In this paper, a novel direct scheme to solve a set of time-delay fractional optimal control problems is introduced. The method firstly uses a set of Dickson polynomials as basis functions to approximate the states and control variables of the system. Next, the context of these basis functions and the use of a collocation method allow to transform the problem into a system of nonlinear algebraic equations. Finally, the unknown coefficients and control parameters in the original problem can be easily estimated by resolving the new system of equations. Given the high efficiency of the Dickson polynomials to deal with time-delay fractional systems, the proposed strategy involves a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The convergence analysis of the proposed method is presented, along with some illustrative examples which demonstrate its most relevant features.

中文翻译：

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带 DICKSON 多项式的非线性时滞分数阶微分方程的最优控制

在本文中，介绍了一种新的直接方案来解决一组时滞分数最优控制问题。该方法首先使用一组 Dickson 多项式作为基函数来逼近系统的状态和控制变量。接下来，这些基函数的上下文和搭配方法的使用允许将问题转换为非线性代数方程组。最后，通过求解新的方程组，可以很容易地估计原始问题中的未知系数和控制参数。鉴于 Dickson 多项式处理时滞分数系统的高效率，所提出的策略涉及根据离散化过程和任意节点的范围用于直接轨迹优化的非常可调的框架。