@inproceedings{9665d825edfb4d379b6791ddc75df677,
title = "Geometric optimal control for symmetry breaking cost functions",
abstract = "We consider an optimal control problem defined on a Lie group whose associated Hamiltonian function is left-invariant under the action of a subgroup of the Lie group. Necessary conditions for optimality are derived using Lie-Poisson reduction for semidirect products, which allows us to study the Hamiltonian system in a space of lower dimension. Our main contribution is a reduced sufficient condition for optimality that relies on the nonexistence of conjugate points. We derive coordinate formulae for computing conjugate points in the reduced Hamiltonian system, and we relate these conjugate points to local optimality in the original optimal control problem. These conditions are applied to an optimal control problem that can be used to model either a kinematic airplane or a Kirchhoff elastic rod in a gravitational field.",
author = "Borum, {Andy D.} and Timothy Bretl",
note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",
year = "2014",
doi = "10.1109/CDC.2014.7040306",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "February",
pages = "5855--5861",
booktitle = "53rd IEEE Conference on Decision and Control,CDC 2014",
address = "United States",
edition = "February",
}