Conflict-Controlled Processes / Edition 1

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This volume advances a new method for the solution of game problems of pursuit-evasion, which efficiently solves a wide range of game problems. In the case of 'simple motions' it fully substantiates the classic 'parallel pursuit' rule well known on a heuristic level to the designers of control systems. This method can be used for the solution of differential games of group and consecutive pursuit, the problem of complete controllability, and the problem of conflict interaction of a group of controlled objects, both for number under state constraints and under delay of information. These problems are not practically touched upon in other monographs. Some basic notions from functional and convex analysis, theory of set-valued maps and linear control theory are sufficient for understanding the main content of the book. This book will be of interest to specialists, as well as graduate and post-graduate students in applied mathematics and mechanics, and researchers in the mathematical theory of control, games theory and its applications.
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Editorial Reviews

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functioning under conflict and uncertainty conditions. At the heart of the book is the Method of Resolving Functions which was realized within the class of quasistrategies for pursuers and then applied to the solution of the problems of "hand-to-hand", group, and successive pursuit. The gist of the method consists in constructing on the basis of known process parameters certain numeral functions which integrally describe the course of conflict controlled process (degree of the trajectory proximity to the terminal set) and play a key role for solving specific problems. The volume's six chapters cover auxiliary mathematical results; the Method of Resolving Functions; group pursuit; complete conflict controllability; successive pursuit; and interaction of group of controlled objects. Some basic notions from functional and convex analysis, the theory of set-valued maps, and the linear control theory (provided in Chapter 1) are prerequisites for understanding the volume. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780792345220
  • Publisher: Springer Netherlands
  • Publication date: 4/30/1997
  • Series: Mathematics and Its Applications (closed) Series , #405
  • Edition description: 1997
  • Edition number: 1
  • Pages: 404
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.94 (d)

Table of Contents

1 Auxiliary Mathematical Results 1
2 The Method of Resolving Functions 31
3 Group Pursuit 179
4 Complete Conflict Controllability 249
5 Successive Pursuit 281
6 Interaction of Group of Controlled Objects 321
Bibliographic Commentary 371
References 375
Index 401
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