The uniform global output regulation problem

In this paper, we present a new approach to the global output regulation problem. In this approach, a controller should be designed in such a way that the closed-loop system is uniformly convergent. This requirement allows to extend the theory developed for the local output regulation problem to what we call the uniform global output regulation problem. Such extension is made using global invariant manifold theorems, which serve as global counterparts of the center manifold theorems. It is shown that within the proposed approach solvability of the (extended) regulator equations is a basic necessary condition for the solvability of the uniform global output regulation problem. As an illustration, we present a solution to the uniform global output regulation problem for a class of nonlinear systems.

[1]  G. P. Szegö,et al.  Stability theory of dynamical systems , 1970 .

[2]  E. Davison,et al.  Multivariable tuning regulators: The feedforward and robust control of a general servomechanism problem , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[3]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[4]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[5]  Jie Huang,et al.  On a nonlinear multivariable servomechanism problem , 1990, Autom..

[6]  Stephen P. Boyd,et al.  Control System Analysis and Synthesis via Linear Matrix Inequalities , 1993, 1993 American Control Conference.

[7]  Christopher I. Byrnes,et al.  Output regulation for nonlinear systems: an overview , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[8]  H. Nijmeijer,et al.  Convergent systems and the output regulation problem , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Hélène Frankowska Global output regulation of nonlinear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  Christopher I. Byrnes,et al.  Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation , 2003, IEEE Trans. Autom. Control..

[11]  Nathan van de Wouw,et al.  Convergent dynamics, a tribute to Boris Pavlovich Demidovich , 2004, Syst. Control. Lett..

[12]  A. Isidori,et al.  Topics in Control Theory , 2004 .

[13]  Jie Huang,et al.  A general formulation and solvability of the global robust output regulation problem , 2005, IEEE Trans. Autom. Control..