Geometric Control Theory and Sub-Riemannian Geometry [Paperback]

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.

Presenting state-of-the-art research in a highly applicable field, this collection features papers by leading scientists combining these two methodologies, in honor of the groundbreaking work of Andrei Agrachev. It includes a chapter on open problems.

1 A. A. Agrachev - Some open problems.- 2 D. Barilari, A. Lerario - Geometry of Maslov cycles.- 3 Y. Baryshnikov, B. Shapiro - How to Run a Centipede: a Topological Perspective.- 4 B. Bonnard, O. Cots, L. Jassionnesse - Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces.- 5 J-B. Caillau, C. Royer - On the injectivity and nonfocal domains of the ellipsoid of revolution.- 6 P. Cannarsa, R. Guglielmi - Null controllability in large time for the parabolic Grushin operator with singular potential.- 7 Y. Chitour, M. Godoy Molina, P. Kokkonen - The rolling problem: overview and challenges.- 8 A. A. Davydov, A. S. Platov - Optimal stationary exploitation of size-structured popullc(