Control and Dynamic Systems V17

Front Cover

Control and Dynamic Systems: Advances in Theory and Applications

Copyright Page

Table of Contents

Contributors

Preface

Contents of Previous Volumes

Chapter 1. An Overview of Differential Games

I. Games

II. General Formulation

III. Two-Person Games

IV. Solution Techniques

V. Applications

VI. Future of Differential Games

References

Chapter 2. Use of Parameter Optimization Methods to Determine the Existence of Game Theoretic Saddle Points

I. Introduction

II. Solutions to Differential Game Problems

III. Polynomial Approximations and Saddle Points

IV. Vertical Plane Pursuit-Evasion with Range Payoff

V. Conclusions

References

Chapter 3. Solution Techniques for Realistic Pursuit-Evasion Games

I. Introduction

II. Problem Statement

III. Modeling Considerations

IV. Linear Differential Games with Bounded Controls

V. Singular Perturbation Technique for Nonlinear Pursuit-Evasion Games

VI. Concluding Remarks

References

Chapter 4. Differential Dynamic Programming Techniques in Differential Games

I. Introduction

II. The Optimal Control Problem

III. Solving the Optimal Control Problem

IV. Optimal Miss Distance for a Variable Speed Model

V. Sequence of Events

VI. Conclusions

References

Chapter 5. Stochastic Differential Game Techniques

I. Introduction

II. General Problem Formulation

III. Solution Concepts and Difficulties

IV. Perfect- Information/Noise-Corrupted Game

V. Payoff Relationships

VI. Noise-Corrupted/Noise-Corrupted Games

VII. A Pursuit-Evasion Example

VIII. Conclusions and Remarks

References

Chapter 6. Algorithms for Differential Games with Bounded Control and State

I. Introduction

II. Problem Statement

III. Algorithm for Security-Level Strategies

IV. Linear-Quadratic Differential Game

V. Nonlinear Stochastic Missile Antimissile Problem

VI. Conclusions

References

Chapter 7. Air Combat Systems Analysis Techniques

I. Differential Games and Military Systems Decisions

II. Differential Game/Barrier Theory

III. The Simplest Model

IV. Limited Pursuer Model

V. Relative Evaluation of Fighter A/C Capability: An Application

VI. The Barrier and Its Use in Air-to-Air Combat Role Decision

VII. Recommendations

Appendix

References

Chapter 8. Reachable Set Methods

I. Reformulation of a Differential Game

II. Methodology Development

III. Applications to Missile Guidance

IV. Conclusions

References

Chapter 9. Zero-Sum Dynamic Games

I. Introduction

II. Zero-Sum Static Games

III. Formulation of Zero-Sum Games

IV. The Theory of Zero-Sum Games

V. The Tank versus Gun Problem

VI. Continuous Models, Discounted Costs, and Other Extensions

References

Chapter 10. Singular Differential Game Techniques and Closed-Loop Strategies

I. Introduction

II. Linear-Quadratic Singular Differential Games with Bounds on Control

III. Numerical Techniques

IV. Closed-Loop Solutions

V. Conclusion and Remarks

Appendix

References

Index