期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 45, 期 3, 页码 588-596出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2014.2331460
关键词
Adaptive control; asymptotic stabilization; fuzzy approximation; global stability; proportional-derivative (PD) control; uncertain nonlinear system
类别
资金
- Seed Fund from the Engineering Design and Innovation Center, National University of Singapore [R-261-503-002-133]
- MINDEF-NUS Joint Applied Research and Development Cooperation Programme [MINDEF/NUS/JPP/13/01/01]
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.
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