Extremal trajectories and Maxwell strata in sub-Riemannian problem on group of motions of pseudo-Euclidean plane

DOI10.1007/s10883-014-9239-2zbMath1301.49116arXiv1305.1338OpenAlexW3102319921WikidataQ115383683 ScholiaQ115383683MaRDI QIDQ459032

Yasir Awais Butt, Yuri L. Sachkov, Aamer Iqbal Bhatti

Publication date: 8 October 2014

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1338

zbMATH Keywords

sub-Riemannian geometryelliptic coordinatespseudo-Euclidean planeextremal trajectoriesMaxwell strata

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Geometric methods (93B27) Analysis on real and complex Lie groups (22E30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimization of shapes other than minimal surfaces (49Q10) Sub-Riemannian geometry (53C17)

Related Items (11)

On extensions of sub-Riemannian structures on Lie groups ⋮ Cut locus and optimal synthesis in sub-Riemannian problem on the Lie group SH(2) ⋮ Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups ⋮ On sub-Riemannian and Riemannian structures on the Heisenberg groups ⋮ Maxwell strata and conjugate points in the sub-Riemannian problem on the Lie group SH(2) ⋮ Cut time in sub-riemannian problem on engel group ⋮ The normal sub-Riemannian geodesic flow on E(2) generated by a left-invariant metric and a right-invariant distribution ⋮ Comparison theorems for conjugate points in sub-Riemannian geometry ⋮ Sufficient Conditions for a Path-Connected Set of Local Solutions to an Optimal Control Problem ⋮ Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry ⋮ Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

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