Copyright © IF AC System Structure and ConTrol. Prague. Czech Republic. 200 I IFAC l:OC> Publications www.elsevier.comllocatelifac ROBUST REGULATION FOR NONLINEAR SYSTEMS VIA AN OBSERVED-BASED GENERALIZED IMMERSION* B. Castillo-Toledo 1 and S. Celikovsky 2 t 1 CINVESTAV-IPN, Unidad Guadalajara A. P. 31-438, Pza. La Luna, Col. Verde Valle , Guadalajara, Jalisco, M€xico. C. P. 44550. 2 Institute of Information Theory and Automation Czech Academy of Sciences, P. O. Box 18, 18208 Praha 8, Libeu, Czech Republic Abstract . The problem of output regulation of the system affected by unknown constant parameteres 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 S<K:alled 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. Copyright ©2001 [FAC Keywords. Robust output regulation, observer-based generalized immersion, dynamic feedback. l. INTRODUCTION A central problem in control theory and ap- plications is to design a control law to achieve asymptotic tracking with disturbance rejection in nonlinear systems. When the class of reference inputs and disturbances are generated by an au- tonomous differential equations, this problem is called nonlinear output regulation problem, or, alternatively, nonlinear servomechanism problem, see e.g. Isidori and Byrnes 1990 and Isidori 1995. The problem can precisely be formulated as fol- lows: • Work supported by Mexican Consejo Nacional de Cien- cia y Tecnologia under grants 26358-A and 990488 tSupported by the Grant Agency of the Academy of Sciences of the Czech Republic through grant 2075702 363 Consider a nonlinear plant described by x= f(x , w, u, JJ) e = h(x, w, JJ) (1) where the first equation of (1) describes the dy- namics of a plant, whose state x is defined in a neighborhood U of the origin in Rn, with control