the design and implementation flexibility. To circumvent the problem of nonconvex stability conditions, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a novel scalar implantation transformation technique. Besides, the partition approximation of membership functions with local information of membership functions is used to promote stability analysis and synthesis of controllers. The positive and relaxed stability conditions for static output-feedback tracking control with <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> performance being taken into account are obtained in terms of sum-of-squares. Finally, a simulation example is presented to verify the effectiveness of the proposed tracking control approach.
AbstractList Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this article, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transforming the nonconvexity conditions when both positive and stability conditions exist into convexity conditions that can be solved by the convex programming techniques. This article focuses on the static output-feedback tracking control issue of positive polynomial fuzzy-model-based systems. The purpose of the tracking control is to design an appropriate static output feedback polynomial fuzzy controller which can drive the system states of the nonlinear plant to follow those of a stable reference model subject to an [Formula Omitted] performance. The concept of imperfectly matched premises is employed to enhance the design and implementation flexibility. To circumvent the problem of nonconvex stability conditions, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a novel scalar implantation transformation technique. Besides, the partition approximation of membership functions with local information of membership functions is used to promote stability analysis and synthesis of controllers. The positive and relaxed stability conditions for static output-feedback tracking control with [Formula Omitted] performance being taken into account are obtained in terms of sum-of-squares. Finally, a simulation example is presented to verify the effectiveness of the proposed tracking control approach.
Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this article, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transforming the nonconvexity conditions when both positive and stability conditions exist into convexity conditions that can be solved by the convex programming techniques. This article focuses on the static output-feedback tracking control issue of positive polynomial fuzzy-model-based systems. The purpose of the tracking control is to design an appropriate static output feedback polynomial fuzzy controller which can drive the system states of the nonlinear plant to follow those of a stable reference model subject to an <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> performance. The concept of imperfectly matched premises is employed to enhance the design and implementation flexibility. To circumvent the problem of nonconvex stability conditions, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a novel scalar implantation transformation technique. Besides, the partition approximation of membership functions with local information of membership functions is used to promote stability analysis and synthesis of controllers. The positive and relaxed stability conditions for static output-feedback tracking control with <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> performance being taken into account are obtained in terms of sum-of-squares. Finally, a simulation example is presented to verify the effectiveness of the proposed tracking control approach.
Author Lam, H. K.
Zhong, Zhixiong
Xiao, Bo
Fu, Lining
Liu, Fucai
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Snippet Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and...
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Analytical models
Control systems
Convexity
Design improvements
Fuzzy control
Fuzzy systems
imperfectly matched premises
membership-function-dependent stability analysis
Model-based systems
Nonlinear control
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Observers
Output feedback
Polynomials
positive polynomial fuzzy-model-based (PPFMB)
scalar implantation transformation (SIT)
Stability analysis
static output-feedback tracking control
Systems analysis
Tracking control
Title Static Output-Feedback Tracking Control for Positive Polynomial Fuzzy Systems
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