A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

TLDR

The nonlinear systems considered exhibit unmodeled dynamics with unstructured uncertainties and dynamic disturbances, whose bounds are unknown and not linearly parameterized. The paper proposes an adaptive fuzzy output‑feedback controller for single‑input single‑output nonlinear systems that lack state measurements. The method employs fuzzy logic to approximate the unstructured uncertainties, a state observer to estimate unmeasured states, and combines backstepping with a small‑gain approach to achieve stability. Simulations show that the closed‑loop system is semiglobally uniformly ultimately bounded, demonstrating the effectiveness of the proposed controller.

Abstract

In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.