Generalized Lie Algebroids - Examples by Distinguished Lie Algebroids with Applications to Optimal Control

2018/08/20 by Arcus, Constantin M., Peyghan, Esmaeil, Sharahi, Esa
#2010: 00A69 #53B50 #58A32 #58B34 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1808.06297

Abstract

We will prove that the generalized Lie algebroid is a distinguished example by Lie algebroid. The generality of it with respect to the Lie algebroid is similar with the generality of the pull-back vector bundle with respect to the vector bundle. Next, we will prove that the proof of Theorem 3.1 from [15] is a misconception and the mentioned Theorem has no validity. Finally, we anatomize an optimal control problem solvable in the generalized Lie algebroid framework whereas Lie algebroid instrumentation can not solve it.

Related

• The geometry of Lie algebroids and its applications to optimal control
• Optimal Control Theory on almost-Lie Algebroids
• The generalized Lie algebroids and their applications
• Mechanical control systems on Lie algebroids
• Optimal control problems on the co-adjoint Lie groupoids