Kybernetika 40 no. 2, 207-220, 2004

Generalized immersion and nonlinear robust output regulation problem

Bernardino Castillo-Toledo, Sergej Čelikovský and Stefano Di Gennaro


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 via the so-called immersion to an observable linear system with outputs. Nevertheless, 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. Such a {\em 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. The main result obtained here is that under reasonable assumptions both the full and partial exosystem measurement problems are equivalently solvable. Examples together with computer simulation are included to clarify the suggested approach.