Discrete second-order Euler-Poincar\'e equations. Applications to optimal control
Mathematical Physics
2011-09-23 v1 Differential Geometry
math.MP
Numerical Analysis
Abstract
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler-Lagrange equations. Interesting applications as, for instance, a discrete derivation of the Euler-Poincar\'e equations for second-order Lagrangians and its application to optimal control of a rigid body, and of a Cosserat rod are shown at the end of the paper.
Cite
@article{arxiv.1109.4716,
title = {Discrete second-order Euler-Poincar\'e equations. Applications to optimal control},
author = {Leonardo Colombo and Fernando Jimenez and David Martin de Diego},
journal= {arXiv preprint arXiv:1109.4716},
year = {2011}
}
Comments
18 pages