Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric

DOI10.1051/cocv:2004018zbMath1072.49001OpenAlexW2112555562WikidataQ57084373 ScholiaQ57084373MaRDI QIDQ5465563

Claudio Altafini

Publication date: 9 August 2005

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2004__10_4_526_0

zbMATH Keywords

optimal controlreductionLie groupsemidirect productgroup symmetrygeometric splinessecond order variational problems

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15) Robot dynamics and control of rigid bodies (70E60) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lagrange's equations (70H03) Manifolds of metrics (especially Riemannian) (58D17)

Related Items

Neighboring extremal optimal control for mechanical systems on Riemannian manifolds ⋮ Feedback control of spin systems ⋮ High-order splines on Riemannian manifolds ⋮ Reduction by Symmetry in Obstacle Avoidance Problems on Riemannian Manifolds ⋮ Variational dynamic interpolation for kinematic systems on trivial principal bundles ⋮ Incoherent control of open quantum systems ⋮ Weak geodesic flow on a semidirect product and global solutions to the periodic Hunter-Saxton system ⋮ Variational calculus on Lie algebroids ⋮ Dynamic interpolation for obstacle avoidance on Riemannian manifolds

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