Global Asymptotic Stabilization Using Adaptive Fuzzy PD Control

It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2015-03, Vol.45 (3), p.574-582
Main Authors: Pan, Yongping, Yu, Haoyong, Sun, Tairen
Format: Article
Language:English
Subjects:
Adaptive control
Approximation methods
Asymptotic stability
asymptotic stabilization
Closed loop systems
Control systems
fuzzy approximation
global stability
Nonlinear systems
PD control
proportional-derivative (PD) control
Stability analysis
uncertain nonlinear system
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Summary:It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in the presence of FAEs for a class of uncertain affine nonlinear systems. Variable-gain PD control is designed to globally stabilize the plant. An optimal FAE is shown to be bounded by the norm of the plant state vector multiplied by a globally invertible and nondecreasing function, which provides a pivotal property for stability analysis. Without discontinuous control compensation, the closed-loop system achieves global and partially asymptotic stability in the sense that all plant states converge to zero. Compared with previous adaptive approximation-based global/asymptotic stabilization approaches, the major advantage of our approach is that global stability and asymptotic stabilization are achieved concurrently by a much simpler control law. Illustrative examples have further verified the theoretical results.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2014.2331460