Title :
A geometric approach to discrete mechanics for optimal control theory
Author :
Jiménez, Fernando ; De Diego, David Martín
Author_Institution :
Inst. de Cienc. Mat., CSIC, Madrid, Spain
Abstract :
In this paper, we will discuss some new developments in the design of numerical methods for optimal control problems for controlled Lagrangian systems. We will construct these geometric integrators using discrete variational calculus. The derived techniques are also valid for reduced systems, including systems defined on Lie algebras and Atiyah bundles. We will illustrate with several theoretical examples the wide range of application of this theory.
Keywords :
Lie algebras; geometry; optimal control; variational techniques; Atiyah bundles; Lie algebra; controlled Lagrangian systems; discrete mechanics; discrete variational calculus; geometric approach; geometric integrators; optimal control problems; optimal control theory; reduced systems; Algebra; Approximation methods; Equations; Force; Manifolds; Mechanical systems; Optimal control;
Conference_Titel :
Decision and Control (CDC), 2010 49th IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
978-1-4244-7745-6
DOI :
10.1109/CDC.2010.5717181
