Zusammenfassung
Das Dualitätskonzept ist für lineare Systeme etabliert, wobei im zeitvarianten Fall der Begriff des adjungierten Systems ins Spiel kommt. Es war außerdem eine stete Quelle der Inspiration über den linearen Fall hinaus. Einige Beziehungen zwischen dem linearen zeitvarianten Fall und der Analyse sowie dem Entwurf nichtlinearer Systeme werden in Erinnerung gebracht und aus einem neuen Winkel betrachtet. Dabei spielen die Linearisierung um Trajektorien und eine Betrachtung unabhängig von Zustandsdarstellungen eine Schlüsselrolle. Regler- und Beobachterentwurf werden mit Hilfe sog. kanonischer Formen ebenfalls diskutiert.
Abstract
Duality is a well-established concept in linear systems theory, with the notion of the adjoint system coming into play in the time-varying case. Beyond the linear case it has been a continuous source of inspiration. Several relations between the linear time-varying case and nonlinear systems analysis and design are recalled and viewed from a new perspective. Linearization about trajectories plays a crucial role in that discussion. Furthermore, general representations are considered in addition to state representations. Control design and observers are treated using so-called canonical forms.
Dieser Beitrag ist Herrn Prof. Dr.-Ing. Dr. h.c. Michael Zeitz anlässlich seines 80. Geburtstags gewidmet.
Über den Autor / die Autorin
Prof. Dr.-Ing. habil. Joachim Rudolph leitet den Lehrstuhl für Systemtheorie und Regelungstechnik an der Universität des Saarlandes. Hauptarbeitsgebiete: Regler- und Beobachterentwurf für nichtlineare Regelstrecken, algebraische Methoden, lineare und nichtlineare unendlichdimensionale Systeme; Anwendungen in der Mechatronik.
Danksagung
Der Autor dankt Herrn Prof. i.R. Dr.-Ing. Dr. h.c. M. Zeitz für einen bereits über mehr als drei Jahrzehnte andauernden, inspirierenden und fruchtbaren wissenschaftlichen Austausch, der u. a. im vorliegenden Beitrag deutlich werden dürfte.
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