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. Twoparty and multiparty 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 twoparty and multiparty 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
 Preface
 Acknowledgments
 About the Companion Website
 1: Differential Game Theory and Applications to Missile Guidance

2: Optimum Control and Differential Game Theory
 2.1 Introduction
 2.2 Calculus of Optima (Minimum or Maximum) for a Function
 2.3 Dynamic Optimum Control Problem
 2.4 Optimal Control for a Linear Dynamical System
 2.5 Optimal Control Applications in Differential Game Theory
 2.6 Extension of the Differential Game Theory to MultiParty Engagement
 2.7 Summary and Conclusions
 References
 Appendix: Vector Algebra and Calculus
 A2.1 A Brief Review of Matrix Algebra and Calculus
 A2.2 Characteristic Equations and Eigenvalues
 A2.3 Differential of Linear, BiLinear, and Quadratic Forms
 A2.4 Partial Differentiation of Scalar Functions w.r.t. a Vector
 A2.5 Partial Differentiation of Vector Functions w.r.t. a Vector
 A2.6 The Hessian Matrix
 A2.7 Partial Differentiation of Scalar Quadratic and Bilinear Functions w.r.t. a Vector
 A2.8 First and Second Variations of Scalar Functions
 A2.9 Properties of First and Second Variations for Determining the Nature (Min/Max Values) of Scalar Functions
 A2.10 Linear System Dynamical Model

3: Differential Game Theory Applied to TwoParty Missile Guidance Problem
 3.1 Introduction
 3.2 Development of the Engagement Kinematics Model
 3.3 Optimum Interceptor/Target Guidance for a TwoParty Game
 3.4 Solution of the Riccati Differential Equations
 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
 A3.1 Verifying the Positive SemiDefiniteness of Matrix [S]
 A3.2 Derivation of Riccati Differential Equations
 A3.3 Solving the Matrix Riccati Differential Equation
 A3.4 Solution of the Vector Riccati Deferential Equation
 A3.5 Sight Line Rates for Small Angles and Rates

4: ThreeParty Differential Game Theory Applied to Missile Guidance Problem
 4.1 Introduction
 4.2 Engagement Kinematics Model
 4.3 ThreeParty Differential Game Problem and Solution
 4.4 Solution of the Riccati Differential Equations
 4.5 Discussion and Conclusions
 References
 Appendix
 A4.1 Derivation of the Riccati Equations
 A4.2 Analytical Solution for Riccati Differential Equations
 A4.3 State Feedback Gains
 A4.4 Disturbance Inputs
 A4.5 Guidance Disturbance Inputs

5: Four DegreesofFreedom (DOF) Simulation Model for Missile Guidance and Control Systems
 5.1 Introduction
 5.2 Development of the Engagement Kinematics Model
 5.3 Vehicle Navigation Model
 5.4 Vehicle Body Angles and Flight Path Angles
 5.5 Vehicle Autopilot Dynamics
 5.6 Aerodynamic Considerations
 5.7 Conventional Guidance Laws
 5.8 Overall State Space Model
 5.9 Conclusions
 References
 Appendix
 A5.1 State Space Dynamic Model
 A5.2 Aerodynamic Forces and Equations of Motion
 A5.3 Computing Collision Course Missile Heading Angles
 6: ThreeParty Differential Game Missile Guidance Simulation Study
 Index
 EULA
Product Information
 Title: Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance
 Author(s):
 Release date: May 2017
 Publisher(s): Wiley
 ISBN: 9781119168478