本論文係應用最佳控制理論與奇攝動法，分析飛行體在三度空間中之最短時間攔截軌跡。在此研究中，根據系統變數變化快慢之特性，將追擊者之飛行路線角與方位角劃分為快變數，而追擊者之速度和追擊者與目標之相對距離劃分為慢變數，之後應用最佳控制理論導出最佳化之必要條件，再以奇攝動法分析求得一近似解，為驗證理論之正確性，以電腦進行數值模擬，結果顯示本文應用奇攝動法所得之導引律，除了成功攔截目標外亦能表現最佳軌跡之特性，的確為一先進、實用之導引律。

In this thesis, the optimal control theory and singular perturbation method are applied analyze the three-dimensional minimum time interception trajectory. In this study the state variables of the system are divided into fast variables and slow v In this thesis, the optimal control theory and singular perturbation method are applied analyze the three-dimensional minimum time interception trajectory. In this study the state variables of the system are divided into fast variables and slow variables according to changing rates. Thus far, the flight-path angle and heading angles are denoted as fast variables, the velocity and relative position are denoted as slow variables. According the necessary conditions for optimality are derived, by using the optimal control theory and the singular perturbation method is employed to determine the approximate solution. In order to validate the theory, numerical simulations are conducted. It is found that by using the guidance law derived in this thesis, not only the target can be successfully intercepted, but also the optimality of the interception trajectory can be characterized. Indeed, the resulted guidance law is a stata of the art and practical one.

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