Adaptive output feedback controller for a class of uncertain nonlinear systems

Abstract

This paper addresses the problem of asymptotic tracking of an arbitrary smooth bounded reference output sequence in the presence of step like disturbances for a class of uncertain nonlinear multi-outputs systems, namely systems that could be described by the usual lower triangular representation thanks to an appropriate state transformation. These performances are shown to be achieved by combining an appropriate high gain state feedback control with a high gain adaptive observer under persistent of excitation condition. A filtered integral action is incorporated into the underlying state feedback control design to get a robust compensation of step like disturbances while reducing appropriately the noise control system sensitivity. The persistent excitation condition allows to avoid those useful parameter adaptation robustness design features as parameter projection or parameter adaptation freezing. This makes it possible to put the emphasis on the adaptive control design. As an illustrative example, the proposed adaptive control design is used to address the servo problem of a nonlinear double integrator using only the measurements of the position.