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 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.