本論文之主旨在於應用參數最佳化法，分析飛機於風場中等高度飛行之最省燃料軌跡。研究中以速度與傾斜角之正切函數為控制變數，並以飛機之燃料消耗質量為性能指標。速度之最佳化係以最小燃料消耗率為基石，轉彎控制則設為未定係數之時間多項式函數。在給定終端條件限制之下，本論文推導出其最佳化之必要條件，進而求解出符合這些條件之最佳控制。為了更進一步闡釋理論，本論文以一數值範例之分析作為說明。分析結果顯示，以時間二次多項式函數為轉彎控制已足以使燃料消耗為最少。

The objective of this thesis is to analyze the constant-altitude minimum-fuel trajectories for an aircraft under the wind effect by applying a parametric optimization method. In this study, the velocity and the tangent function of bank angle are considered as the control variables and the mass of fuel consumption is assumed to be the performance index. The optimization of the velocity is based on the principle of minimizing the mass rate of fuel consumption and the control of turn is assumed to be a polynomial function of the time with the coefficients to be determined. With a set of constraint conditions given at the terminal time, the necessary conditions for optimization are derived in this thesis and the solutions for the optimal controls are determined accordingly. To further illustrate the theory, a numerical example is given in this thesis to conduct the analysis. The results of analysis show that, for the control of turn, a second-order polynomial function of the time is good enough to minimize the mass of fuel consumption.

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