Lie group projection operator approach: Optimal control on T SO(3)

2011 ◽  
Author(s):  
Alessandro Saccon ◽  
A. Pedro Aguiar ◽  
John Hauser
Keyword(s):  
Optimal Control ◽  
Lie Group ◽  
Projection Operator ◽  
Operator Approach

Optimal Control on Lie Groups: Implementation Details of the Projection Operator Approach

2011 ◽  
Vol 44 (1) ◽  
pp. 14567-14572 ◽  
Author(s):  
Alessandro Saccon ◽  
John Hauser ◽  
A. Pedro Aguiar
Keyword(s):  
Optimal Control ◽  
Lie Groups ◽  
Projection Operator ◽  
Operator Approach

Optimal Control on Lie Groups: The Projection Operator Approach

2013 ◽  
Vol 58 (9) ◽  
pp. 2230-2245 ◽  
Author(s):  
Alessandro Saccon ◽  
John Hauser ◽  
A. Pedro Aguiar
Keyword(s):  
Optimal Control ◽  
Lie Groups ◽  
Projection Operator ◽  
Operator Approach

scholarly journals COMMUTATORS OF SKEW-SYMMETRIC MATRICES

2005 ◽  
Vol 15 (03) ◽  
pp. 793-801 ◽  
Author(s):  
ANTHONY M. BLOCH ◽  
ARIEH ISERLES
Keyword(s):  
Optimal Control ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Group ◽  
Geometric Integration ◽  
Symmetric Matrices ◽  
Frobenius Norm

In this paper we develop a theory for analysing the "radius" of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra 𝔰𝔬(n) of skew symmetric matrices where we prove [Formula: see text], X, Y ∈ 𝔰𝔬(n), for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control.

Optimal control on Schrödinger Lie group and the behaviour of the dynamics

2016 ◽  
pp. dnw045
Author(s):  
Soumya Ranjan Sahoo ◽  
Soumya Prakash Sahoo ◽  
Amit Jena ◽  
K. C. Pati
Keyword(s):  
Optimal Control ◽  
Lie Group
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