Asymptotic Stabilization via Adaptive Fuzzy Control

This paper certifies that standard adaptive fuzzy control (AFC) can guarantee asymptotic stabilization performance rather than uniformly ultimately boundedness (UUB) even in the presence of fuzzy approximation errors (FAEs). Under a direct AFC scheme, the resulting optimal FAE is shown to be bounded by the norm of the plant state vector multiplying a globally invertible and nondecreasing function, which provides a pivotal property for asymptotic stability analysis. Without any additional control compensation, the closed-loop system is proved to be partially and asymptotically stable in the sense that all involved signals are UUB and the plant state variables converge to zero. The resulting control law is certainly continuous since it only contains an adaptive fuzzy system. Compared with previous adaptive approximation-based asymptotic stabilization approaches, the proposed approach not only simplifies control design, but also relaxes constraint conditions on the controlled plant. A simulation example of inverted pendulum control is provided to verify the discovery of this study.