Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance.

Intro -- Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance -- Contents -- Preface -- Acknowledgments -- About the Companion Website -- 1 Differential Game Theory and Applications to Missile Guidance -- 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 Prisoners Dilemma -- 1.3.2 The Game of Tic-Tac-Toe -- 1.4 Game Theory Concepts Generalized -- 1.4.1 Discrete-Time Game -- 1.4.2 Continuous-Time Differential Game -- 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 -- 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 Boundary (Transversality) Conditions -- 2.3.3 Sufficient Conditions for Optimality -- 2.3.4 Continuous Optimal Control with Fixed Initial Condition and Unspecified Final Time -- 2.3.5 A Further Property of the Hamiltonian -- 2.3.6 Continuous Optimal Control with Inequality Control Constraints-the Pontryagins 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: 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, Bi-Linear, 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 -- A2.9.1 Extension to Multi-Vector Case -- A2.10 Linear System Dynamical Model -- 3 Differential Game Theory Applied to Two-Party Missile Guidance Problem -- Nomenclature -- Abbreviations -- 3.1 Introduction -- 3.2 Development of the Engagement Kinematics Model -- 3.2.1 Relative Engage Kinematics of n Versus 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 -- 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 Feedback 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 -- A3.1 Verifying the Positive Semi-Definiteness of Matrix [S] -- A3.2 Derivation of Riccati Differential Equations -- A3.3 Solving the Matrix Riccati Differential Equation -- A3.3.1 Inversion of Matrix -- A3.3.2 Solution of the Inverse Matrix Riccati Differential Equation -- A3.4 Solution of the Vector Riccati Deferential Equation -- A3.4.1 Analytic Solution of the VRDE-Case2 -- A3.5 Sight Line Rates for Small Angles and Rates -- 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 -- 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 Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems -- 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 -- 5.3 Vehicle Navigation Model -- 5.3.1 Application of Quaternion to Navigation -- 5.4 Vehicle Body Angles and Flight Path Angles -- 5.4.1 Computing Body Rates (pi, qi, ri) -- 5.5 Vehicle Autopilot Dynamics -- 5.6 Aerodynamic Considerations -- 5.7 Conventional Guidance Laws -- 5.7.1 Proportional Navigation (PN) Guidance -- 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 -- A5.1 State Space Dynamic Model -- A5.2 Aerodynamic Forces and Equations of Motion -- A5.2.1 Yaw-Plane Equations -- A5.2.2 Pitch-Plane Kinematics Equations -- A5.2.3 Calculating the Aerodynamic Forces -- A5.2.4 Body Incidence -- A5.3 Computing Collision Course Missile Heading Angles -- A5.3.1 Computing ( TS) Given (VT, T, T, S, S) -- A5.3.2 Computing ( MS)cc Given (VM, TS) -- A5.3.3 Computing the Closing Velocity (VC) and Time-to-Go (Tgo) -- A5.3.4 Computing the Collision Course Missile (Az. and El.) Heading: ( M)cc -- ( M)cc -- A5.3.5 Example: Computing 2-DOF Collision Course Missile Heading Angles -- 6 Three-Party Differential Game Missile Guidance Simulation Study -- 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 Simulation Including Disturbance Inputs -- 6.5 Conclusions -- 6.5.1 Useful Future Studies -- References -- Appendix -- A6.1 Analytical Solution for Riccati Equations -- Addendum -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.