Geometric Control Theory and Sub-Riemannian Geometry

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

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.

• control system
• geometric control
• sub-Riemannian geometry

• 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

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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