Yavin / Pachter Pursuit-Evasion Differential Games

1. Auflage 2014
ISBN: 978-1-4832-9593-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 14, 351 Seiten, Web PDF

Reihe: International Series in Modern Applied Mathematics and Computer Science

Twenty papers are devoted to the treatment of a wide spectrum of problems in the theory and applications of dynamic games with the emphasis on pursuit-evasion differential games. The problem of capturability is thoroughly investigated, also the problem of noise-corrupted (state) measurements. Attention is given to aerial combat problems and their attendant modelling issues, such as variable speed of the combatants, the three-dimensionality of physical space, and the combat problem, i.e. problems related to 'role determination'.

Autoren/Hrsg.

Yavin, Y.

Pachter, M.

Inhaltsverzeichnis

1;Front Cover;1
2;Pursuit-Evasion Differential Games;4
3;Copyright Page;5
4;Table of Contents;6
5;Foreword;8
6;Preface;10
7;CHAPTER 1. ADAPTIVE CONTROL FOR AVOIDANCE OR EVASION IN AN UNCERTAIN ENVIRONMENT;12
7.1;1. INTRODUCTION;12
7.2;2. PROBLEM STATEMENT;12
7.3;3. AVOIDANCE WITH MEMORYLESS CONTROLLERS;14
7.4;4. AVOIDANCE FOR THE COMPLETE UNCERTAIN SYSTEM;16
7.5;5. LINEAR SYSTEMS;18
7.6;6. EXAMPLE: LINEAR SYSTEM;19
7.7;7. EVADING A PURSUER OF UNKNOWN SPEED;20
7.8;REFERENCES;22
8;CHAPTER 2. PURSUIT-EVASION DIFFERENTIAL GAMES WITH UNCERTAINTIES IN DYNAMICS;24
8.1;1. STATEMENT OF THE PROBLEM;24
8.2;2. THE WORST-CASE APPROACH;26
8.3;3. THE F-FUNCTION METHOD FOR DIFFERENTIAL GAMES WITH UNCERTAINTIES;27
8.4;4. CONTROL THEOREM FOR THE GAMES OF CLASS A;32
8.5;REFERENCES;45
9;CHAPTER 3. THE BARRIER IN A PURSUIT-EVASION GAME WITH TWO TARGETS;48
9.1;1. INTRODUCTION;48
9.2;2. GENERAL PROBLEM STATEMENT;48
9.3;3. PURSUIT-EVASION EXAMPLE, WINNING ZONES;50
9.4;4. SEMI-BARRIERS, SEMI-PERMEABLE SETS, BARRIER;52
9.5;5. CONCLUSION;56
9.6;REFERENCES;56
10;CHAPTER 4. THE GEOMETRIC APPROACH TO THE CONSTRUCTION OF THE BARRIER SURFACE IN DIFFERENTIAL GAMES;58
10.1;1. INTRODUCTION AND PROBLEM STATEMENT;58
10.2;2. ISAACS1 CONSTRUCTION OF THE BARRIER;59
10.3;3. A NEW NECESSARY CONDITION;61
10.4;4. THE PARAMETER DEPENDENCE OF THE BARRIER MODE IN THE HOMICIDAL CHAUFFEUR DIFFERENTIAL GAME;63
10.5;5. AN INVESTIGATION INTO THE PARAMETER DEPENDENCE OF THE BARRIER IN THE GAME OF TWO CARS;67
10.6;6. CONCLUDING REMARKS;77
10.7;REFERENCES;78
11;CHAPTER 5. SIMPLE-MOTION PURSUIT-EVASION IN THE HALF PLANE;80
11.1;1. INTRODUCTION;80
11.2;2. THE STATE SPACE;81
11.3;3. THE DIVIDING SURFACE;83
11.4;4. THE WALL PURSUIT GAME;83
11.5;5. THE OPTIMAL SOLUTION IN V AND THE DIFFERENTIAL GAME OF DEFENDING A TARGET;84
11.6;6. CAPTURABILITY;85
11.7;7. THE GLOBAL SOLUTION (IN V U P);86
11.8;8. AN ALTERNATIVE APPROACH BASED ON ISAACS RETROGRADE METHOD;88
11.9;9. CONCLUDING REMARKS;92
11.10;REFERENCES;93
12;CHAPTER 6. SIMPLE LINEAR PURSUIT-EVASION GAMES;94
12.1;1. INTRODUCTION;94
12.2;2. PROBLEM FORMULATION;94
12.3;3. SOLUTION TO GAME P3—TERMINAL COST;95
12.4;4. SOLUTION TO GAME P1—PURSUIT;97
12.5;5. CAPTURE IN THE ISOTROPIC ROCKET;98
12.6;6. SOLUTION TO GAME P1—EVASION;100
12.7;7. AVOIDANCE IN THE ISOTROPIC ROCKET;101
12.8;8. BARRIER IN SIMPLE LINEAR GAMES;102
12.9;9. A SIMPLE CHASE;104
12.10;10. DISCUSSION;105
12.11;REFERENCES;106
13;CHAPTER 7. AN APPROACH TO THREE-DIMENSIONAL AIRCRAFT PURSUIT-EVASION;108
13.1;1. INTRODUCTION;108
13.2;2. DYNAMIC MODELING;110
13.3;3. THREE-DIMENSIONAL ENERGY STATE;112
13.4;4. NONLINEAR CONTROL LAW;114
13.5;5. LINEAR CONTROL LAW;116
13.6;6. IMPLEMENTATION ISSUES;120
13.7;7. CONCLUDING REMARKS;120
13.8;REFERENCES;121
14;CHAPTER 8. AIRCRAFT PURSUIT-EVASION PROBLEMS WITH VARIABLE SPEEDS;122
14.1;1. INTRODUCTION;122
14.2;2. THE CONCEPT OF THE EXTREMAL TRAJECTORY MAP (ETM);123
14.3;3. CONSTRUCTION OF AIRCRAFT ETMs;125
14.4;4. THE FEEDBACK SOLUTION;127
14.5;5. SOME EXAMPLES;128
14.6;6. CONCLUSIONS;131
14.7;REFERENCES;131
15;CHAPTER 9. A TWO-TARGET GAME ANALYSIS IN LINE-OF-SIGHT COORDINATES;134
15.1;1. INTRODUCTION;134
15.2;2. PROBLEM FORMULATION;135
15.3;3. PURSUIT-EVASION GAME SOLUTION;137
15.4;4. TWO-TARGET GAME SOLUTION;144
15.5;5. CONCLUSIONS;148
15.6;REFERENCES;149
15.7;APPENDIX;149
16;CHAPTER 10. A STOCHASTIC TWO-TARGET PURSUIT-EVASION DIFFERENTIAL GAME WITH THREE PLAYERS MOVING IN A PLANE;152
16.1;1. INTRODUCTION;152
16.2;2. FORMULATION OF THE PROBLEM;152
16.3;3. SUFFICIENT CONDITIONS ON OPTIMAL STRATEGIES;156
16.4;4. A NUMERICAL STUDY AND CONCLUSIONS;158
16.5;5. A PURSUIT-EVASION DIFFERENTIAL GAME;159
16.6;6. CONCLUDING REMARKS;159
16.7;REFERENCES;159
17;CHAPTER 11. STOCHASTIC GUIDANCE LAWS IN SATELLITE PURSUIT-EVASION;162
17.1;INTRODUCTION;162
17.2;PROBLEM DEFINITION AND FORMULATION;162
17.3;CONTROL ALGORITHM;164
17.4;NUMERICAL RESULTS;165
17.5;SUMMARY AND CONCLUSIONS;167
17.6;REFERENCES;167
17.7;ON CLOSED-LOOP CONTROLS IN PURSUIT-EVASION;168
17.8; INTRODUCTION;168
17.9;STATEMENT OF THE OPTIMAL CONTROL PROBLEM;169
17.10;A HYBRID NEAR-OPTIMAL CLOSED-LOOP ALGORITHM;170
17.11;THE HORIZONTAL INTERCEPTION PROBLEM;171
17.12;EXPERIMENTAL SETUP;172
17.13;RESULTS;173
17.14;DISCUSSION;176
17.15;CONCLUSION;177
17.16;REFERENCES;177
18;CHAPTER 12. PURSUIT-EVASION IN MEDIUM-RANGE AIR-COMBAT SCENARIOS;178
18.1;1. INTRODUCTION;178
18.2;2. PROBLEM STATEMENT;179
18.3;3. ZERO-SUM AND NON-ZERO-SUM DIFFERENTIAL GAME FORMULATION;182
18.4;4. NUMERICAL TECHNIQUE;183
18.5;5. NUMERICAL EXAMPLES;186
18.6;6. CONCLUSIONS;190
18.7;REFERENCES;190
19;CHAPTER 13. PARTIALLY OBSERVABLE LINEAR-QUADRATIC STOCHASTIC PURSUIT-EVASION GAMES;192
19.1;1. INTRODUCTION;192
19.2;2. PROBLEM STATEMENT;192
19.3;3. LINEAR NONANTICIPATIVE STRATEGIES;193
19.4;4. FILTERING EQUATION FOR THE OPTIMAL LINEAR ESTIMATE;194
19.5;5. OPTIMAL LINEAR NONANTICIPATIVE STRATEGIES;196
19.6;REFERENCES;200
20;CHAPTER 14. PURSUIT-EVASION DIFFERENTIAL GAMES WITH DECEPTION OR INTERRUPTED OBSERVATION;202
20.1;1. INTRODUCTION;202
20.2;2. THE FUNDAMENTAL EQUATIONS;203
20.3;3. GAME (a);204
20.4;4. GAME (b);208
20.5;5. GAME (c);209
20.6;6. CONCLUSIONS;214
20.7;REFERENCES;214
21;CHAPTER 15. RABBIT AND HUNTER GAME: TWO DISCRETE STOCHASTIC FORMULATIONS;216
21.1;1. INTRODUCTION;216
21.2;2. THE GENERAL SET UP;216
21.3;3. THE STATIONARY GAME;217
21.4;4. FIRST VERSION OF THE NON-STATIONARY GAME;231
21.5;5. SECOND VERSION OF THE NON-STATIONARY GAME;233
21.6;REFERENCE;236
22;CHAPTER 16. AN N-PERSON NONCOOPERATIVE DISCOUNTED VECTOR VALUED DYNAMIC GAME WITH A STOPPED SETf;238
22.1;1. INTRODUCTION;238
22.2;2. FORMULATION OF AN n-PERSON DISCOUNTED VECTOR VALUED DYNAMIC GAME WITH A STOPPED SET;239
22.3;3. SOME ASSUMPTIONS AND THE DOMINATION STRUCTURE IN A VECTOR VALUED n-PERSON DYNAMIC GAME;241
22.4;4. THE EXISTENCE OF A D-CONVEX EQUILIBRIUM POINT IN THE DISCOUNTED MARKOV GAME;243
22.5;5. EQUILIBRIUM POINT OF THE MODIFIED GAME RELATED TO A D-CONVEX EQUILIBRIUM;246
22.6;6. D-CONVEX NONCOOPERATIVE EQUILIBRIUM POINT AND SUPER-GRADIENTS;247
22.7;REFERENCES;248
23;CHAPTER 17. ON WORST CASE DESIGN STRATEGIES!;250
23.1;1. INTRODUCTION;250
23.2;2. MAIN RESULTS;251
23.3;3. DETERMINISTIC SYSTEMS;254
23.4;4. CONCLUDING REMARKS;255
23.5;REFERENCES;256
24;CHAPTER 18. LINEAR-QUADRATIC STOCHASTIC DIFFERENTIAL GAMES FOR DISTRIBUTED PARAMETER SYSTEMS;258
24.1;1. INTRODUCTION;258
24.2;2. MATHEMATICAL PRELIMINARIES AND PROBLEM FORMULATION;258
24.3;3. REFORMULATION IN A DIFFERENT STATE SPACE;259
24.4;5. REPRESENTATION OF THE GAIN OPERATORS;267
24.5;6. CONCLUSION;270
24.6;REFERENCES;270
25;CHAPTER 19. ARTIFICIAL INTELLIGENCE IN AIR COMBAT GAMES;272
25.1;1. GENERAL OVERVIEW;272
25.2;2. IMPLEMENTATION;275
25.3;REFERENCES;285
26;CHAPTER 20. A PURSUIT-EVASION BIBLIOGRAPHY—VERSION 1;286
27;SUBJECT INDEX;352