DISCRETE SECOND-ORDER EULER-POINCARE EQUATIONS. APPLICATIONS TO OPTIMAL CONTROL

被引：10

作者：

Colombo, Leonardo ^{[1
]}

Jimenez, Fernando ^{[1
]}

Martin de Diego, David ^{[1
]}

机构：

[1] Inst Ciencias Matemat CSIC UAM UC3M UCM, Madrid 28049, Spain

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2012年 / 9卷 / 04期

关键词：

Optimal control; discrete mechanics; Euler-Poincare equations; mechanics on Lie groups; OPTIMAL ATTITUDE-CONTROL; MECHANICS;

D O I：

10.1142/S0219887812500375

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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-Poincare 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.

引用

页数：20

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