Adaptive Fuzzy Control with High Accuracy for Uncertain Nonlinear Systems

For a class of uncertain affine nonlinear systems with unknown boundary functions, an adaptive fuzzy controller (AFC) with the characteristic of high tracking accuracy is proposed in this paper. Based on the theory of variable universe fuzzy system, it is proved that the optimal fuzzy approximation error (FAE) has local convergence property under certain conditions. By using the tracking errors as inputs and selecting suitable adaptive parameters, an AFC with optimal FAE local convergence is developed. Under the key assumption that the optimal FAE is bounded, it is proved that the closed-loop system is stable in the sense that all involving variables are bounded and the tracking errors converge to zero. This approach can theoretically eliminate the effect of the FAE on the tracking errors without additional compensator, thus it can achieve high tracking accuracy with smooth control input. Simulated application of a single-link manipulator demonstrates the effectiveness of this approach.