Towards universal nonlinear output regulation

We consider the design of dynamic error-feedback regulators which are, in some sense, "universal" within the considered class of nonlinear systems. The standard regulator problem in presence of a linear exosystem is tackled processing the least possible amount of information regarding both the plant and the exosystem models. Asymptotic regulation is required to hold and for any initial conditions, and regardless of the value of the unknown parameters of both the plant and the exosystem model. It turns out that, for the class of polynomial minimum-phase nonlinear systems in output-feedback form, it is possible to build a regulator of this kind, starting from the knowledge of the relative degree, the sign of the high-frequency gain and upper bounds on the degree of the polynomials and the number of distinct harmonics generated by the exosystem. The solution relies upon recent results on regulation with self-tuning internal models and on standard adaptive high-gain stabilization. We regard this result as a first step towards the synthesis of universal regulators for larger classes of systems.