Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach

This paper proposes an adaptive fuzzy robust control method for SISO nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamic disturbances. Fuzzy logic systems are used to approximate the nonlinear uncertainties, with no prior knowledge of their bounds. Based on the modeled nonlinear uncertainties using fuzzy logic systems, a stable adaptive fuzzy backstepping robust controller is proposed by combining the backstepping technique with the small-gain approach. It is mathematically proven that the proposed adaptive fuzzy control approach can guarantee that the closed-loop system is uniformly bounded. The effectiveness of the proposed approach is illustrated via two examples.