Singular extremals on Lie groups

DOI10.1007/BF01212270zbMath0925.93132OpenAlexW2089568113WikidataQ115393898 ScholiaQ115393898MaRDI QIDQ1891658

Richard Montgomery

Publication date: 8 November 1999

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01212270

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Linear-quadratic optimal control problems (49N10) Differential forms in global analysis (58A10) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Methods of local Riemannian geometry (53B21)

Related Items

Sard property for the endpoint map on some Carnot groups, Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric, Higher dimensional holonomy map for rules submanifolds in graded manifolds, Extremals in some classes of Carnot groups, On the Maslov and the Morse index for constrained variational problems., Some properties of abnormal extremals on Lie groups, A survey of singular curves in sub-Riemannian geometry, A note on Carnot geodesics in nilpotent Lie groups, Characterizations of Hamiltonian geodesics in sub-Riemannian geometry, Variational formulas for submanifolds of fixed degree, An approach to the relativistic brachistochrone problem by sub-Riemannian geometry, Optimal control of the sphere \(S^n\) rolling on \(E^n\), Generic singularities of distributions of codimension 2 and bi-Hamiltonian structures, Length spectra of sub-Riemannian metrics on compact Lie groups, Properties of reachable sets in the sub-Lorentzian geometry, Path planning on compact Lie groups using a homotopy method., Variational formulas for curves of fixed degree

Cites Work

• Large deviations and the Malliavin calculus
• Sub-Riemannian geometry
• A weak regularity theorem for real analytic optimal control problems
• How fat is a fat bundle
• Fat bundles and symplectic manifolds
• Calculus of variations via the Griffiths formalism
• Some regularity theorems for Carnot-Caratheodory metrics
• Rigidity of integral curves of rank 2 distributions
• The exponential map for the Lagrange problem on differentiable manifolds
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