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The Resource Geometric and numerical optimal control : application to swimming at Low Reynolds number and magnetic resonance imaging, Bernard Bonnard, Monique Chyba, Jérémy Rouot

Geometric and numerical optimal control : application to swimming at Low Reynolds number and magnetic resonance imaging, Bernard Bonnard, Monique Chyba, Jérémy Rouot

Label
Geometric and numerical optimal control : application to swimming at Low Reynolds number and magnetic resonance imaging
Title
Geometric and numerical optimal control
Title remainder
application to swimming at Low Reynolds number and magnetic resonance imaging
Statement of responsibility
Bernard Bonnard, Monique Chyba, Jérémy Rouot
Creator
Contributor
Author
Subject
Language
eng
Summary
This book introduces readers to techniques of geometric optimal control as well as the exposure and applicability of adapted numerical schemes. It is based on two real-world applications, which have been the subject of two current academic research programs and motivated by industrial use - the design of micro-swimmers and the contrast problem in medical resonance imaging. The recently developed numerical software has been applied to the cases studies presented here. The book is intended for use at the graduate and Ph. D. level to introduce students from applied mathematics and control engineering to geometric and computational techniques in optimal control.--
Member of
Assigning source
Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorDate
1952-
http://library.link/vocab/creatorName
Bonnard, Bernard
Dewey number
515/.642
Index
no index present
LC call number
QA402.3
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1969-
http://library.link/vocab/relatedWorkOrContributorName
  • Chyba, Monique
  • Rouot, Jérémy
Series statement
SpringerBriefs in mathematics
http://library.link/vocab/subjectName
Control theory
Label
Geometric and numerical optimal control : application to swimming at Low Reynolds number and magnetic resonance imaging, Bernard Bonnard, Monique Chyba, Jérémy Rouot
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Acknowledgements; Contents; About the Authors; 1 Historical Part-Calculus of Variations; 1.1 Statement of the Problem in the Holonomic Case; 1.2 Hamiltonian Equations; 1.3 Hamilton-Jacobi-Bellman Equation; 1.4 Second Order Conditions; 1.5 The Accessory Problem and the Jacobi Equation; 1.6 Conjugate Point and Local Morse Theory; 1.7 From Calculus of Variations to Optimal Control Theory and Hamiltonian Dynamics; 2 Weak Maximum Principle and Application to Swimming at Low Reynolds Number; 2.1 Pre-requisite of Differential and Symplectic Geometry; 2.2 Controllability Results
  • 2.2.1 Sussmann-Nagano Theorem2.2.2 Chow-Rashevskii Theorem; 2.3 Weak Maximum Principle; 2.4 Second Order Conditions and Conjugate Points; 2.4.1 Lagrangian Manifold and Jacobi Equation; 2.4.2 Numerical Computation of the Conjugate Loci Along a Reference Trajectory; 2.5 Sub-riemannian Geometry; 2.5.1 Sub-riemannian Manifold; 2.5.2 Controllability; 2.5.3 Distance; 2.5.4 Geodesics Equations; 2.5.5 Evaluation of the Sub-riemannian Ball; 2.5.6 Nilpotent Approximation; 2.5.7 Conjugate and Cut Loci in SR-Geometry; 2.5.8 Conjugate Locus Computation; 2.5.9 Integrable Case
  • 2.5.10 Nilpotent Models in Relation with the Swimming Problem2.6 Swimming Problems at Low Reynolds Number; 2.6.1 Purcell's 3-Link Swimmer; 2.6.2 Copepod Swimmer; 2.6.3 Some Geometric Remarks; 2.6.4 Purcell Swimmer; 2.7 Numerical Results; 2.7.1 Nilpotent Approximation; 2.7.2 True Mechanical System; 2.7.3 Copepod Swimmer; 2.8 Conclusion and Bibliographic Remarks; 3 Maximum Principle and Application to Nuclear Magnetic Resonance and Magnetic Resonance Imaging; 3.1 Maximum Principle; 3.2 Special Cases; 3.3 Application to NMR and MRI; 3.3.1 Model; 3.3.2 The Problems
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319947914
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1046977761
  • (OCoLC)1046977761
Label
Geometric and numerical optimal control : application to swimming at Low Reynolds number and magnetic resonance imaging, Bernard Bonnard, Monique Chyba, Jérémy Rouot
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Acknowledgements; Contents; About the Authors; 1 Historical Part-Calculus of Variations; 1.1 Statement of the Problem in the Holonomic Case; 1.2 Hamiltonian Equations; 1.3 Hamilton-Jacobi-Bellman Equation; 1.4 Second Order Conditions; 1.5 The Accessory Problem and the Jacobi Equation; 1.6 Conjugate Point and Local Morse Theory; 1.7 From Calculus of Variations to Optimal Control Theory and Hamiltonian Dynamics; 2 Weak Maximum Principle and Application to Swimming at Low Reynolds Number; 2.1 Pre-requisite of Differential and Symplectic Geometry; 2.2 Controllability Results
  • 2.2.1 Sussmann-Nagano Theorem2.2.2 Chow-Rashevskii Theorem; 2.3 Weak Maximum Principle; 2.4 Second Order Conditions and Conjugate Points; 2.4.1 Lagrangian Manifold and Jacobi Equation; 2.4.2 Numerical Computation of the Conjugate Loci Along a Reference Trajectory; 2.5 Sub-riemannian Geometry; 2.5.1 Sub-riemannian Manifold; 2.5.2 Controllability; 2.5.3 Distance; 2.5.4 Geodesics Equations; 2.5.5 Evaluation of the Sub-riemannian Ball; 2.5.6 Nilpotent Approximation; 2.5.7 Conjugate and Cut Loci in SR-Geometry; 2.5.8 Conjugate Locus Computation; 2.5.9 Integrable Case
  • 2.5.10 Nilpotent Models in Relation with the Swimming Problem2.6 Swimming Problems at Low Reynolds Number; 2.6.1 Purcell's 3-Link Swimmer; 2.6.2 Copepod Swimmer; 2.6.3 Some Geometric Remarks; 2.6.4 Purcell Swimmer; 2.7 Numerical Results; 2.7.1 Nilpotent Approximation; 2.7.2 True Mechanical System; 2.7.3 Copepod Swimmer; 2.8 Conclusion and Bibliographic Remarks; 3 Maximum Principle and Application to Nuclear Magnetic Resonance and Magnetic Resonance Imaging; 3.1 Maximum Principle; 3.2 Special Cases; 3.3 Application to NMR and MRI; 3.3.1 Model; 3.3.2 The Problems
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319947914
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1046977761
  • (OCoLC)1046977761

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