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Main Title: Self-conjugate differential and difference operators arising in the optimal control of descriptor systems
Author(s): Mehrmann, Volker
Scholz, Lena
Type: Research Paper
Abstract: We analyze the structure of the linear differential and difference operators associated with the necessary optimality conditions of optimal control problems for descriptor systems in continuous- and discrete-time. It has previously been shown that in continuous-time the associated optimality system is a self-conjugate operator associated with a self-adjoint pair of coefficient matrices and we show that the same is true in the discrete-time setting. We also extend these results to the case of higher order systems. Finally, we discuss how to turn higher order systems with this structure into first order systems with the same structure.
Subject(s): differential-algebraic equation
self-conjugate difference operator
self-adjoint pair
discrete-time optimal control
necessary optimality condition
congruence transformation
higher order systems
Issue Date: 2-Aug-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 93C05 Linear systems
93C55 Discrete-time systems
93C15 Systems governed by ordinary differential equations
65L80 Methods for differential-algebraic equations
49K15 Problems involving ordinary differential equations
34H05 Control problems
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 26
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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