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.

翻译：本文比较了不同数值格式在逼近非完整系统最优控制中庞特里亚金极大值原理必要条件时的性能表现。回缩映射被用作构建相应哈密顿方程几何积分器的种子。首先，我们得到了分布$\mathcal{D}$上离散化映射的内蕴形式。随后，我们通过具体算例阐释该构造方法，并比较不同辛积分器与非辛积分器的性能表现。