為使飛機燃油做最有效的運用，本論文希望透過GPS及INS獲取飛機目前位置與速度資訊，再透過最佳化方法求出最佳飛行速度與高度，在最佳化方法的使用上，主要分為直接法與間接法，二者間最大之不同為直接法會先將問題離散化後再求最佳解，而間接法則為直接將問題利用偏微分的方式求解泛函數的最佳化，在計算較複雜之問題，如：飛行路徑最佳化時，間接法的求解過程須要大量的偏微分計算，導致計算難度提高，此外，間接法對於初始值的品質極為敏感，而直接法利用離散化的方法省去了大量的偏微分計算，且直接法對於初始值的品質較不敏感，故本研究以直接法搭配Matlab作為飛行路徑最佳化之求解方法。
本研究使用飛機質點運動方程式建立飛機運動模型，並比較使用攻角及推力作為控制變數及單純使用推力作為控制變數對於計算最佳飛行軌跡的差異，並針對不同問題設計對應之最佳化性能指標，如：於不同高度下計算最大航程之最佳飛行速度、於不同高度下計算最長航時之最省油飛行速度，以及歸航模式下以最少油耗作爬升、巡航及下降之速度與飛行路徑角計算。

In order to make the most effective use of aircraft fuel, this paper hopes to obtain aircraft position and speed information through GPS/INS, and use the optimization method to find the optimal flight velocity. The optimization method is mainly divided into two types: the direct method and the indirect method. The biggest difference of indirect method and direct method is that the direct method discretizes the problem first and then solves the optimization, and when calculating the complicated problem of flight path optimization, there will be a lot of partial differential calculations in the solution process in the direct method. It will cause the difficulty of calculation and it is difficult to solve, and the direct method is extremely sensitive to the guess of the initial value, so this study chooses the direct method as the solution method for flight path optimization, and solves it with Matlab.
This research will modeling aircraft motion with equation of motion for mass point, and use both thrust and angle of attack as control variable. According to different mission define difference performance index, such as calculate the optimal flight velocity at different altitudes in maximum range, and the most fuel-efficient flight speed at different altitudes during the longest flight time, last is the optimal velocity and flight path angle for climbing, optimal flight velocity for cruising and optimal flight path angle descent with the least fuel consumption in the homing mode.

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