标题： 非完整系统的最优控制中的重投影映射 显示英文标题

标题： Retraction maps in optimal control of nonholonomic systems

摘要： 本文中，我们比较了不同数值格式在逼近非完整系统最优控制的庞特里亚金最大值原理必要条件时的表现。 重退映射被用作种子来构建对应哈密顿方程的几何积分器。首先，我们在分布$\mathcal{D}$上获得了离散化映射的一个内在表述。然后，我们在一个特定例子上说明这一构造过程，在该例子中检验并比较了几种辛积分器与非辛积分器的性能。 显示英文摘要

摘要： In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct geometric integrators for the corresponding Hamilton equations. First, we obtain an intrinsic formulation of a discretization map on a distribution $\mathcal{D}$. Then, we illustrate this construction on a particular example for which the performance of different symplectic integrators is examined and compared with that of non-symplectic integrators.