In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana–Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.

在这项工作中，我们提出了一种基于移位勒让德多项式的数值方法，用于解决一类分数最优控制问题。导数在Atangana–Baleanu导数意义上进行描述。为了解决该问题，考虑了AB分数积分和乘法的运算矩阵，以及用于约束极值的Lagrange乘法器方法。该方法将主要问题简化为非线性代数方程组。在此框架中，通过求解获得的系统，可以计算出近似解。还证明了该方法获得的近似解的数值解的误差估计。最后，给出了一些说明性示例，以证明所提出方案的准确性和有效性。