Transitivity of Families of Invariant Vector Fields on The Semidirect Products of Lie Groups

DOI10.2307/1998897zbMath0519.49023OpenAlexW4237335635MaRDI QIDQ3668371

Gauthier Sallet, Ivan Kupka, Bernard Bonnard, Velimir Jurdjevic

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/1998897

zbMATH Keywords

transitivitycontrollability of affine systemsinvariant vector fields on Lie groupsSerret-Frenet moving frames

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Controllability (93B05) Lie algebras of Lie groups (22E60) Attainable sets, reachability (93B03) Curves in Euclidean and related spaces (53A04) Lie algebras and Lie superalgebras (17B99) Controllability of vector fields on (C^infty) and real-analytic manifolds (57R27)

Related Items (17)

Control sets for bilinear and affine systems ⋮ Unnamed Item ⋮ Maximal semigroups and controllability in products of Lie groups ⋮ Existence of sub-Lorentzian longest curves ⋮ Invariant Control Systems on Lie Groups ⋮ Maximal subsemigroups of Lie groups that are total ⋮ Control systems on three-dimensional Lie groups: equivalence and controllability ⋮ Infinitesimally generated subsemigroups of motion groups ⋮ Linear control semigroups acting on projective space ⋮ Errata to: ``Infinitesimally generated subsemigroups of motion groups ⋮ Unitary immersions of nonlinear systems ⋮ On subsemigroups of semisimple Lie groups ⋮ Control theory on Lie groups ⋮ An estimation of the controllability time for single-input systems on compact Lie Groups ⋮ Controllability of invariant systems on Lie groups and homogeneous spaces. ⋮ Cone constraints for solutions of homogeneous bilinear systems ⋮ Lyapunov and minimum-time path planning for drones

Cites Work

• Control systems subordinated to a group action: Accessibility
• Control systems on Lie groups
• Controllability of Nonlinear Systems on Compact Manifolds
• A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control Problems
• Controllability of nonlinear systems

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