Adaptive output feedback regulation of a class of nonlinear systems: convergence and robustness

In this paper we consider a minimum-phase, input-output linearizable system that is represented globally by an nth-order differential equation. The nonlinearities of the system depend linearly on unknown parameters which belong to a known convex set. We design a semiglobal adaptive output feedback controller to ensure boundedness of all state variables and regulation of the output to zero (an open-loop equilibrium condition). It is shown that the adaptive controller is robust with respect to bounded disturbances in the sense that the mean square regulation error is of the order of the magnitude of the disturbance. Moreover, if the disturbance vanishes when the input and output are identically zero and if its slope is sufficiently small, then the adaptive controller will ensure convergence of the regulation error.