Dedications
Forward
Acknowledgements
1. Differential Game Theory and Applications to Missile Guidance
Abstract
Nomenclature
Abbreviations
1.1. Introduction
1.1.1. Need for Missile Guidance - Past, Present and Future
1.2. Game Theoretic Concepts and Definitions
1.3. Game Theory Problem Examples
1.3.1. Prisoner’s Dilemma
1.3.1.1. Observations and Generalisation from the above Example
1.3.2. The Game of Tic-tac-toe
1.3.2.1. Observations and Generalisation from the Tic-Tac-Toe Example:
1.4. Game Theory Concepts Generalised
1.4.1. Discrete-time Games
1.4.2. Continuous-time Differential Games
1.5. Differential Game Theory Application to Missile Guidance
1.6. Two-party and Three-party Pursuit-Evasion Game
1.7. Book Chapter Summaries
1.7.1. A Note on the Terminology used in the Book
References
2. Optimum Control and Differential Game Theory
Abstract
Nomenclature
Abbreviations
2.1. Introduction
2.2. Calculus of Optima (Minimum or Maximum) for a Function
2.2.1. On the Existence of the Necessary and Sufficient Conditions for an Optima
2.2.2. Steady State Optimum Control Problem with Equality Constraints Utilizing Lagrange Multipliers
2.2.3. Steady State Optimum Control Problem for a Linear System with Quadratic Cost Function
2.3. Dynamic Optimum Control Problem
2.3.1. Optimal Control with Initial and Terminal Conditions Specified
2.3.2. Sufficient Conditions for Optimality
2.3.3. Continuous Optimal Control with Fixed Initial Condition and Unspecified Final Time.
2.3.4. Continuous Optimal Control with Inequality Control Constraints – the Pontryagin’s Minimum (Maximum) Principle
2.4. Optimal Control for a Linear Dynamical System
2.4.1. The LQPI Problem – Fixed Final Time
2.5. Optimal Control Applications in Differential Game Theory
2.5.1. Two-Party Game Theoretic Guidance for Linear Dynamical Systems
2.5.2. Three-Party Game Theoretic Guidance for Linear Dynamical Systems
2.6. Extension of the Differential Game Theory to Multi-party Engagement
2.7. Summary and Conclusions
References
Appendix
3. Differential Game Theory Applied to Two-party Missile Guidance Problem
Abstract
Nomenclature
Abbreviations
3.1. Introduction
3.2. Development of the Engagement Kinematics Model
3.2.1. Relative Engage Kinematics of n vs. m Vehicles.
3.2.2. Vector/Matrix Representation
3.3. Optimum Interceptor/Target Guidance for a Two-party Game
3.3.1. Construction of the Differential Game Performance Index
3.3.2. Weighting Matrices p e S, R , R
3.3.3. Solution of the Differential Game Guidance Problem
3.4. Solution of the Riccati Differential Equations
3.4.1. Solution of the Matrix Riccati Differential Equations (MRDE)
3.4.2. State Feed-back Guidance Gains
3.4.3. Solution of the Vector Riccati Differential Equations (VRDE)
3.4.4. Analytical Solution of the VRDE for the Special Case
3.4.5. Mechanization of the Game Theoretic Guidance
3.5. Extension of the Game Theory to Optimum Guidance
3.6. Relationship with the Proportional Navigation (PN) and the augmented PN Guidance
3.7. Conclusions
References
Appendix
4. Three-party Differential Game Theory Applied to Missile Guidance Problem
Nomenclature
Abbreviations
4.1. Introduction
4.2. Engagement Kinematics Model
4.2.1. Three-Party Engagement Scenario
4.3. Three-Party Differential Game Problem and Solution
4.4. Solution of the Riccati Differential Equations
4.4.1. Solution of the Matrix Riccati Differential Equation (MRDE)
4.4.2. Solution of the Vector Riccati Differential Equation (VRDE)
4.4.3. Further Consideration of Performance Index (PI) Weightings
4.4.4. Game Termination Criteria and Outcomes
4.5. Discussion and Conclusions
References
Appendix
5. Four Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems
Abstract
Nomenclature
Abbreviations
5.1. Introduction
5.2. Development of the Engagement Kinematics Model
5.2.1. Translational Kinematics for Multi-Vehicle Engagement
5.2.2. Vector/Matrix Representation
5.2.3. Rotational Kinematics: Relative Range, Range Rates, Sightline Angles and Rates
5.2.3.1. Range and Range Rates
5.2.3.2. Sightline Rates
5.3. Vehicle Navigation Model
5.3.1. Application of Quaternions to Navigation
5.4. Vehicle Body Angles and Flight Path Angles
5.4.1. Computing Body Rates
5.5. Vehicle Autopilot Dynamics
5.6. Aerodynamic Considerations
5.7. Conventional Guidance Laws
5.7.1. Proportional Navigation (PN) Guidance
5.7.1.1. PN Version 1
5.7.1.2. PN Version 2
5.7.2. Augmented Proportional Navigation (APN) Guidance
5.7.3. Optimum Guidance and Game Theory Based Guidance
5.8. Overall State Space Model
5.9. Conclusions
References
Appendix
6. Three-party Differential Game Missile Guidance Simulation Study
Abstract
Nomenclature
Abbreviations
6.1. Introduction
6.2. Engagement Kinematics Model
6.3. Game Theory Problem and the Solution
6.4. Discussion of the Simulation Results
6.4.1. Game Theory Guidance Demonstrator Simulation
6.4.2. Game Theory Guidance Demonstrator Simulation
6.5. Conclusions
6.5.1. Useful Future Studies
References
Appendix
Addendum
Index
(leitura online e APP)
