Differential game theory with applications to missiles and autonomous systems guidance / Farhan A. Faruqi.

Enhanced descriptions from Syndetics:

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:

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 provided by Syndetics

• Preface (p. xi)
• Acknowledgments (p. xiii)
• About the Companion Website (p. xv)
• 1 Differential Game Theory and Applications to Missile Guidance (p. 1)
• Nomenclature (p. 1)
• Abbreviations (p. 2)
• 1.1 Introduction (p. 2)
• 1.1.1 Need for Missile Guidance-Past, Present, and Future (p. 2)
• 1.2 Game Theoretic Concepts and Definitions (p. 3)
• 1.3 Game Theory Problem Examples (p. 4)
• 1.3.1 Prisoner's Dilemma (p. 4)
• 1.3.2 The Game of Tic-Tac-Toe (p. 6)
• 1.4 Game Theory Concepts Generalized (p. 8)
• 1.4.1 Discrete-Time Game (p. 8)
• 1.4.2 Continuous-Time Differential Game (p. 9)
• 1.5 Differential Game Theory Application to Missile Guidance (p. 10)
• 1.6 Two-Party and Three-Party Pursuit-Evasion Game (p. 11)
• 1.7 Book Chapter Summaries (p. 11)
• 1.7.1 A Note on the Terminology Used In the Book (p. 13)
• References (p. 14)
• 2 Optimum Control and Differential Game Theory (p. 16)
• Nomenclature (p. 16)
• Abbreviations (p. 17)
• 2.1 Introduction (p. 17)
• 2.2 Calculus of Optima (Minimum or Maximum) for a Function (p. 18)
• 2.2.1 On the Existence of the Necessary and Sufficient Conditions for an Optima (p. 18)
• 2.2.2 Steady State Optimum Control Problem with Equality Constraints Utilizing Lagrange Multipliers (p. 19)
• 2.2.3 Steady State Optimum Control Problem for a Linear System with Quadratic Cost Function (p. 22)
• 2.3 Dynamic Optimum Control Problem (p. 23)
• 2.3.1 Optimal Control with Initial and Terminal Conditions Specified (p. 23)
• 2.3.2 Boundary (Transversality) Conditions (p. 25)
• 2.3.3 Sufficient Conditions for Optimality (p. 29)
• 2.3.4 Continuous Optimal Control with Fixed Initial Condition and Unspecified Final Time (p. 30)
• 2.3.5 A Further Property of the Hamiltonian (p. 35)
• 2.3.6 Continuous Optimal Control with Inequality Control Constraints-the Pontryagin's Minimum (Maximum) Principle (p. 36)
• 2.4 Optimal Control for a Linear Dynamical System (p. 38)
• 2.4.1 The LQPI Problem-Fixed Final Time (p. 38)
• 2.5 Optimal Control Applications in Differential Game Theory (p. 40)
• 2.5.1 Two-Party Game Theoretic Guidance for Linear Dynamical Systems (p. 41)
• 2.5.2 Three-Party Game Theoretic Guidance for Linear Dynamical Systems (p. 44)
• 2.6 Extension of the Differential Game Theory to Multi-Party Engagement (p. 50)
• 2.7 Summary and Conclusions (p. 50)
• References (p. 51)
• Appendix (p. 53)
• 3 Differential Game Theory Applied to Two-Party Missile Guidance Problem (p. 63)
• Nomenclature (p. 63)
• Abbreviations (p. 64)
• 3.1 Introduction (p. 64)
• 3.2 Development of the Engagement Kinematics Model (p. 67)
• 3.2.1 Relative Engage Kinematics of n Versus m Vehicles (p. 68)
• 3.2.2 Vector/Matrix Representation (p. 69)
• 3.3 Optimum Interceptor/Target Guidance for a Two-Party Game (p. 70)
• 3.3.1 Construction of the Differential Game Performance Index (p. 70)
• 3.3.2 Weighting Matrices S, R P , R e (p. 72)
• 3.3.3 Solution of the Differential Game Guidance Problem (p. 73)
• 3.4 Solution of the Riccati Differential Equations (p. 75)
• 3.4.1 Solution of the Matrix Riccati Differential Equations (MRDE) (p. 75)
• 3.4.2 State Feedback Guidance Gains (p. 76)
• 3.4.3 Solution of the Vector Riccati Differential Equations (VRDE) (p. 77)
• 3.4.4 Analytical Solution of the VRDE for the Special Case (p. 78)
• 3.4.5 Mechanization of the Game Theoretic Guidance (p. 79)
• 3.5 Extension of the Game Theory to Optimum Guidance (p. 79)
• 3.6 Relationship with the Proportional Navigation (PN) and the Augmented PN Guidance (p. 81)
• 3.7 Conclusions (p. 82)
• References (p. 82)
• Appendix (p. 84)
• 4 Three-Party Differential Game Theory Applied to Missile Guidance Problem (p. 102)
• Nomenclature (p. 102)
• Abbreviations (p. 103)
• 4.1 Introduction (p. 103)
• 4.2 Engagement Kinematics Model (p. 104)
• 4.2.1 Three-Party Engagement Scenario (p. 105)
• 4.3 Three-Party Differential Game Problem and Solution (p. 107)
• 4.4 Solution of the Riccati Differential Equations (p. 111)
• 4.4.1 Solution of the Matrix Riccati Differential Equation (MRDE) (p. 111)
• 4.4.2 Solution of the Vector Riccati Differential Equation (VRDE) (p. 112)
• 4.4.3 Further Consideration of Performance Index (PI) Weightings (p. 115)
• 4.4.4 Game Termination Criteria and Outcomes (p. 116)
• 4.5 Discussion and Conclusions (p. 116)
• References (p. 117)
• Appendix (p. 118)
• 5 Four Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems (p. 125)
• Nomenclature (p. 125)
• Abbreviations (p. 126)
• 5.1 Introduction (p. 126)
• 5.2 Development of the Engagement Kinematics Model (p. 126)
• 5.2.1 Translational Kinematics for Multi-Vehicle Engagement (p. 126)
• 5.2.2 Vector/Matrix Representation (p. 128)
• 5.2.3 Rotational Kinematics: Relative Range, Range Rates, Sightline Angles, and Rates (p. 128)
• 5.3 Vehicle Navigation Model (p. 130)
• 5.3.1 Application of Quaternion to Navigation (p. 131)
• 5.4 Vehicle Body Angles and Flight Path Angles (p. 133)
• 5.4.1 Computing Body Rates (p i , q i , r i ) (p. 134)
• 5.5 Vehicle Autopilot Dynamics (p. 135)
• 5.6 Aerodynamic Considerations (p. 135)
• 5.7 Conventional Guidance Laws (p. 136)
• 5.7.1 Proportional Navigation (PN) Guidance (p. 136)
• 5.7.2 Augmented Proportional Navigation (APN) Guidance (p. 137)
• 5.7.3 Optimum Guidance and Game Theory-Based Guidance (p. 137)
• 5.8 Overall State Space Model (p. 138)
• 5.9 Conclusions (p. 138)
• References (p. 139)
• Appendix (p. 140)
• 6 Three-Party Differential Game Missile Guidance Simulation Study (p. 150)
• Nomenclature (p. 150)
• Abbreviations (p. 150)
• 6.1 Introduction (p. 151)
• 6.2 Engagement Kinematics Model (p. 151)
• 6.3 Game Theory Problem and the Solution (p. 154)
• 6.4 Discussion of the Simulation Results (p. 157)
• 6.4.1 Game Theory Guidance Demonstrator Simulation (p. 157)
• 6.4.2 Game Theory Guidance Simulation Including Disturbance Inputs (p. 160)
• 6.5 Conclusions (p. 162)
• 6.5.1 Useful Future Studies (p. 162)
• References (p. 163)
• Appendix (p. 164)
• Addendum (p. 165)
• Index (p. 189)