Data-driven harmonic output regulation of a class of nonlinear systems

The paper deals with the data-based design of state-feedback controllers that solve the output regulation problem for a class of nonlinear systems. Inspired by recent developments in model-based output regulation design techniques and in data-driven control design for nonlinear systems, we derive a data-dependent semidefinite program that, when solved, directly returns a controller that steers the regulation error to a periodic signal whose Fourier series has identically zero coefficients up to a certain order set by the controller. When specialized to the case of linear systems, the result appears to improve upon existing work on data-driven regulation. Numerical results illustrate the findings.