In this article, we propose a higher order neural network, namely the functional link neural network (FLNN), for the model of linear and nonlinear delay fractional optimal control problems (DFOCPs) with mixed control‐state constraints. We consider DFOCPs using a new fractional derivative with nonlocal and nonsingular kernel that was recently proposed by Atangana and Baleanu. The derivative possesses more important characteristics that are very useful in modelling. In the proposed method, a fractional Chebyshev FLNN is developed. At the first step, the delay problem is transformed to a nondelay problem, using a Padé approximation. The necessary optimality condition is stated in a form of fractional two‐point boundary value problem. By applying the fractional integration by parts and by constructing an error function, we then define an unconstrained minimization problem. In the optimization problem, trial solutions for state, co‐state and control functions are utilized where these trial solutions are constructed by using single‐layer fractional Chebyshev neural network model. We then minimize the error function using an unconstrained optimization scheme based on the gradient descent algorithm for updating the network parameters (weights and bias) associated with all neurons. To show the effectiveness of the proposed neural network, some numerical results are provided.

中文翻译：

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分数切比雪夫函数链接神经网络优化方法，用Atangana-Baleanu导数求解延迟分数最优控制问题

在本文中，我们针对具有混合控制状态约束的线性和非线性延迟分数最优控制问题（DFOCP）模型，提出了一个高阶神经网络，即功能链接神经网络（FLNN）。我们考虑使用Atangana和Baleanu最近提出的具有非局部和非奇异核的新分数导数的DFOCP。导数具有在建模中非常有用的更重要的特征。在提出的方法中，开发了分数Chebyshev FLNN。第一步，使用Padé逼近将延迟问题转换为非延迟问题。必要的最优条件以分数两点边值问题的形式表示。通过部分应用分数积分并构造误差函数，然后，我们定义无约束的最小化问题。在优化问题中，通过使用单层分数切比雪夫神经网络模型构造这些试验解决方案，利用了状态，共状态和控制功能的试验解决方案。然后，我们使用基于梯度下降算法的无约束优化方案来最小化误差函数，以更新与所有神经元相关的网络参数（权重和偏差）。为了显示所提出的神经网络的有效性，提供了一些数值结果。然后，我们使用基于梯度下降算法的无约束优化方案最小化误差函数，以更新与所有神经元相关的网络参数（权重和偏差）。为了显示所提出的神经网络的有效性，提供了一些数值结果。然后，我们使用基于梯度下降算法的无约束优化方案来最小化误差函数，以更新与所有神经元相关的网络参数（权重和偏差）。为了显示所提出的神经网络的有效性，提供了一些数值结果。