This article presents an efficient numerical method for solving fractional optimal control problems (FOCPs) by utilizing the Hermite scaling function operational matrix of fractional‐order integration. The proposed technique is applied to transform the state and control variables into nonlinear programming (NLP) parameters at collocation points. The NLP solver is then used to solve FOCP. Furthermore, the L₂‐error estimates in the approximation of unknown variables and the approximation of block pulse operational matrix of fractional‐order integration are derived and illustrative examples are included to demonstrate the applicability of the proposed method. Moreover, the results are compared with the Haar wavelet collocation method, hybrid of block‐pulse and Taylor polynomials method, Bernstein polynomials method, and the Boubaker hybrid function method to show the superiority of the proposed method.

中文翻译：

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带有误差估计的Hermite比例函数的搭配方法来求解非线性分数最优控制问题

本文提出了一种利用分数阶积分的Hermite缩放函数运算矩阵来解决分数最优控制问题（FOCP）的有效数值方法。所提出的技术用于将状态和控制变量转换为搭配点处的非线性编程（NLP）参数。然后使用NLP求解器求解FOCP。此外，L ₂推导了未知变量近似中的误差估计和分数阶积分的块脉冲运算矩阵中的误差估计，并包括了说明性示例，以证明所提出方法的适用性。此外，将结果与Haar小波配置方法，块脉冲和泰勒多项式混合方法，Bernstein多项式方法以及Boubaker混合函数方法进行比较，以证明该方法的优越性。