Necessary Conditions for Output Regulation with Exosystem Modelled by Differential Inclusions

The problem of output regulation has always been tackled in frameworks in which the references to be tracked and the disturbances to be rejected are generated by an autonomous differential equation, referred to as the exosystem. This assumption, that is routinely used in the design of asymptotic regulators, plays also a fundamental role in the formulation of the regulation problem and in the definition of the basic concepts such as the steady state and the zero dynamics of nonlinear systems. In this paper we show that the concepts of steady state, zero dynamics and the output regulation problem can be equivalently defined in a framework in which the exosystem is generated by a differential inclusion

Robust design of nonlinear internal models without adaptation

We propose a solution to the problem of semiglobal output regulation for nonlinear minimum-phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals. Rather, the proposed approach relies upon regression-like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude, phase and frequency. The design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input. If this is not the case, a bounded steady-state regulation error is ensured whose amplitude, though, can be arbitrarily decreased by acting on a design parameter of the regulator