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首页> 外文期刊>Proceedings of the Institution of Mechanical Engineers >Introducing a novel algorithm for minimum-time low-thrust orbital transfers with free initial condition
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Introducing a novel algorithm for minimum-time low-thrust orbital transfers with free initial condition

机译：引入一种新颖的算法，用于具有自由初始条件的最小时间低推力轨道转移

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In this work, a new algorithm is presented with regard to the free initial condition for solving optimal control problems. The reason for presentation of such an algorithm is to develop a suitable method that simplifies difficulties of the optimal control problems that researchers face in common methods of optimal control theory. Also, initial condition as true anomaly is considered to be free in this optimal control problem. To do so, issues such as optimal control theory, orthogonal functions in the Hilbert space, and evolutionary optimizations such as genetic algorithm-particle swarm optimization and imperial competition algorithm are utilized. The algorithm was solved for low-thrust orbital transfer problems which included nonlinear dynamic equations. To validate the algorithm, simplified Edelbaum low-thrust equations are compared with the proposed analytical solutions. Next, the algorithm is investigated for the low-thrust orbital transfers with respect to the equinoctial orbital equations of the minimum-time problem. Results are achieved for two evolutionary optimization methods genetic algorithm-particle swarm optimization and imperial competition algorithm and three orthogonal functions such as Fourier, Chebyshev, and Legendre. Two optimization methods and three orthogonal functions are covered and compared precisely. With respect to the results, this algorithm has the capability to overcome difficulties of the optimal control problems and can be considered as a novelty in this field for the free initial condition problems.
机译：在这项工作中，针对自由初始条件提出了一种新算法，用于解决最优控制问题。提出这种算法的原因是要开发一种合适的方法，以简化研究人员在最优控制理论的常用方法中面临的最优控制问题的难度。同样，在这种最优控制问题中，作为真正异常的初始条件被认为是免费的。为此，利用了诸如最优控制理论，希尔伯特空间中的正交函数以及诸如遗传算法-粒子群优化和帝国竞争算法之类的进化优化等问题。该算法针对包含非线性动力学方程的低推力轨道传递问题进行了求解。为了验证该算法，将简化的Edelbaum低推力方程与提出的解析解决方案进行了比较。接下来，针对最小时间问题的等时轨道方程，研究了低推力轨道转移的算法。通过两种进化优化方法，遗传算法-粒子群优化和帝国竞争算法，以及傅立叶，切比雪夫和勒让德三个正交函数，获得了结果。覆盖并精确比较了两种优化方法和三种正交函数。关于结果，该算法具有克服最佳控制问题的能力，并且可以被认为是自由初始条件问题在该领域中的新颖性。

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