A Bessel collocation method for solving fractional optimal control problems
A Bessel collocation method for solving fractional optimal control problems
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DOI：
10.1016/j.apm.2014.06.003
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发表时间：
2015-01
影响因子：
5
通讯作者：
E. Tohidi;H. S. Nik
中科院分区：
文献类型：
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作者：
E. Tohidi;H. S. Nik
本文利用截断贝塞尔级数的配点方法，间接求解线性和非线性分式最优控制问题。因此，必要的（也是充分的，在大多数情况下）的最优性条件的非线性（或线性）分数两点边值问题（TPBVP）的形式。为了求解这一问题，我们推广了一种新的数值方法（称之为Bessel配点法）。这种推广的最大优点之一是，不需要使用微分运算矩阵，而且新的推广思想可以在任何数学软件中实现。数值算例验证了该方法的准确性。所有的数值计算都是在PC机上用MAPLE 13编写的程序进行的。
In the present paper, we apply the truncated Bessel series approximation by using collocation scheme, for solving linear and nonlinear fractional optimal control problems (OCPs) indirectly. Therefore, the necessary (and also sufficient in most cases) optimality conditions are stated in a form of nonlinear (or linear) fractional two-point boundary value problem (TPBVP). For solving this mentioned TPBVP, we generalize a new numerical method (which is called the Bessel collocation method). One of the best advantages of this generalization is that, there is no need to use operational matrices of differentiation and also the new generalized idea can be implemented in any mathematical software. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.