Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Systems via Backstepping and Small-Gain Approach

This paper focuses on an input-to-state practical stability (ISpS) problem of nonlinear systems which possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances. The dynamic disturbances depend on the states and the measured output of the system, and its assumption conditions are relaxed compared with the common restrictions. Based on an input-driven filter, fuzzy logic systems are directly used to approximate the unknown and desired control signals instead of the unknown nonlinear functions, and an integrated backstepping technique is used to design an adaptive output-feedback controller that ensures robustness with respect to unknown parameters and uncertain nonlinearities. This paper, by applying the ISpS theory and the generalized small-gain approach, shows that the proposed adaptive fuzzy controller guarantees the closed-loop system being semi-globally uniformly ultimately bounded. A main advantage of the proposed controller is that it contains only three adaptive parameters that need to be updated online, no matter how many states there are in the systems. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.