Embedded geodesic problems and optimal control for matrix Lie groups
AM Bloch, PE Crouch, N Nordkvist… - Journal of Geometric …, 2011 - aimsciences.org
This paper is devoted to a detailed analysis of the geodesic problem on matrix Lie groups,
with left invariant metric, by examining representations of embeddings of geodesic flows in …
with left invariant metric, by examining representations of embeddings of geodesic flows in …
[PDF][PDF] Optimal control and geodesics on matrix Lie groups
PE Crouch, N Nordkvist, AK Sanyal - Proc. 9th Portuguese Conference on …, 2010 - Citeseer
In this paper we analyze left invariant geodesic problems on matrix Lie groups from both the
continuous and discrete viewpoint; the discrete approach approximates the continuous …
continuous and discrete viewpoint; the discrete approach approximates the continuous …
Optimal control and geodesics on quadratic matrix Lie groups
AM Bloch, PE Crouch, JE Marsden… - Foundations of …, 2008 - Springer
The purpose of this paper is to extend the symmetric representation of the rigid body
equations from the group SO (n) to other groups. These groups are matrix subgroups of the …
equations from the group SO (n) to other groups. These groups are matrix subgroups of the …
Continuous and discrete embedded optimal control problemsand their application to the analysis of Clebsch optimal controlproblems and mechanical systems
AM Bloch, PE Crouch, N Nordkvist - Journal of Geometric …, 2013 - aimsciences.org
In this paper we define “embedded optimal control problems” which prescribe parametrized
families of well defined associated optimal control problems. We show that the extremal …
families of well defined associated optimal control problems. We show that the extremal …
Geodesic boundary value problems with symmetry
This paper shows how left and right actions of Lie groups on a manifold may be used to
complement one another in a variational reformulation of optimal control problems …
complement one another in a variational reformulation of optimal control problems …
Optimal control and geodesic flows
AM Bloch, PE Crouch - Systems & control letters, 1996 - Elsevier
In this paper we analyze and generalize, from the point of view of the maximum principle, a
class of nonlinear optimal control problems originally introduced in Brockett (1994). The …
class of nonlinear optimal control problems originally introduced in Brockett (1994). The …
Optimal control problems on matrix Lie groups
M Puta - New Developments in Differential Geometry, Budapest …, 1999 - Springer
X = LFi(X)Ui(t), x = Ax+Bu, Page 1 OPTIMAL CONTROL PROBLEMS ON MATRIX LIE
GROUPS MIRCEA PUTA Seminarul de Geometrie-Topoiogie, Universitatea de Vest din Timi§oara …
GROUPS MIRCEA PUTA Seminarul de Geometrie-Topoiogie, Universitatea de Vest din Timi§oara …
Higher-order variational problems on Lie groups and optimal control applications
L Colombo, DM de Diego - Journal of Geometric Mechanics, 2014 - aimsciences.org
In this paper, we describe a geometric setting for higher-order Lagrangian problems on Lie
groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an …
groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an …
[图书][B] Integrable Hamiltonian systems on complex Lie groups
V Jurdjevic - 2005 - books.google.com
Studies the elastic problems on simply connected manifolds $ M_n $ whose orthonormal
frame bundle is a Lie group $ G $. This title synthesizes ideas from optimal control theory …
frame bundle is a Lie group $ G $. This title synthesizes ideas from optimal control theory …
On the geometry of higher-order variational problems on Lie groups
L Colombo, DM de Diego - arXiv preprint arXiv:1104.3221, 2011 - arxiv.org
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie
groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an …
groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an …