Robust adaptive output feedback control of nonlinear systems without persistence of excitation

Abstract

We consider a recent method for adaptive output feedback control of nonlinear systems. The method deals with a single-input-single-output minimum phase nonlinear system represented by an nth-order differential equation. A Lyapunovbased design that employs parameter projection, control saturation, and a high-gain observer has been shown to achieve semiglobal tracking. One drawback of that recent result is that tracking error convergence is shown under a persistence of excitation condition, which is uncommon in traditional adaptive control results where persistence of excitation is needed to show parameter convergence but not tracking error convergence. In this paper, we prove tracking error convergence without persistence of excitation. We then proceed to provide two other extensions. First, we show that the adaptive controller is robust with respect to sufficiently small bounded disturbance. Second, by adding a robustifying control component, we show that the controller is robust for a wide class of, not-necessarily-small, bounded disturbance, provided an upper bound on the disturbance is known.