A Novel Mixed Control Approach for Fuzzy Systems via Membership Functions Online Learning Policy

This article focuses on the <inline-formula><tex-math notation="LaTeX">\mathcal {L}_{2}-\mathcal {L} _{\infty}/ \mathcal {H}_{\infty}</tex-math></inline-formula> optimization control issue for a family of nonlinear plants by Takagi-Sugeno (T-S) fuzzy approach with a...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 30; no. 9; pp. 3812 - 3822
Main Authors: Pan, Yingnan, Li, Qi, Liang, Hongjing, Lam, Hak-Keung
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Actuator failure
Actuators
Algorithms
Control systems
Cost function
Distance learning
dynamic output feedback control
Dynamic stability
Feedback control
Fuzzy control
Fuzzy sets
Fuzzy systems
Indexes
learning algorithm
Machine learning
Matching
membership functions (MFs) online optimization
Optimization
Output feedback
Performance indices
Real-time systems
Takagi-Sugeno model
Takagi–Sugeno (T–S) fuzzy model
Task analysis
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary:This article focuses on the <inline-formula><tex-math notation="LaTeX">\mathcal {L}_{2}-\mathcal {L} _{\infty}/ \mathcal {H}_{\infty}</tex-math></inline-formula> optimization control issue for a family of nonlinear plants by Takagi-Sugeno (T-S) fuzzy approach with actuator failure. First, considering unmeasurable system states, sufficient criteria for devising fuzzy imperfect premise matching dynamic output feedback controller to maintain asymptotic stability while guaranteeing a mixed performance for T-S fuzzy systems are provided. Therewith, in the light of feasible areas of dynamic output feedback controller membership functions (MFs), a new MFs online learning policy using gradient descent algorithm is proposed to learn the real-time values of MFs to acquire a better <inline-formula><tex-math notation="LaTeX">\mathcal {L}_{2}-\mathcal {L}_{\infty}/ \mathcal {H}_{\infty}</tex-math></inline-formula> control effect. Different from the traditional method using an imperfect premise matching scheme, under the proposed optimization algorithm, the trajectory of mixed performance index is lowered effectively. Afterward, a sufficient criterion is presented for assuring the convergence of the error of the cost function. Finally, the superiority of this online optimization learning policy is confirmed via simulations.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2021.3130201