Generalized Adjoint Systems

72 Pages·2015·0.925 MB·English

by  Demetrios Serakos (auth.)

SPRINGER BRIEFS IN OPTIMIZATION
Demetrios Serakos
Generalized
Adjoint Systems
123
SpringerBriefs in Optimization
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Demetrios Serakos
Generalized Adjoint Systems
123
DemetriosSerakos
Dahlgren,VA,USA
ISSN2190-8354 ISSN2191-575X (electronic)
SpringerBriefsinOptimization
ISBN978-3-319-16651-3 ISBN978-3-319-16652-0 (eBook)
DOI10.1007/978-3-319-16652-0
LibraryofCongressControlNumber:2015935202
MathematicsSubjectClassification(2010):93A30,47A05,93A10,46B25
SpringerChamHeidelbergNewYorkDordrechtLondon
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Foreword
This book is the result of a theoretical development and examination of the
generalizedadjointconceptandtheconditionsunderwhichsystemsanalysisusing
adjointsisvalid.Theresultsdevelopedinthisbookareusefulaidsfortheanalysis
and modeling of physical systems, including the development of guidance and
controlalgorithms,andindevelopingsimulations.1Thisbookdefinesanddevelops
the generalized adjoint of an input–output system. The generalized adjoint of a
system may be used to represent the inverse of a system, which may be used in
systems analysis. Furthermore, the generalized adjoint condenses system behavior
inawaythatfacilitatesanalysisoftheeffectofnoiseanddisturbanceonasystem.
An earlier version of this book appeared as a Naval Surface Warfare Center,
DahlgrenDivisiontechnicalreport.2
The author is indebted to Professor W.L. Root (1919–2007) for his help with
theearlierdraftswhichbecamethisbook.Also,thankstoMs.RaziaAmzadfrom
Springer.
1JohnE.Gray.
2D.Serakos,“GeneralizedAdjointSystems,”NSWCDD/TR12/79,NavalSurfaceWarfareCenter,
DahlgrenDivision,Dahlgren,VA22448.Postedonwww.dtic.mil.Thisversionwasnotsponsored
by NSWCDD and does not necessarily reflect the views or policies of the U.S. Navy or U.S.
Government.
vii

Contents
1 Introduction ................................................................... 1
2 Preliminaries .................................................................. 5
3 SpacesofTimeFunctionsConsistingofInput–OutputSystems ........ 13
4 AGeneralizedAdjointSystem .............................................. 17
5 AGeneralizedAdjointMap ................................................. 21
6 OnInvertibilityUsingtheGeneralizedAdjointSystem.................. 27
InvertibilityforF andFa ..................................................... 27
OnFa AstheInverseofF .................................................... 29
Summary........................................................................ 43
7 NoiseandDisturbanceBoundsUsingAdjoints............................ 45
8 Example........................................................................ 47
9 SummaryandConclusions .................................................. 55
A OntheInput–OutputSystemTopology .................................... 57
References.......................................................................... 65
ix