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Necessary and sufficient conditions in the optimal control for general nonlinear differential-algebraic equations

Please always quote using this URN:urn:nbn:de:0296-matheon-3562
  • We study optimal control problems for general unstructured nonlinear differential-algebraic equations of arbitrary index. In particular, we derive necessary conditions in the case of linear-quadratic control problems and extend them to the general nonlinear case. We also present a Pontryagin maximum principle for general unstructured nonlinear DAEs in the case of restricted controls. Moreover, we discuss the numerical solution of the resulting two-point boundary value problems and present a numerical example.

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Metadaten
Author:Peter Kunkel, Volker Mehrmann
URN:urn:nbn:de:0296-matheon-3562
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/10/31
Release Date:2006/09/09
Tag:
Institute:Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Hxx Control problems [See also 49J15, 49K15, 93C15] / 34H05 Control problems [See also 49J15, 49K15, 93C15]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K15 Problems involving ordinary differential equations
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C10 Nonlinear systems
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C15 Systems governed by ordinary differential equations [See also 34H05]
Preprint Number:355
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