TY - BOOK ID - 699378 TI - Geometric Control Theory and Sub-Riemannian Geometry AU - Stefani, Gianna. AU - Boscain, Ugo. AU - Gauthier, Jean-Paul. AU - Sarychev, Andrey. AU - Sigalotti, Mario. PY - 2014 SN - 331902132X 3319021311 1322133670 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Geometry, Riemannian. KW - Control theory. KW - Dynamics KW - Machine theory KW - Riemann geometry KW - Riemannian geometry KW - Generalized spaces KW - Geometry, Non-Euclidean KW - Semi-Riemannian geometry KW - Mathematical optimization. KW - Global analysis. KW - Global differential geometry. KW - Calculus of Variations and Optimal Control; Optimization. KW - Global Analysis and Analysis on Manifolds. KW - Differential Geometry. KW - Geometry, Differential KW - Optimization (Mathematics) KW - Optimization techniques KW - Optimization theory KW - Systems optimization KW - Mathematical analysis KW - Maxima and minima KW - Operations research KW - Simulation methods KW - System analysis KW - Calculus of variations. KW - Global analysis (Mathematics). KW - Manifolds (Mathematics). KW - Differential geometry. KW - Topology KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Isoperimetrical problems KW - Variations, Calculus of KW - Differential geometry UR - https://www.unicat.be/uniCat?func=search&query=sysid:699378 AB - 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. ER -