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BOUBAKER HYBRID FUNCTIONS AND THEIR APPLICATION TO SOLVE FRACTIONAL OPTIMAL CONTROL AND FRACTIONAL VARIATIONAL PROBLEMS

机译:BOUBAKER混合函数及其在求解分数最优控制和分数变分问题中的应用

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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.
机译:构建了块脉冲函数和Boubaker多项式的新混合体,以解决具有二次性能指标和分数变分问题(FVP)的不等式约束分数最优控制问题(FOCP)。首先,首次提出了Boubaker混合函数的Riemann-Liouville积分算子的一般形式。然后将其用于将问题简化为优化问题,可以通过现有方法解决。这样,我们就可以找到FOCP的极值,而无需在不等式轨迹上添加松弛变量。我们还表明,如果增加碱基数,则该方法中使用的近似值会收敛。通过一些实例的数值结果表明了该方法的适用性和有效性,并与现有结果进行了比较,表明了该方法的优越性。

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