Non-smooth disturbance rejection in nonlinear systems using nonlinear internal model

This paper deals with estimation and rejection of unknown non-smooth disturbances in nonlinear systems in the output feedback form. The specific non-smooth disturbances considered in this paper are the square-wave disturbances with known frequencies. The other information such as the amplitudes and phases are unknown. The rejection takes an indirect approach by estimating the disturbance first and then designing the feedback control based on the estimated disturbances. To estimate the disturbance, filters are designed to extract the contribution to the state from the disturbances and a novel nonlinear internal model is constructed using the integrals over half of the period and nonlinear functions. The proposed control design asymptotically rejects the unknown square-wave disturbances and ensures the boundedness of all the variable.