Lorentzian problems on the Heisenberg group
I.A. Galyaev, Yu.L. Sachkov
TL;DR
This paper investigates Lorentzian optimal control problems on the Heisenberg group, deriving extremal trajectories and analyzing reachability and existence of solutions using Pontryagin's maximum principle.
Contribution
It introduces a novel application of the Pontryagin maximum principle to Lorentzian problems on the Heisenberg group, providing explicit extremal trajectories and reachability analysis.
Findings
Parameterization of abnormal and normal extremal trajectories
Reachability sets characterized for the problems
Existence results for optimal trajectories established
Abstract
Three left-invariant Lorentzian problems on the Heisenberg group are considered. The Pontryagin maximum principle was applied to both problems and a parameterization of abnormal and normal extremal trajectories was obtained. Reachability sets and the existence of optimal trajectories are investigated.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · advanced mathematical theories