Geometric and numerical optimal control : application to swimming at Low Reynolds number and magnetic resonance imaging /: application to swimming at Low Reynolds number and magnetic resonance imaging. (2018)

• Record Type: Book
• Further Information: Note: Bernard Bonnard, Monique Chyba, Jérémy Rouot.
• Authors: Bonnard, Bernard, 1952-; Chyba, Monique, 1969-; Rouot, Jérémy
• 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 515/.642; Mathematics; Control theory; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Control theory; Mathematics; Calculus of Variations and Optimal Control; Optimization; Neurosciences; Applications of Mathematics; Mathematical Modeling and Industrial Mathematics; Computer Appl. in Life Sciences; Medical -- Neuroscience; Mathematics -- Applied; Science -- Life Sciences -- General; Neurosciences; Applied mathematics; Mathematical modelling; Biology, life sciences; Mathematical optimization; Neurosciences; Biology_xData processing; Mathematics -- Calculus; Calculus of variations; Electronic books
• Languages: English
• ISBNs: 9783319947914; 3319947915
• Related ISBNs: 9783319947907; 3319947907
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 2, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.