Geometric Control Theory and Sub-Riemannian Geometry

  • Gianna Stefani
  • Ugo Boscain
  • Jean-Paul Gauthier
  • Andrey Sarychev
  • Mario Sigalotti

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Andrei A. Agrachev
    Pages 1-13
  3. Davide Barilari, Antonio Lerario
    Pages 15-35
  4. Yuliy Baryshnikov, Boris Shapiro
    Pages 37-51
  5. Bernard Bonnard, Olivier Cots, Lionel Jassionnesse
    Pages 53-72
  6. Jean-Baptiste Caillau, Clément W. Royer
    Pages 73-85
  7. Yacine Chitour, Mauricio Godoy Molina, Petri Kokkonen
    Pages 103-122
  8. Boris Doubrov, Igor Zelenko
    Pages 133-152
  9. Bruno Franchi, Valentina Penso, Raul Serapioni
    Pages 153-166
  10. Velimir Jurdjevic
    Pages 219-239
  11. Maria Karmanova, Sergey Vodopyanov
    Pages 241-262
  12. Irina Markina, Stephan Wojtowytsch
    Pages 287-311

About this book


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.


control system geometric control sub-Riemannian geometry

Editors and affiliations

  • Gianna Stefani
    • 1
  • Ugo Boscain
    • 2
  • Jean-Paul Gauthier
    • 3
  • Andrey Sarychev
    • 1
  • Mario Sigalotti
    • 4
  1. 1.Dipartimento di Matematica e Informatica “U.Dini”Università degli Studi di FirenzeFirenzeItaly
  2. 2.CNRSCMAP, École Polytechnique, INRIA Saclay, Team GECOPalaiseauFrance
  3. 3.LSISUniversité de ToulonLa Garde CedexFrance
  4. 4.INRIA Saclay, Team GECOCMAP, École PolytechniquePalaiseauFrance

Bibliographic information