Robust adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems with unknown control directions

In this paper, the adaptive fuzzy backstepping control problem is considered for a class of single-input single-output (SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. Within this approach, Nussbaum gain functions are introduced to solve the problem of unknown control directions. The unknown nonlinear functions are approximated by employing adaptive fuzzy systems. The stability analysis of the closed-loop system in the sense of Lyapunov guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a small neighborhood of the origin. The feasibility of the developed control approach is illustrated by numerical simulation.