Higher-order variational problems on Lie groups and optimal control applications

DOI10.3934/jgm.2014.6.451zbMath1307.70018OpenAlexW2328201720MaRDI QIDQ2514344

Leonardo Colombo, David Martín de Diego

Publication date: 3 February 2015

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2014.6.451

zbMATH Keywords

Lie groupsoptimal control of mechanical systemshigher-order tangent bundlesPontryagin's bundleSkinner-Rusk formalism

Mathematics Subject Classification ID

Constrained dynamics, Dirac's theory of constraints (70H45) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Higher-order theories for problems in Hamiltonian and Lagrangian mechanics (70H50)

Related Items (17)

Second-order constrained variational problems on Lie algebroids: applications to optimal control ⋮ The variational discretization of the constrained higher-order Lagrange-Poincaré equations ⋮ Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids ⋮ Variational integrators for mechanical control systems with symmetries ⋮ Second-order variational problems on Lie groupoids and optimal control applications ⋮ Lagrangian dynamics on matched pairs ⋮ A general framework for quantum splines ⋮ Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles ⋮ Unnamed Item ⋮ Second order Lagrangian dynamics on double cross product groups ⋮ Reductions of topologically massive gravity II. First order realizations of second order Lagrangians ⋮ On the geometry of the Schmidt-Legendre transformation ⋮ Geometric integrators for higher-order variational systems and their application to optimal control ⋮ Higher-order analogs of Lie algebroids via vector bundle comorphisms ⋮ Regularity properties of fiber derivatives associated with higher-order mechanical systems ⋮ Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians ⋮ Dynamic interpolation for obstacle avoidance on Riemannian manifolds

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