This paper proposes an efficient adaptive control parameterization method for solving optimal control problems. In this method, mesh density functions are used to generate mesh points. In the first step, the problem is solved by control parameterization on uniform mesh points. Then at each step, the approximate control obtained from the previous step is applied to construct a mesh density function, and consequently a new adapted set of mesh points. Several numerical examples are included to demonstrate that the adaptive control parameterization method is more accurate than a uniform control parameterization one.

中文翻译：

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密度函数的自适应控制参数化方法求解最优控制问题

本文提出了一种解决最优控制问题的有效自适应控制参数化方法。在这种方法中，网格密度函数用于生成网格点。第一步，通过对均匀网格点进行控制参数化来解决该问题。然后，在每个步骤中，将从上一步骤获得的近似控制应用于构造网格密度函数，并因此构造一组新的网格点。包括几个数值示例，以证明自适应控制参数化方法比统一控制参数化方法更准确。