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Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance

Book Description

Differential Game Theory with Applications to Missiles and Autonomous Systems explains the use of differential game theory in autonomous guidance and control systems.

The book begins with an introduction to the basic principles before considering optimum control and game theory. Two-party and multi-party game theory and guidance are then covered and, finally, the theory is demonstrated through simulation examples and models and the simulation results are discussed. Recent developments in the area of guidance and autonomous systems are also presented.

Key features:

  • Presents new developments and how they relate to established control systems knowledge. 
  • Demonstrates the theory through simulation examples and models.
  • Covers two-party and multi-party game theory and guidance.
  • Accompanied by a website hosting MATLAB® code.

The book is essential reading for researchers and practitioners in the aerospace and defence industries as well as graduate students in aerospace engineering.

Table of Contents

  1. Preface
  2. Acknowledgments
  3. About the Companion Website
  4. 1: Differential Game Theory and Applications to Missile Guidance
    1. 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
    5. 1.5 Differential Game Theory Application to Missile Guidance
    6. 1.6 Two-Party and Three-Party Pursuit-Evasion Game
    7. 1.7 Book Chapter Summaries
    8. References
  5. 2: Optimum Control and Differential Game Theory
    1. 2.1 Introduction
    2. 2.2 Calculus of Optima (Minimum or Maximum) for a Function
    3. 2.3 Dynamic Optimum Control Problem
    4. 2.4 Optimal Control for a Linear Dynamical System
    5. 2.5 Optimal Control Applications in Differential Game Theory
    6. 2.6 Extension of the Differential Game Theory to Multi-Party Engagement
    7. 2.7 Summary and Conclusions
    8. References
    9. Appendix: Vector Algebra and Calculus
    10. A2.1 A Brief Review of Matrix Algebra and Calculus
    11. A2.2 Characteristic Equations and Eigenvalues
    12. A2.3 Differential of Linear, Bi-Linear, and Quadratic Forms
    13. A2.4 Partial Differentiation of Scalar Functions w.r.t. a Vector
    14. A2.5 Partial Differentiation of Vector Functions w.r.t. a Vector
    15. A2.6 The Hessian Matrix
    16. A2.7 Partial Differentiation of Scalar Quadratic and Bilinear Functions w.r.t. a Vector
    17. A2.8 First and Second Variations of Scalar Functions
    18. A2.9 Properties of First and Second Variations for Determining the Nature (Min/Max Values) of Scalar Functions
    19. A2.10 Linear System Dynamical Model
  6. 3: Differential Game Theory Applied to Two-Party Missile Guidance Problem
    1. 3.1 Introduction
    2. 3.2 Development of the Engagement Kinematics Model
    3. 3.3 Optimum Interceptor/Target Guidance for a Two-Party Game
    4. 3.4 Solution of the Riccati Differential Equations
    5. 3.5 Extension of the Game Theory to Optimum Guidance
    6. 3.6 Relationship with the Proportional Navigation (PN) and the Augmented PN Guidance
    7. 3.7 Conclusions
    8. References
    9. Appendix
    10. A3.1 Verifying the Positive Semi-Definiteness of Matrix [S]
    11. A3.2 Derivation of Riccati Differential Equations
    12. A3.3 Solving the Matrix Riccati Differential Equation
    13. A3.4 Solution of the Vector Riccati Deferential Equation
    14. A3.5 Sight Line Rates for Small Angles and Rates
  7. 4: Three-Party Differential Game Theory Applied to Missile Guidance Problem
    1. 4.1 Introduction
    2. 4.2 Engagement Kinematics Model
    3. 4.3 Three-Party Differential Game Problem and Solution
    4. 4.4 Solution of the Riccati Differential Equations
    5. 4.5 Discussion and Conclusions
    6. References
    7. Appendix
    8. A4.1 Derivation of the Riccati Equations
    9. A4.2 Analytical Solution for Riccati Differential Equations
    10. A4.3 State Feedback Gains
    11. A4.4 Disturbance Inputs
    12. A4.5 Guidance Disturbance Inputs
  8. 5: Four Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems
    1. 5.1 Introduction
    2. 5.2 Development of the Engagement Kinematics Model
    3. 5.3 Vehicle Navigation Model
    4. 5.4 Vehicle Body Angles and Flight Path Angles
    5. 5.5 Vehicle Autopilot Dynamics
    6. 5.6 Aerodynamic Considerations
    7. 5.7 Conventional Guidance Laws
    8. 5.8 Overall State Space Model
    9. 5.9 Conclusions
    10. References
    11. Appendix
    12. A5.1 State Space Dynamic Model
    13. A5.2 Aerodynamic Forces and Equations of Motion
    14. A5.3 Computing Collision Course Missile Heading Angles
  9. 6: Three-Party Differential Game Missile Guidance Simulation Study
    1. Abbreviations
    2. 6.1 Introduction
    3. 6.2 Engagement Kinematics Model
    4. 6.3 Game Theory Problem and the Solution
    5. 6.4 Discussion of the Simulation Results
    6. 6.5 Conclusions
    7. References
    8. Appendix
    9. A6.1 Analytical Solution for Riccati Equations
    10. Addendum
  10. Index
  11. EULA