A flat-zone modification for robust adaptive control of nonlinearoutput feedback systems with unknown high-frequency gains

This note deals with adaptive control of perturbed nonlinear output feedback systems with unknown high-frequency gains. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. A flat-zone modification is proposed to incorporate both the bound estimation and Nussbaum gain design in the nonlinear adaptive control. To ensure the differentiability of stabilizing functions needed for backstepping design, high order terms are introduced in the Lyapunov function candidate with a flat zone around the neighborhood of the origin. The output tracking error converges to an arbitrarily small interval around zero