Optimal control on the Heisenberg group

DOI10.1023/A:1021787121457zbMath0956.49013OpenAlexW194976377MaRDI QIDQ1972805

A. Anzaldo-Meneses, Felipe Monroy-Pérez

Publication date: 13 April 2000

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

Full work available at URL: https://doi.org/10.1023/a:1021787121457

zbMATH Keywords

optimal controlHeisenberg groupextremal curves

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Analysis on other specific Lie groups (43A80) Optimality conditions for problems involving ordinary differential equations (49K15) Controllability, observability, and system structure (93B99) Manifolds and measure-geometric topics (49Q99)

Related Items (15)

On sub-Riemannian and Riemannian structures on the Heisenberg groups ⋮ Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions ⋮ The step-2 nilpotent \((n,n(n+1)/2)\) sub-Riemannian geometry ⋮ Hardy-type inequalities for the Carnot-Carathéodory distance in the Heisenberg group ⋮ Symmetries in geometric control theory using Maple ⋮ Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric ⋮ On symmetries of a sub-Riemannian structure with growth vector \((4, 7)\) ⋮ Invariant Control Systems on Lie Groups ⋮ Extremal trajectories and Maxwell strata in sub-Riemannian problem on group of motions of pseudo-Euclidean plane ⋮ Sufficient conditions for dispersiveness of invariant control affine systems on the Heisenberg group ⋮ Some properties of abnormal extremals on Lie groups ⋮ Quadratic Hamilton-Poisson systems in three dimensions: equivalence, stability, and integration ⋮ Cost-extended control systems on Lie groups ⋮ Sufficient Conditions for a Path-Connected Set of Local Solutions to an Optimal Control Problem ⋮ Control theory on Lie groups

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