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 andWagner-Ichijy ¯o connection, that is a special case of Ichijy ¯o connection, is studied. Moreover, theWagner 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.
