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Geometric Control Theory and Sub-Riemannian Geometry

  • Book
  • © 2014

Overview

Editors:
  1. Gianna Stefani

    1. Dipartimento di Matematica e Informatica “U.Dini”, Università degli Studi di Firenze, Firenze, Italy

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  2. Ugo Boscain

    1. CNRS, CMAP, École Polytechnique, INRIA Saclay, Team GECO, Palaiseau, France

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  3. Jean-Paul Gauthier

    1. LSIS, Université de Toulon, La Garde Cedex, France

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  4. Andrey Sarychev

    1. Dipartimento di Matematica e Informatica “U.Dini”, Università degli Studi di Firenze, Firenze, Italy

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  5. Mario Sigalotti

    1. INRIA Saclay, Team GECO, CMAP, École Polytechnique, Palaiseau, France

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  • Feature chapter on open problems
  • Presents state of the art of the research in the field
  • Collects papers by top level scientists
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer INdAM Series (SINDAMS, volume 5)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xii
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  2. Some open problems

    • Andrei A. Agrachev
    Pages 1-13

  3. Geometry of Maslov cycles

    • Davide Barilari, Antonio Lerario
    Pages 15-35

  4. How to Run a Centipede: a Topological Perspective

    • Yuliy Baryshnikov, Boris Shapiro
    Pages 37-51

  5. Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces

    • Bernard Bonnard, Olivier Cots, Lionel Jassionnesse
    Pages 53-72

  6. On the injectivity and nonfocal domains of the ellipsoid of revolution

    • Jean-Baptiste Caillau, Clément W. Royer
    Pages 73-85

  7. Null controllability in large time for the parabolic Grushin operator with singular potential

    • Piermarco Cannarsa, Roberto Guglielmi
    Pages 87-102

  8. The rolling problem: overview and challenges

    • Yacine Chitour, Mauricio Godoy Molina, Petri Kokkonen
    Pages 103-122

  9. Optimal stationary exploitation of size-structured population with intra-specific competition

    • Alexey A. Davydov, Anton S. Platov
    Pages 123-132

  10. On geometry of affine control systems with one input

    • Boris Doubrov, Igor Zelenko
    Pages 133-152

  11. Remarks on Lipschitz domains in Carnot groups

    • Bruno Franchi, Valentina Penso, Raul Serapioni
    Pages 153-166

  12. Differential-geometric and invariance properties of the equations of Maximum Principle (MP)

    • Revaz V. Gamkrelidze
    Pages 167-175

  13. Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces

    • Nicola Garofalo
    Pages 177-199

  14. Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds

    • Roberta Ghezzi, Frédéric Jean
    Pages 201-218

  15. The Delauney-Dubins Problem

    • Velimir Jurdjevic
    Pages 219-239

  16. On Local Approximation Theorem on Equiregular Carnot-Carathéodory Spaces

    • Maria Karmanova, Sergey Vodopyanov
    Pages 241-262

  17. On curvature-type invariants for natural mechanical systems on sub-Riemannian structures associated with a principle G-bundle

    • Chengbo Li
    Pages 263-285

  18. On the Alexandrov Topology of sub-Lorentzian Manifolds

    • Irina Markina, Stephan Wojtowytsch
    Pages 287-311

  19. The regularity problem for sub-Riemannian geodesics

    • Roberto Monti
    Pages 313-332

  20. A case study in strong optimality and structural stability of bang-singular extremals

    • Laura Poggiolini, Gianna Stefani
    Pages 333-350
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Keywords

About this book

Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

Editors and Affiliations

  • Dipartimento di Matematica e Informatica “U.Dini”, Università degli Studi di Firenze, Firenze, Italy

    Gianna Stefani, Andrey Sarychev

  • CNRS, CMAP, École Polytechnique, INRIA Saclay, Team GECO, Palaiseau, France

    Ugo Boscain

  • LSIS, Université de Toulon, La Garde Cedex, France

    Jean-Paul Gauthier

  • INRIA Saclay, Team GECO, CMAP, École Polytechnique, Palaiseau, France

    Mario Sigalotti

About the editors

Prof. Gianna Stefani: From 1997 is Full Professor at University of Florence, Italy.

Prof. Ugo Boscain: Directeur de recherche CNRS (DR2) at the Center of Applied Mathematics and Probability (CMAP) of Ecole Polytechnique; Professeur charge de course in numerical analysis and optimization at Ecole Polytechnique (department of applied mathematics); Deputy team leader of the equipe-INRIA GECO Inria Saclay.

Prof. Jean-Paul Gauthier: Experience of JP Gauthier In Scientific Research (January 2011), Including; Research Team Management and Industrial Collaborations; JP Gauthier has scientific experience in several areas (pluridisciplinary); Honorary Member of Institut Universitaire de France (Promotion 1992).

Prof. Andrey Sarychev: Full Professor (Professore Ordinario di I Fascia) at the Department of Mathematics and Informatics U.Dini (DiMaI), University of Florence, Italy, since January 2013. Prof. Mario Sigalotti: Chargé de recherche de première classe (CR1) - Établissement : INRIA Saclay – Île-de-France - Équipe-projet : GECO.

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