Boubaker Hybrid Functions and their Application to Solve Fractional Optimal Control and Fractional Variational Problems
Boubaker Hybrid Functions and their Application to Solve Fractional Optimal Control and Fractional Variational Problems
复制标题
DOI：
10.21136/am.2018.0083-18
复制
发表时间：
2018-10
影响因子：
0.7
通讯作者：
K. Rabiei;Y. Ordokhani
中科院分区：
文献类型：
--
作者：
K. Rabiei;Y. Ordokhani
构造了一种新的块脉冲函数和Boubaker多项式的混合函数，用于求解具有二次型性能指标的不等式约束的分数阶最优控制问题和分数阶变分问题.首先，首次给出了Boubaker混合函数的Riemann-Liouville积分算子的一般形式。然后应用该方法将问题归结为优化问题，并利用已有的方法进行求解。通过这种方式，我们找到了FOCP的极值，而无需向不等式轨迹添加松弛变量。我们还表明，如果基地的数量增加，在这种方法中使用的近似是收敛的。数值算例表明了该方法的适用性和有效性，并与已有结果进行了比较，表明了该方法的优越性。
A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this way we find the extremum value of FOCPs without adding slack variables to inequality trajectories. Also we show that if the number of bases is increased, the used approximations in this method are convergent. The applicability and validity of the method are shown by numerical results of some examples, moreover, a comparison with the existing results shows the preference of this method.