Adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small-gain approach

This paper considers the adaptive fuzzy robust control problem for a class of single-input and single-output (SISO) stochastic nonlinear systems in strict-feedback form. The systems under study possess unstructured uncertainties, unknown dead-zone, uncertain dynamics and unknown gain functions. In the controller design, fuzzy logic systems are adopted to approximate the unknown functions, and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics. By combining the backstepping technique with the stochastic small-gain approach, a novel adaptive fuzzy robust control scheme is developed. It is shown that the proposed control approach can guarantee that the closed-loop system is input-state-practically stable (ISpS) in probability, and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters. Simulation results are provided to illustrate the effectiveness of the proposed control approach.