本論文提出並探討使用適應控制法來設計三維飛彈導引律。傳統於卡氏座標或球座標下所得運動方程式較為複雜，為避免此一缺點,本文採用視線(Line-of-Sight, LOS)固定座標系來描述飛彈與目標物之間的相對運動。採用此座標系的優點在於可導出類似二維極座標下之運動方程式，有利於理論的分析及運算。首先本文將提出一簡單且易於實現的自適應律理想比例導引律(AIPN)，並探討其性質與性能。針對目標物無逃逸的狀況，可求出相對運動方程式的解析解。另一方面，本文亦應用狀態相依 Riccati 方程式 ( state-dependent Riccati equation, SDRE) 於飛彈導引律上。使用 SDRE 法的好處是它可提供系統化的控制律推導，且可直接由權重矩陣以及狀態係數矩陣來影響控制律的性能。在使用 SDRE 法時我們將使用不同的狀態係數矩陣並比較其性能。透過例子可知，若能選擇了一組合適的權重矩陣以及狀態係數矩陣AIPN與SDRE導引律的性能相當接近。但在計算效率上，AIPN則遠優於SDRE。為了模擬空戰時目標物的逃逸，作者亦建立一套互動式模擬系統，目標物的逃逸方式可即時透過搖桿來控制。此系統可提供遊戲般互動的模擬飛彈追擊過程，且由於是模組化的建構，變換導引律相當方便，可謂提供了一富彈性且生動的驗證方式。

In this thesis, we propose and study two types of three dimensional missile guidance laws. At first, a simple yet effective adaptive ideal proportional navigation (AIPN) guidance law is considered. All the formulation and analysis are performed in a line-of-sight (LOS) fixed natural coordinate. With the aid of this coordinate, the closed-form solution for the case of nonmaneuvering target is derived. Also, a state feedback control law is constructed by using the state-dependent Riccati equation (SDRE) technique. The performance is affected directly by the choice of the state-dependent coefficient (SDC) form and weighting matrices. Different SDC forms will be considered and compared through numerical examples. Through numerical examples, we concluded that the performances of AIPN and SDRE are close if the SDC form and weighting matrices are chosen properly. But AIPN has great computational efficiency than that of SDRE. To mimic the random escape strategies adopted by pilot during air combat, an interactive simulation system was constructed.
In this system, target's maneuvering can be controlled through a game-like interface, a joystick input. The simulation system provides a flexible and helpful environment to verify the missile guidance laws.

Contents

Abstract i
Acknowledgement iii
Nomenclature iv
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Formulation of Missile Guidance 5
2.1 Relative Dynamics of Guidance Problem . . . . . . . . . . . . . . . . . . . 5
3 Adaptive Ideal Proportional Navigation 9
3.1 Quick Review Of IPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Adaptive GIPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Capture of Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 State Dependent Riccati Technique 16
4.1 SDRE Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 SDRE Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 Controllable and Observable Parameterization . . . . . . . . . . . . . . . . 20
5 Virtual Reality Simulation System 22
5.1 Module of Target Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2 Module of Missile Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.3 Module of Guidance Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4 Virtual Reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6 Numerical Examples 29
7 Conclusion 41
A The Recursive Algorithm of Constructing Distribution 42
Bibliography 43

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