A design solution to the problem of adaptive output regulation for nonlinear minimum-phase systems

We propose a solution to the problem of adaptive output regulation for nonlinear minimum-phase systems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals. The proposed approach relies upon regression tools to derive a nonlinear internal model able to offset the presence of an {em unknown} number of harmonics of uncertain amplitude, phase and frequency. The design methodology guarantees asymptotic regulation in the case the dimension of the regulator is sufficiently large in relation to the effective number of harmonics acting on the system. On the other hand, in the case of under-dimensioned internal model, a bounded steady-state regulation error is ensured whose amplitude, though, can be arbitrarily decreased by acting on a design parameter of the regulator. The proposed tool is also shown to be effective to deal with the larger class of nonlinear but linearly parameterized uncertain exosystems.