Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance (eBook)

Farhan A. Faruqi, Defence Science and Technology Organisation, Australia Professor Dr. Farhan A. Faruqi is the Head of the Intelligent Autonomous Systems Research Guidance and Control Group in the Defence Science and Technology Organisation in Australia. He is also an Adjunct Professor at the University of South Australia. His main areas of expertise include autonomous systems navigation; guidance and control; target tracking; and intelligent autonomous systems. He has more than twenty years' experience in the Aerospace and Defence Industry in the UK, USA, and Australia.

Preface xi

Acknowledgments xiii

About the Companion Website xv

1. Differential Game Theory and Applications to Missile Guidance 1

Nomenclature 1

Abbreviations 2

1.1 Introduction 2

1.2 Game Theoretic Concepts and Definitions 3

1.3 Game Theory Problem Examples 4

1.4 Game Theory Concepts Generalized 8

1.5 Differential Game Theory Application to Missile Guidance 10

1.6 Two-Party and Three-Party Pursuit-Evasion Game 11

1.7 Book Chapter Summaries 11

References 14

2. Optimum Control and Differential Game Theory 16

Nomenclature 16

Abbreviations 17

2.1 Introduction 17

2.2 Calculus of Optima (Minimum or Maximum) for a Function 18

2.3 Dynamic Optimum Control Problem 23

2.4 Optimal Control for a Linear Dynamical System 38

2.5 Optimal Control Applications in Differential Game Theory 40

2.6 Extension of the Differential Game Theory to Multi-Party Engagement 50

2.7 Summary and Conclusions 50

References 51

Appendix 53

3. Differential Game Theory Applied to Two-Party Missile Guidance Problem 63

Nomenclature 63

Abbreviations 64

3.1 Introduction 64

3.2 Development of the Engagement Kinematics Model 67

3.3 Optimum Interceptor/Target Guidance for a Two-Party Game 70

3.4 Solution of the Riccati Differential Equations 75

3.5 Extension of the Game Theory to Optimum Guidance 79

3.6 Relationship with the Proportional Navigation (PN) and the Augmented PN Guidance 81

3.7 Conclusions 82

References 82

Appendix 84

4. Three-Party Differential Game Theory Applied to Missile Guidance Problem 102

Nomenclature 102

Abbreviations 103

4.1 Introduction 103

4.2 Engagement Kinematics Model 104

4.3 Three-Party Differential Game Problem and Solution 107

4.4 Solution of the Riccati Differential Equations 111

4.5 Discussion and Conclusions 116

References 117

Appendix 118

5. Four Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems 125

Nomenclature 125

Abbreviations 126

5.1 Introduction 126

5.2 Development of the Engagement Kinematics Model 126

5.3 Vehicle Navigation Model 130

5.4 Vehicle Body Angles and Flight Path Angles 133

5.5 Vehicle Autopilot Dynamics 135

5.6 Aerodynamic Considerations 135

5.7 Conventional Guidance Laws 136

5.8 Overall State Space Model 138

5.9 Conclusions 138

References 139

Appendix 140

6. Three-Party Differential Game Missile Guidance Simulation Study 150

Nomenclature 150

Abbreviations 150

6.1 Introduction 151

6.2 Engagement Kinematics Model 151

6.3 Game Theory Problem and the Solution 154

6.4 Discussion of the Simulation Results 157

6.5 Conclusions 162

References 163

Appendix 164

Addendum 165

Index 189