Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challenging work. Hence, in this article, a numerical method is proposed to solve fractional infinite horizon optimal control problems. At the first stage, a domain transformation technique is used to map the infinite domain to a finite horizon. Also, fractional derivative defined on an unbounded domain is converted into an equivalent derivative on a finite domain. Then, a new shifted Legendre pseudospectral method is utilized to solve the obtained finite problem and a nonlinear programming problem is suggested to approximate the optimal solutions. Finally, some numerical examples are given to show the efficiency of the method.

中文翻译：

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分数阶无限视界最优控制问题的伪谱方法

迄今为止，研究人员提出了几种数值方法来解决有限水平分数最优控制问题，而在无限域上求解分数最优控制问题是一项艰巨的工作。因此，在本文中，提出了一种数值方法来解决分数阶无限地平线最优控制问题。在第一阶段，使用域转换技术将无限域映射到有限范围。同样，将在无界域上定义的分数导数转换为有限域上的等效导数。然后，采用一种新的移位勒让德伪谱方法来求解所获得的有限问题，并提出了一个非线性规划问题来逼近最优解。最后，通过数值算例说明了该方法的有效性。