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Titel:On Output Feedback Control of Infinite-dimensional Systems
Weiterer Titel:Über Ausgangsregelung unendlichdimensionaler Systeme
Autor:Dr.rer.nat. Selig, Tilman [Autor]
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Dateien vom 01.09.2015 / geändert 01.09.2015
URL für Lesezeichen:http://www.db-thueringen.de/servlets/DocumentServlet?id=26328
URN (NBN):urn:nbn:de:gbv:ilm1-2015000297
Status:Dokument veröffentlicht
Beitragende:Prof. Dr. Ilchmann, Achim [Betreuer/Doktorvater]
Prof. Dr. rer. nat. Reis, Timo [Gutachter]
Prof. Dr. Opmeer, Mark [Gutachter]
Stichwörter:Systemtheorie, Regelung, Funnelregelung, Ausgangsrückführung, Störgrößenunterdrückung, Modellreduktion
Evaluationstyp:Für die Langzeitarchivierung vorgesehen
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik » 510 Mathematik » 515 Analysis
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Beschreibungen:Zusammenfassung (dt.)

In this thesis we consider time-invariant infinite-dimensional well-posed linear systems that convert an input signal u into an output signal y. In the theory of compatible well-posed linear systems, these processes are described by a differential equation of the formx'(t)=Ax(t)+ Bu(t), y(t)=Cx(t)+Du(t),where A, B, C and D are possibly unbounded operators between infinite-dimensional Hilbert spaces. Generalizing ideas from the finite-dimensional theory, we consider various types of state space transformations in order to analyze the structure of these systems. For systems with compact Hankel operator, we construct output normalizing and balancing transformations with an application to model order reduction. For systems of natural relative degree we employ transformations to obtain operator versions of the well-known Byrnes-Isidori form and a similar, but less popular, zero dynamics form. We establish a universal definition of zero-dynamics for infinite-dimensional systems, and show that they are determined by a single strongly continuous semigroup if the systems has a natural relative degree. Thereby we exploit the aforementioned forms. An analogous result is proven for a special boundary control system described by a heat equation. After these theoretical preparations, two practically applicable output control techniques are proven to work: The first one is funnel control, a very simple control strategy that makes the output follow the reference trajectory in a strict way, i.e. it evolves inside of a funnel that can be specified by the user. While the control law is a very simple algebraic calculation, the challenge is to prove that it works. We show that the funnel control is successfully applicable to systems of relative degree one with exponentially stable zero dynamics and to the previously mentioned boundary control system.The second output control strategy that we employ aims at minimizing noise amplification of the closed-loop system. It is a special version of the famous H^\infty-control problem, and closely related to linear quadratic optimal control. While the solution of these well-studied problems always comprises an infinite-dimensional observer that is impossible to implement in practice, we construct a finite-dimensional controller using an approximation method known as balanced truncation. We prove furthermore that this finite-dimensional controller achieves the control objective with a decline in performance that depends on the approximation error.
Hochschule/Fachbereich:Technische Universität Ilmenau » Fakultät für Mathematik und Naturwissenschaften
Dokument erstellt am: 01.09.2015
Dateien geändert am: 30.11.2015
Promotionsantrag am: 30.04.2015
Datum der Promotion: 16.07.2015