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.

中文翻译：

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具有最优控制应用的李代数体几何结构研究

我们构造π*π中的ρ￡-协变导数作为π*π中的协变导数到￡πE的推广。此外，我们引入Berwald和Yano导数作为π*π中的ρ￠-协变导数的两个重要类别，研究它们的特性。最后，我们使用一些几何结构和李代数上的庞特里亚金极大原理来解决一个最优控制问题。