Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach

In this paper, a direct adaptive fuzzy robust control approach is proposed for single input and single output (SISO) strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamical disturbances. No prior knowledge of the boundary of the nonlinear uncertainties is required. Fuzzy logic systems are used to approximate the intermediate stabilizing functions, and a stable direct adaptive fuzzy backstepping robust control approach is developed by combining the backstepping technique with the fuzzy adaptive control theory. The stability of the closed-loop system and the convergence of the system output are proved based on the small-gain theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.