论文标题
使用跳跃功能近似的网状细化方法，用于通过非平滑解决方案解决最佳控制问题
Mesh Refinement Method for Solving Optimal Control Problems with Nonsmooth Solutions Using Jump Function Approximations
论文作者
论文摘要
描述了使用Legendre-Gauss-Radau搭配解决最佳控制问题的网格改进方法。该方法通过基于跳跃函数近似的边缘检测方案来检测控制解决方案中的不连续性。当发现不连续性时，网格将通过针对性的$ h $投资方法进行完善，从而将不连续位置与网格点进行了括起来。使用先前开发的技术对网格的其余平滑部分进行了完善。该方法在两个示例中进行了证明，结果表明，与先前开发的方法相比，该方法使用更少的网格细化迭代解决了不连续的控制解决方案的最佳控制问题，而计算时间较少。
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.
