Differential Games

Differential games theory is the most appropriate discipline for the modelling and analysis of real life conflict problems.
The theory of differential games is here treated with an emphasis on the construction of solutions to actual problems with singular surfaces. The reader is provided with the knowledge necessary to put the theory of differential games into practice.

1 A Preview Example. - 1. 1 Introduction. - 1. 2 A Simple Differential Game. - 1. 3 Preliminary Analysis. - 1. 4 A Heuristic Solution. - 1. 5 Problems. - 2 The Vocabulary For Differential Games. - 2. 1 Introduction. - 2. 2 The State Vector and the Game-Set. - 2. 3 The Equations of Motion. - 2. 4 Termigation of a Differential Game. - 2. 5 Plays. - 2. 6 Outcomes. - 2. 7 Strategies. - 2. 8 Problems. - 3 The Solution Concept. - 3. 1 Introduction. - 3. 2 The Solution Quintet. - 3. 3 The Extended Solution Concept. - 3. 4 Problems. - 4 Semipermeability of Surfaces. - 4. 1 Introduction. - 4. 2 Smooth Semipermeable Surfaces. - 4. 3 Semipermeability of Composite Surfaces. - 4. 4 Problems. - 5 Necessary Conditions. - 5. 1 Introduction. - 5. 2 Properties of the Target Set. - 5. 3 Semipermeability of the Boundary of the Escape Set F. - 5. 4 Properties of Optimal Trajectories. - 5. 5 The Isaacs Equations. - 5. 6 The Adjoint Equations. - 5. 7 Problems. - 6 Sufficient Conditions. - 6. 1 Introduction. - 6. 2 The Sufficiency Theorem. - 6. 3 Validity of Partial Solutions. - 6. 4 Estimatioms of the Value Function. - 6. 5 Problems. - 7 Regular Construction. - 7. 1 Introduction. - 7. 2 The Regular Procedure. - 7. 3 Examples. - 7. 4 Linear Quadratic Games. - 7. 5 Problems. - 8 Construction of SPS. - 8. 1 Introduction. - 8. 2 Construction of Semipermeable Surfaces. - 8. 3 Examples. - 8. 4 Problems. - 9 A Topography of the Value Map. - 9. 1 Introduction. - 9. 2 Barriers and Safe Contact. - 9. 3 Switch Surfaces. - 9. 4 Dispersal Surfaces. - 9. 5 Universal and Focal Surfaces. - 9. 6 Corner Surfaces. - 10 Necessary Conditions (Singular). - 10. 1 Introduction. - 10. 2 The Projection Lemma. - 10. 3 Open Barriers. - 10. 4 Isaacs Equations for Singular Arcs. - 10. 5 Junctions to Singular Arcs. - 10. 6 Adjoint Equations for Singular Arcs. - 10. 7 Properties of Regular Switch Surfaces. - 10. 8 The Chatter Equivalent of Singular Arcs. - 10. 9 Sufficient conditions. - 10. l0 Problems. - 11 Dispersal Surfaces. - 11. 1 introduction. - 11. 2 Region of Multiple Choices. - 11. 3 Characterization of Dispersal Surfaces. - 11. 4 Examples. - 11. 5 Problems. - 12 Singular Arcs of Safe Contact. - 12. 1 Introduction. - 12. 2 Characterization of Safe Contact. - 12. 3 Construction of Safe Contact Arcs. - 12. 4 Examples. - 12. 5 Problems. - 13 Universal and Focal Surfaces. - 13. 1 Introduction. - 13. 2 Characterization of Universal Surfaces. - 13. 3 Examples. - 13. 4 Characterization of Focal Surfaces. - 13. 5 Construction of Focal Surfaces. - 13. 6 An Example of a Focal Surface. - 13. 7 Problems. - 14 Corner Surfaces. - 14. 1 Introduction. - 14. 2 Characterization of Corner Surfaces. - 14. 3 The Switch Envelope. - 14. 4 Chatter Equivalent of SE. - 14. 5 The Equivocal Surface. - 14. 6 Chatter Equivalent of ES. - 14. 7 Problems. - 15 The Envelope Barrier. - 15. 1 Introduction. - 15. 2 The Envelope Barrier. - 15. 3 Examples.