Approximate regulation for nonlinear systems in presence of periodic disturbances

In this work we present a new approach to the problem of output regulation for nonlinear systems in presence of periodic disturbances, possibly with an infinite number of harmonics. We show that, by adding a linear internal model, approximate regulation is achieved if the disturbance is small enough. Nominally all the harmonic included in the internal model are absent in the periodic steady state regulation error. Furthermore we show that the regulation error can be made arbitrarily small (in the ℒ₂ sense) by enlarging the dimension of the internal model. The novel approach relies on forwarding technique. An example is provided to show the efficacy of the result.