A mesh refinement method is described for solving optimal control problems using Legendre-Gauss-Radau collocation. The method detects discontinuities in the control solution by employing an edge detection scheme based on jump function approximations. When discontinuities are identified, the mesh is refined with a targeted h-refinement approach whereby the discontinuity locations are bracketed with mesh points. The remaining smooth portions of the mesh are refined using previously developed techniques. The method is demonstrated on two examples, and results indicate that the method solves optimal control problems with discontinuous control solutions using fewer mesh refinement iterations and less computation time when compared with previously developed methods.

中文翻译：

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使用跳跃函数近似求解非光滑解最优控制问题的网格细化方法

描述了使用 Legendre-Gauss-Radau 搭配求解最优控制问题的网格细化方法。该方法通过采用基于跳跃函数近似的边缘检测方案来检测控制解中的不连续性。当识别出不连续性时，将使用有针对性的h细化方法来细化网格，其中不连续性位置用网格点括起来。网格的其余平滑部分使用先前开发的技术进行细化。该方法在两个例子中得到演示，结果表明，与以前开发的方法相比，该方法使用更少的网格细化迭代和更少的计算时间来解决具有不连续控制解的最优控制问题。