Discrete second-order Euler-Poincaré equations. Applications to optimal control

Details Discrete second-order Euler-Poincaré equations. Applications to optimal control Discrete second-order Euler-Poincaré equations. Applications to optimal control

2011-09-22

arxiv.org/abs/1109.4716v1

Physics

Mathematical Physics

18 pages

Scientific paper

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.

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