Generalized Immersion and Nonlinear Robust Output Regulation Problem

The problem of output regulation of the system affected by unknown constant parameters is considered here. Under certain assumptions, such a problem is known to be solvable using error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equations and the existence of a finite dimensional immersion of the exogenous system with outputs into the one having suitable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs, but for many interesting cases, this kind of finite dimensional immersion is difficult or even impossible to find. In order to achieve constructive procedures for wider classes, this paper investigates a more general type of immersion, namely to nonlinear system containing a copy of exosystem or its part. Such a generalized immersion enables to solve robust output regulation problem via dynamic feedback compensator using error and exosystem state measurement. When the exosystem states are not completely measurable, a modified observed-based generalized immersion is then presented. Examples together with computer simulation are included to clarify the suggested approach.