Control perspectives on numerical algorithms and matrix problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
2006
|
| Schriftenreihe: | Advances in design and control
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 272 S. Ill., graph. Darst. |
| ISBN: | 0898716020 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | CONTROL PERSPECTIVES ON NUMERICAL ALGORITHMS AND MATRIX PROBLEMS AMIT
BHAYA EUGENIUS KASZKUREWICZ FEDERAL UNIVERSITY OF RIO DE JANEIRO RIO DE
JANEIRO, BRAZIL SIAJTL SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
PHILADELPHIA CONTENTS LIST OF FIGURES XI LIST OF TABLES XVII PREFACE XIX
1 BRIEF REVIEW OF CONTROL AND STABILITY THEORY 1 1.1 CONTROL THEORY
BASICS 1 1.1.1 FEEDBACK CONTROL TERMINOLOGY 1 1.1.2 PID CONTROL FOR
DISCRETE-TIME SYSTEMS 6 1.2 OPTIMAL CONTROL THEORY 8 1.3 LINEAR SYSTEMS,
TRANSFER FUNCTIONS, REALIZATION THEORY 10 1.4 BASICS OF STABILITY OF
DYNAMICAL SYSTEMS 15 1.5 VARIABLE STRUCTURE CONTROL SYSTEMS 27 1.6
GRADIENT DYNAMICAL SYSTEMS 31 1.6.1 NONSMOOTH GDSS: PERSIDSKII-TYPE
RESULTS 35 1.7 NOTES AND REFERENCES 38 2 ALGORITHMS AS DYNAMICAL SYSTEMS
WITH FEEDBACK 41 2.1 CONTINUOUS-TIME DYNAMICAL SYSTEMS THAT FIND ZEROS
42 2.2 ITERATIVE ZERO FINDING ALGORITHMS AS DISCRETE-TIME DYNAMICAL
SYSTEMS 56 2.3 ITERATIVE METHODS FOR LINEAR SYSTEMS AS FEEDBACK CONTROL
SYSTEMS . . 70 2.3.1 CLF/LOC DERIVATION OF MINIMAL RESIDUAL AND KRYLOV
SUBSPACE METHODS 75 2.3.2 THE CONJUGATE GRADIENT METHOD DERIVED FROM A
PROPORTIONAL-DERIVATIVE CONTROLLER 77 2.3.3 CONTINUOUS ALGORITHMS FOR
FINDING OPTIMA AND THE CONTINUOUS CONJUGATE GRADIENT ALGORITHM 85 2.4
NOTES AND REFERENCES 90 3 OPTIMAL CONTROL AND VARIABLE STRUCTURE DESIGN
OF ITERATIVE METHODS 93 3.1 OPTIMALLY CONTROLLED ZERO FINDING METHODS 94
3.1.1 AN OPTIMAL CONTROL-BASED NEWTON-TYPE METHOD 94 3.2 VARIABLE
STRUCTURE ZERO FINDING METHODS 96 VII VIII CONTENTS 3.2.1 A VARIABLE
STRUCTURE NEWTON METHOD TO FIND ZEROS OF A POLYNOMIAL FUNCTION 99 3.2.2
THE SPURT METHOD 107 3.3 OPTIMAL CONTROL APPROACH TO UNCONSTRAINED
OPTIMIZATION PROBLEMS . 109 3.4 DIFFERENTIAL DYNAMIC PROGRAMMING APPLIED
TO UNCONSTRAINED MINIMIZATION PROBLEMS 118 3.5 NOTES AND REFERENCES 124
4 NEURAL-GRADIENT DYNAMICAL SYSTEMS FOR LINEAR AND QUADRATIC PROGRAMMING
PROBLEMS 127 4.1 GDSS, NEURAL NETWORKS, AND ITERATIVE METHODS 128 4.2
GDSS THAT SOLVE LINEAR SYSTEMS OF EQUATIONS 140 4.3 GDSS THAT SOLVE
CONVEX PROGRAMMING PROBLEMS 146 4.3.1 STABILITY ANALYSIS OF A CLASS OF
DISCONTINUOUS GDSS .... 150 4.4 GDSS THAT SOLVE LINEAR PROGRAMMING
PROBLEMS 154 4.4.1 GDSS AS LINEAR PROGRAMMING SOLVERS 159 4.5 QUADRATIC
PROGRAMMING AND SUPPORT VECTOR MACHINES 167 4.5.1 U-SUPPORT VECTOR
CLASSIFIERS FOR NONLINEAR SEPARATION VIA GDSS 170 4.6 FURTHER
APPLICATIONS: LEAST SQUARES SUPPORT VECTOR MACHINES, K-WINNERS-TAKE-ALL
PROBLEM 173 4.6.1 A LEAST SQUARES SUPPORT VECTOR MACHINE IMPLEMENTED BY
AGDS 173 4.6.2 A GDS THAT SOLVES THE K-WINNERS-TAKE-ALL PROBLEM .... 174
4.7 NOTES AND REFERENCES 177 5 CONTROL TOOLS IN THE NUMERICAL SOLUTION
OF ORDINARY DIFFERENTIAL EQUATIONS AND IN MATRIX PROBLEMS 179 5.1
STEPSIZE CONTROL FOR ODES 179 5.1.1 STEPSIZE CONTROL AS A LINEAR
FEEDBACK SYSTEM 182 5.1.2 OPTIMAL STEPSIZE CONTROL FOR ODES 185 5.2 A
FEEDBACK CONTROL PERSPECTIVE ON THE SHOOTING METHOD FOR ODES . . 191
5.2.1 A STATE SPACE REPRESENTATION OF THE SHOOTING METHOD ... 192 5.2.2
ERROR DYNAMICS OF THE ITERATIVE SHOOTING SCHEME 195 5.3 A DECENTRALIZED
CONTROL PERSPECTIVE ON DIAGONAL PRECONDITIONING . . . 199 5.3.1 PERFECT
DIAGONAL PRECONDITIONING 203 5.3.2 LQ PERSPECTIVE ON OPTIMAL DIAGONAL
PRECONDITIONERS . . .208 5.4 CHARACTERIZATION OF MATRIX D-STABILITY
USING POSITIVE REALNESS OF A FEEDBACK SYSTEM 210 5.4.1 A FEEDBACK
CONTROL APPROACH TO THE D-STABILITY PROBLEM VIA STRICTLY POSITIVE REAL
FUNCTIONS 213 5.4.2 D-STABILITY CONDITIONS FOR MATRICES OF ORDERS 2 AND
3 . . .216 5.5 FINDING ZEROS OF TWO POLYNOMIAL EQUATIONS IN TWO
VARIABLES VIA CONTROLLABILITY AND OBSERVABILITY 218 5.6 NOTES AND
REFERENCES 224 CONTENTS IX 6 EPILOGUE 227 BIBLIOGRAPHY 233 INDEX 255
|
| adam_txt |
CONTROL PERSPECTIVES ON NUMERICAL ALGORITHMS AND MATRIX PROBLEMS AMIT
BHAYA EUGENIUS KASZKUREWICZ FEDERAL UNIVERSITY OF RIO DE JANEIRO RIO DE
JANEIRO, BRAZIL SIAJTL SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
PHILADELPHIA CONTENTS LIST OF FIGURES XI LIST OF TABLES XVII PREFACE XIX
1 BRIEF REVIEW OF CONTROL AND STABILITY THEORY 1 1.1 CONTROL THEORY
BASICS 1 1.1.1 FEEDBACK CONTROL TERMINOLOGY 1 1.1.2 PID CONTROL FOR
DISCRETE-TIME SYSTEMS 6 1.2 OPTIMAL CONTROL THEORY 8 1.3 LINEAR SYSTEMS,
TRANSFER FUNCTIONS, REALIZATION THEORY 10 1.4 BASICS OF STABILITY OF
DYNAMICAL SYSTEMS 15 1.5 VARIABLE STRUCTURE CONTROL SYSTEMS 27 1.6
GRADIENT DYNAMICAL SYSTEMS 31 1.6.1 NONSMOOTH GDSS: PERSIDSKII-TYPE
RESULTS 35 1.7 NOTES AND REFERENCES 38 2 ALGORITHMS AS DYNAMICAL SYSTEMS
WITH FEEDBACK 41 2.1 CONTINUOUS-TIME DYNAMICAL SYSTEMS THAT FIND ZEROS
42 2.2 ITERATIVE ZERO FINDING ALGORITHMS AS DISCRETE-TIME DYNAMICAL
SYSTEMS 56 2.3 ITERATIVE METHODS FOR LINEAR SYSTEMS AS FEEDBACK CONTROL
SYSTEMS . . 70 2.3.1 CLF/LOC DERIVATION OF MINIMAL RESIDUAL AND KRYLOV
SUBSPACE METHODS 75 2.3.2 THE CONJUGATE GRADIENT METHOD DERIVED FROM A
PROPORTIONAL-DERIVATIVE CONTROLLER 77 2.3.3 CONTINUOUS ALGORITHMS FOR
FINDING OPTIMA AND THE CONTINUOUS CONJUGATE GRADIENT ALGORITHM 85 2.4
NOTES AND REFERENCES 90 3 OPTIMAL CONTROL AND VARIABLE STRUCTURE DESIGN
OF ITERATIVE METHODS 93 3.1 OPTIMALLY CONTROLLED ZERO FINDING METHODS 94
3.1.1 AN OPTIMAL CONTROL-BASED NEWTON-TYPE METHOD 94 3.2 VARIABLE
STRUCTURE ZERO FINDING METHODS 96 VII VIII " CONTENTS 3.2.1 A VARIABLE
STRUCTURE NEWTON METHOD TO FIND ZEROS OF A POLYNOMIAL FUNCTION 99 3.2.2
THE SPURT METHOD 107 3.3 OPTIMAL CONTROL APPROACH TO UNCONSTRAINED
OPTIMIZATION PROBLEMS . 109 3.4 DIFFERENTIAL DYNAMIC PROGRAMMING APPLIED
TO UNCONSTRAINED MINIMIZATION PROBLEMS 118 3.5 NOTES AND REFERENCES 124
4 NEURAL-GRADIENT DYNAMICAL SYSTEMS FOR LINEAR AND QUADRATIC PROGRAMMING
PROBLEMS 127 4.1 GDSS, NEURAL NETWORKS, AND ITERATIVE METHODS 128 4.2
GDSS THAT SOLVE LINEAR SYSTEMS OF EQUATIONS 140 4.3 GDSS THAT SOLVE
CONVEX PROGRAMMING PROBLEMS 146 4.3.1 STABILITY ANALYSIS OF A CLASS OF
DISCONTINUOUS GDSS . 150 4.4 GDSS THAT SOLVE LINEAR PROGRAMMING
PROBLEMS 154 4.4.1 GDSS AS LINEAR PROGRAMMING SOLVERS 159 4.5 QUADRATIC
PROGRAMMING AND SUPPORT VECTOR MACHINES 167 4.5.1 U-SUPPORT VECTOR
CLASSIFIERS FOR NONLINEAR SEPARATION VIA GDSS 170 4.6 FURTHER
APPLICATIONS: LEAST SQUARES SUPPORT VECTOR MACHINES, K-WINNERS-TAKE-ALL
PROBLEM 173 4.6.1 A LEAST SQUARES SUPPORT VECTOR MACHINE IMPLEMENTED BY
AGDS 173 4.6.2 A GDS THAT SOLVES THE K-WINNERS-TAKE-ALL PROBLEM . 174
4.7 NOTES AND REFERENCES 177 5 CONTROL TOOLS IN THE NUMERICAL SOLUTION
OF ORDINARY DIFFERENTIAL EQUATIONS AND IN MATRIX PROBLEMS 179 5.1
STEPSIZE CONTROL FOR ODES 179 5.1.1 STEPSIZE CONTROL AS A LINEAR
FEEDBACK SYSTEM 182 5.1.2 OPTIMAL STEPSIZE CONTROL FOR ODES 185 5.2 A
FEEDBACK CONTROL PERSPECTIVE ON THE SHOOTING METHOD FOR ODES . . 191
5.2.1 A STATE SPACE REPRESENTATION OF THE SHOOTING METHOD . 192 5.2.2
ERROR DYNAMICS OF THE ITERATIVE SHOOTING SCHEME 195 5.3 A DECENTRALIZED
CONTROL PERSPECTIVE ON DIAGONAL PRECONDITIONING . . . 199 5.3.1 PERFECT
DIAGONAL PRECONDITIONING 203 5.3.2 LQ PERSPECTIVE ON OPTIMAL DIAGONAL
PRECONDITIONERS . . .208 5.4 CHARACTERIZATION OF MATRIX D-STABILITY
USING POSITIVE REALNESS OF A FEEDBACK SYSTEM 210 5.4.1 A FEEDBACK
CONTROL APPROACH TO THE D-STABILITY PROBLEM VIA STRICTLY POSITIVE REAL
FUNCTIONS 213 5.4.2 D-STABILITY CONDITIONS FOR MATRICES OF ORDERS 2 AND
3 . . .216 5.5 FINDING ZEROS OF TWO POLYNOMIAL EQUATIONS IN TWO
VARIABLES VIA CONTROLLABILITY AND OBSERVABILITY 218 5.6 NOTES AND
REFERENCES 224 CONTENTS " IX 6 EPILOGUE 227 BIBLIOGRAPHY 233 INDEX 255 |
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| index_date | 2024-07-02T15:12:00Z |
| indexdate | 2024-07-09T20:41:34Z |
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| isbn | 0898716020 |
| language | English |
| lccn | 2005057551 |
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| spelling | Bhaya, Amit Verfasser (DE-588)1146241305 aut Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz Philadelphia Society for Industrial and Applied Mathematics 2006 XXV, 272 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in design and control Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Kaszkurewicz, Eugenius Verfasser (DE-588)1146241291 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014897354&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhaya, Amit Kaszkurewicz, Eugenius Control perspectives on numerical algorithms and matrix problems Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie (DE-588)4032317-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4042805-9 |
| title | Control perspectives on numerical algorithms and matrix problems |
| title_auth | Control perspectives on numerical algorithms and matrix problems |
| title_exact_search | Control perspectives on numerical algorithms and matrix problems |
| title_exact_search_txtP | Control perspectives on numerical algorithms and matrix problems |
| title_full | Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz |
| title_fullStr | Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz |
| title_full_unstemmed | Control perspectives on numerical algorithms and matrix problems Amit Bhaya ; Eugenius Kaszkurewicz |
| title_short | Control perspectives on numerical algorithms and matrix problems |
| title_sort | control perspectives on numerical algorithms and matrix problems |
| topic | Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie (DE-588)4032317-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Control theory Numerical analysis Algorithms Mathematical optimization Matrices Kontrolltheorie Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014897354&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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