DISCRETE SECOND-ORDER EULER–POINCARÉ EQUATIONS: APPLICATIONS TO OPTIMAL CONTROL

DOI10.1142/S0219887812500375zbMath1256.93037arXiv1109.4716OpenAlexW2962893271MaRDI QIDQ4902538

Fernando Jiménez, Leonardo Colombo, David Martín de Diego

Publication date: 16 January 2013

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4716

zbMATH Keywords

optimal controlrigid bodyEuler-Poincaré equationsLagrangian systemsgeometric integratorsdiscrete mechanicsCosserat rodmechanics on Lie groups

Mathematics Subject Classification ID

Control of mechanical systems (70Q05) Optimality conditions for problems involving ordinary differential equations (49K15) Lagrange's equations (70H03)

Related Items (9)

High Order Variational Integrators: A Polynomial Approach ⋮ The variational discretization of the constrained higher-order Lagrange-Poincaré equations ⋮ Variational integrators for mechanical control systems with symmetries ⋮ Second-order variational problems on Lie groupoids and optimal control applications ⋮ Discrete dynamical systems over double cross-product Lie groupoids ⋮ A discrete-time Pontryagin maximum principle on matrix Lie groups ⋮ Higher-order discrete variational problems with constraints ⋮ Higher-order variational problems on Lie groups and optimal control applications ⋮ High order variational integrators in the optimal control of mechanical systems

Cites Work

• Optimal attitude control of a rigid body using geometrically exact computations on \(SO(3)\)
• Discrete nonholonomic Lagrangian systems on Lie groupoids
• Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties
• Symmetry reduction of discrete Lagrangian mechanics on Lie groups
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
• Discrete mechanics and variational integrators
• Cubic Splines on Curved Spaces
• Optimal control of underactuated mechanical systems: A geometric approach
• HIGHER-ORDER DISCRETE LAGRANGIAN MECHANICS
• Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids

This page was built for publication: DISCRETE SECOND-ORDER EULER–POINCARÉ EQUATIONS: APPLICATIONS TO OPTIMAL CONTROL