Robust Design of Internal Models by Nonlinear Regression

This paper focuses on the design of robust internal model-based regulators for a class of nonlinear systems and exosystems such that the desired steady state control law fulfills a nonlinear regression formula affine in possible uncertainties. The design methodology builds upon the ideas presented in [9] in the context of linear adaptive output regulation. The design methodology relies upon an assumption of left invertibility of a matrix. Through numerical analysis we show how the design methodology succeeds in relevant cases, such as the cases in which the desired steady state is generated by uncertain Van der Pol, Duffing, and Lorentz oscillators.