Recently, a mesh refinement strategy is presented on pseudospectral methods for solving optimal control problems by using the relative curvature of the state approximation to choose the type of discretization change in each iteration. Nevertheless, this criterion requires a large amount of computational cost in terms of CPU time. The main goal of this paper is to draw attention to select a suitable criterion with fewer computational cost. To this end, we use the arc length of the state approximation in the mesh interval based on the relative error estimate that was recently provided. We also update the number of mesh intervals and the location of mesh points according to the behaviour of the arc length. Indeed, by implementing this criterion, we do not need to solve an optimization problem anymore, and so significantly reduce the computational time as well as CPU times. Finally, we illustrate the accuracy, efficiency and ability of the arc length criterion in comparison with the curvature by offering some numerical examples.

中文翻译：

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在解决最佳控制问题方面对某些网格细化策略进行了基于快速的改进

最近，在伪谱方法上提出了一种网格细化策略，通过使用状态近似的相对曲率选择每次迭代中离散化变化的类型来解决最优控制问题。然而，就CPU时间而言，此标准需要大量的计算成本。本文的主要目的是引起人们的注意，以选择较少的计算成本来选择合适的准则。为此，我们基于最近提供的相对误差估计，在网格间隔中使用状态近似的弧长。我们还根据弧长的行为更新网格间隔的数量和网格点的位置。实际上，通过实施此标准，我们不再需要解决优化问题，从而大大减少了计算时间和CPU时间。最后，通过提供一些数值示例，我们说明了弧长准则与曲率相比的准确性，效率和能力。