Unknown Input Observer-based Output Regulation for Uncertain Minimum Phase Linear Systems Affected by a Periodic Disturbance

This paper deals with the problem of disturbance rejection for uncertain LTI SISO systems perturbed by an unmeasurable external disturbance under the framework of output regulation. The system is assumed to be minimum phase and internally stable, but the model parameters are completely unknown. In addition, no knowledge of the external disturbance, including frequency, amplitude and phase is required to be known in advance. A novel high-order sliding mode-based Unknown Input Observer(UIO) is developed to stabilize the system and reconstruct the external disturbance. The main feature distinguishing the proposed method from the existing ones is that we do not need to integrate a frequency estimator into the adaptive controller or update the frequency estimation in a hybrid manner. Instead, the disturbance is directly duplicated by the aforementioned unknown input observer. The boundedness of states and asymptotic convergence properties are rigorously proved. Finally, the effectiveness of the proposed technique is illustrated by a numerical example.