论文标题
通过缩回图，用于最佳控制问题的前整合积分器
Presymplectic integrators for optimal control problems via retraction maps
论文作者
论文摘要
回缩图用于定义配置歧管的切线束的离散化，为发生动力学的配置歧管的两个副本。可以方便地将这种离散图提起到Cotangent束，以便为汉密尔顿方程式构建符号积分器。 Pontryagin的最大原则由Hamiltonian框架提供了最佳控制问题。这就是为什么我们使用离散图和集成性算法来获取用于最佳控制问题的预叠型积分器的原因。
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the cotangent bundle so that symplectic integrators are constructed for Hamilton's equations. Optimal control problems are provided with a Hamiltonian framework by Pontryagin's Maximum Principle. That is why we use discretization maps and the integrability algorithm to obtain presymplectic integrators for optimal control problems.
