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Fractional infinite-horizon optimal control problems with a feed forward neural network scheme
Network: Computation in Neural Systems ( IF 7.8 ) Pub Date : 2019-10-02 , DOI: 10.1080/0954898x.2019.1688878
Mina Yavari 1 , Alireza Nazemi 1
Affiliation  

ABSTRACT This paper presents a method based on neural networks to solve fractional infinite-horizon optimal control problems s(FIHOCP)s, where the dynamic control system depends on Caputo fractional derivatives. First, with the help of an approximation, the Caputo derivative is replaced to integer-order derivative. Using a suitable change of variable, the IHOCP is transformed into a finite-horizon one. According to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, an unconstrained minimization problem is defined. In the optimization problem, the trial solutions are used for state, costate and control functions where these trial solutions are constructed by using two-layered perceptron neural network. Two numerical results are introduced to explain our main results.

中文翻译:

前馈神经网络方案的分数无限水平最优控制问题

摘要 本文提出了一种基于神经网络的方法来解决分数无限水平最优控制问题 s(FIHOCP),其中动态控制系统依赖于 Caputo 分数阶导数。首先,在近似的帮助下,Caputo 导数被替换为整数阶导数。使用适当的变量变化,将 IHOCP 转换为有限范围的 IHOCP。根据最优控制问题的庞特里亚金最小原理(PMP),通过构造误差函数,定义了一个无约束的最小化问题。在优化问题中,试验解用于状态、辅助和控制函数,这些试验解是通过使用两层感知器神经网络构建的。引入了两个数值结果来解释我们的主要结果。
更新日期:2019-10-02
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