Universal disturbance rejection for nonlinear systems in output feedback form

This note deals with global disturbance rejection via output feedback of a class of uncertain nonlinear systems subject to a class of unknown disturbances. Both the uncertainty in the system model and the uncertainty in the exosystem are tackled concurrently. The disturbances generated from an unknown linear exosystem are completely rejected. The order of the exosystem is assumed known, and the eigenvalues are distinct. The system is assumed in the format of the minimum-phase output feedback form, with no knowledge of the values of any system parameters, including the high-frequency gain. No other assumptions are needed in the control design. A new set of filters are introduced for state estimation. The stability of the internal model is exploited to design a new auxiliary error, involving both the unknown parameters of the reformatted exosystem and those of the system, which makes it possible to group all the unknown parameters in a format suitable to adaptive control design. A Nussbaum gain is introduced in adaptive control design to tackle the unknown high-frequency gain and a number of control coefficients are also made adaptive so that the disturbance rejection is global with respect to unknown frequencies in the disturbances.