Study on geometric structures on Lie algebroids with optimal control applications

Abstract

We construct ρ_£ -covariant derivatives in π*π as the generalization of covariant derivative in π*π to £^π E. Moreover, we introduce Berwald and Yano derivatives as two important classes of ρ_£ -covariant derivatives in π∗π and we study properties of them. Finally, we solve an optimal control problem using some geometric structures and Pontryagin Maximum Principle on Lie algebroids.

Keywords:

• Berwald and Yano-derivatives
• Covariant derivative
• Douglas tensor
• Lie algebroid
• Optimal control

2010 Mathematics Subject Classification:

• 17B66
• 34A26
• 53C05