由於，根據以往最佳控制理論，應用坡度法之數值計算所得最佳飛行軌跡，其計算過於繁複，且收斂不易，在應用上有其難處。本論文係利用參數最佳化法，分析飛機最短時間爬升之軌跡。在此兩點邊界值問題中，最短時間爬升之性能指標為終端時間。本文所採用的參數最佳化法是假設負荷因子為時間的多項式函數其係數為控制參數，並利用最佳控制理論導出最佳化之必要條件。為了驗證理論之正確性，本研究以電腦作數值模擬，並嘗試改變飛機之各種初始及終端條件，分析這些條件對於最佳軌跡之影響。

　　Since the analysis of the optimal trajectories using the optimal control theory associated with the gradient method are numerically very difficult due to the convergence problem, often it can not be applied effectively to solve many typical problems, In this thesis, the parametric optimization method is applied to analyze the minimum time-to-climb trajectory. In this two-point-boundary-value problem(TPBVP), the performance index is the terminal time and the load factor is the control which is assumed to be a polynominal function of the time. The coefficients of the polynominal function are taken as a set of parameters to optimize the performance index. Accordingly, necessary conditions for optimality are derived as a set of nonlinear simultaneous algebraic equations which in combination with the terminal conditions
are used for solving a set of parameters. In order to validate the theory, a numerical problem is given. With the given problem, the effects of initial conditions and final conditions on the mimnimum time-to-climb trajectories are investigated.

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