In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal control problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear programming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated.

本文研究了一种解决无限水平分数最优控制问题的有效数值方法。在Caputo的意义上考虑了这类问题的分数导数。此处开发的方法基于利用变换后的正交函数直接逼近状态和控制函数。从而，原始问题转化为非线性规划问题，可以通过完善的参数优化算法来解决。虽然本解决方案提供了良好的结果并实现了较高的收敛速度，但是在问题的原始时间间隔上解决了无限地平线分数最优控制问题，而没有将其转换为有限问题。