Geometric structures on Finsler Lie algebroids and applications to optimal control

Abstract

In this paper some geometric structures on Finsler Lie algeboids
are studied and $h$-basic distinguished connections are
introduced. Specially, Ichijy\={o} connection that is a special
$h$-basic distinguished connection is investigated. The
generalized Berwald Lie algebroids are presented, as a particular
case of Finsler Lie algebroids and Wagner-Ichijy\={o} connection,
that is a special case of Ichijy\={o} connection, is studied.
Moreover, the Wagner Lie algebroid is introduced and some
equivalent conditions for this space are given. Finally, an
optimal control problem is solved using the Pontryagin Maximum
Principle in the framework of a Finsler Lie algebroid.