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Main Title: Self-adjoint differential-algebraic equations
Author(s): Kunkel, Peter
Mehrmann, Volker
Scholz, Lena
Type: Research Paper
Abstract: Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value problem and show that it is associated with a self-conjugate operator and a self-adjoint pair of matrix functions. We then study general self-adjoint pairs of matrix valued functions and derive condensed forms under orthogonal congruence transformations that preserve the self-adjointness. We analyze the relationship between self-adjoint DAEs and Hamiltonian systems with symplectic flows. We also show how to extract self-adjoint and Hamiltonian reduced systems from derivative arrays.
Subject(s): differential-algebraic equation
self-conjugate operator
self-adjoint pair
optimal control
necessary optimality condition
strangeness index
condensed form
congruence transformation
Hamiltonian system
symplectic flow
Issue Date: 7-Jul-2011
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 93C10 Nonlinear systems
93C15 Systems governed by ordinary differential equations
93B52 Feedback control
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: 2011, 13
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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