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A new fractional homotopy method for solving nonlinear optimal control problems

机译：一种解决非线性最优控制问题的新分数型谐振方法

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摘要

The homotopy methods have long served as powerful tools in solving nonlinear optimal control problems, particularly for which the solutions are highly sensitive to the unknown initial conditions. The principle of homotopy methods is that a homotopic parameter is embedded into the formulations of the optimal control problems, and the original problem can be solved by tracing the optimal solutions of the embedded problems. The existing homotopy methods typically introduce the homotopic parameter into the time variable, the necessary conditions, the performance index or the rightside of the differential equations. In this paper, a new fractional homotopy method is presented, the homotopic parameter of which is embedded into the derivative of the differential equations. By using the proposed method, the optimal solution of the target homotopy problem can be found by solving a series of fractional two-point-boundary-value-problems. Numerical demonstrations in a nonlinear optimal control problem and a three-dimensional minimum-time low-thrust orbital transfer problem are presented to illustrate the applications of the method.
机译：同型方法长期以来在解决非线性最佳控制问题方面的强大工具，特别是解决方案对未知初始条件的溶性高度敏感。同型方法的原理是均匀参数嵌入到最佳控制问题的配方中，并且可以通过跟踪嵌入问题的最佳解决方案来解决原始问题。现有的同型方法通常将同型参数引入时间变量，必要条件，性能指数或差分方程的右侧。本文介绍了一种新的分数同型方法，其同型参数嵌入到微分方程的衍生中。通过使用该方法，通过求解一系列分数两点边界值问题，可以找到目标同态问题的最佳解决方案。提出了非线性最佳控制问题中的数值示范和三维最小时间低推力轨道转移问题以说明该方法的应用。

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