Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Bonnard, Bernard (1952-....)
Chyba, Monique (1969-....)
Rouot, Jérémy
Titre(s) : Geometric and numerical optimal control [Texte électronique] : application to swimming at Low Reynolds number and magnetic resonance imaging / Bernard Bonnard, Monique Chyba, Jérémy Rouot
Publication : Cham : Springer, copyright 2018
Description matérielle : 1 online resource
Collection : SpringerBriefs in mathematics
Lien à la collection : SpringerBriefs in mathematics (Internet)
Note(s) : Bibliogr. p. 106-108
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.
Sujet(s) : Commande, Théorie de la
Indice(s) Dewey :
515.642 (23e éd.) = Théorie de la commande
Identifiants, prix et caractéristiques : ISBN 9783319947914. - ISBN 3319947915. - ISBN 9783319947907 (erroné). - ISBN 3319947907
(erroné)
Identifiant de la notice : ark:/12148/cb45779984b
Notice n° :
FRBNF45779984
(notice reprise d'un réservoir extérieur)
Table des matières : 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.
