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Mathematics | Geometric Control Theory and Sub-Riemannian Geometry

Geometric Control Theory and Sub-Riemannian Geometry

Series: Springer INdAM Series, Vol. 5

Stefani, G., Boscain, U., Gauthier, J.-P., Sarychev, A., Sigalotti, M. (Eds.)

2014, XII, 384 p.

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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
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.

Content Level » Research

Keywords » control system - geometric control - sub-Riemannian geometry

Related subjects » Analysis - Geometry & Topology - Mathematics

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