The Output Regulation Problem for Unmodeled Reference/Disturbance Signals Using High-gain Observers

Based on the regulation theory and high-gain observers, in this paper, a controller for tracking and/or rejecting unmodeled but measurable signals is designed. Considering that the measurable reference/disturbance signals are bounded and smooth, it is proven that the missing dynamical models for such signals can be estimated by high-gain observers of dimensions equal to or greater than one. Then, the corresponding high-gain observers are embedded into an auxiliary system, known as the exosystem, allowing in this way, that the regulation theory can be applied and the new equations to be solved are also given. Because the exosystem is directly constructed from the high-gain observers, the proposed controller is robust in the sense that it is capable of tracking/rejecting any bounded and smooth signal as long as the estimations of the high-gain observers are sufficiently accurate. The existence conditions for such a controller are given, and numerical experiments are used to illustrate the efficacy of the proposed approach.