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Regulation and controlled synchronization for complex dynamical systems

Authors
Publisher
Technische Universiteit Eindhoven
Publication Date
Disciplines
  • Mathematics

Abstract

absreg2.dvi Regulation and controlled synchronization for complex dynamical systems H.J.C. Huijberts � H. Nijmeijer y R.M.A. Willems z1 � Faculty of Mathematics and Computing Science Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven, The Netherlands. Email: [email protected] y Faculty of Mathematical Sciences University of Twente P.O. Box 217 7500 AE Enschede, The Netherlands. Email: [email protected] and Faculty of Mechanical Engineering Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven, The Netherlands z Heijnis & Koelman Dalsteindreef 50-52 1112 XC Diemen The Netherlands Email: [email protected] 1 Research was performed while the third author was with the Department of Mathematics and Computing Science, Eindhoven University of Technology Abstract In this paper we investigate the problem of controlled synchronization as a regulator problem. In controlled synchronization one is given autonomous transmitter dynamics and controlled receiver dynamics. The question is to �nd a (output) feedback controller that achieves match- ing between transmitter and controlled receiver. Several variants of the problem where the standard solvability assumptions for the regulator problem are not met turn out to have a solution. Simulations on two standard synchronization examples are also included. 1 Introduction The regulator problem is a central problem in control theory and deals with the asymptotic tracking of certain classes of prescribed trajectories and asymptotic rejection of undesired disturbances. Over the years, the problem has received a lot of attention. For linear systems the regulator problem was extensively studied in [4] and [5]. For nonlinear systems, the problem was �rst studied in [6] and afterwards in [7] on the one hand and [8] on the other hand. An account of the state of the art on the problem, including both the linear and the nonlinear setting, is given in th

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