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Conflict-Controlled Processes / Edition 1

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Overview

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions. To identify this range of problems we use the term "conflict conĀ­ trolled processes", coined in recent years. As the name itself does not imply the type of dynamics (difference, ordinary differential, difference-differential, integral, or partial differential equations) the differential games falI within its realms. The problems of search and tracking moving objects are also referred to the field of conflict controlled process. The contents of the monograph is confined to studying classical pursuit-evasion problems which are central to the theory of conflict controlled processes. These problems underlie the theory and are of considerable interest to researchers up to now. It should be noted that the methods of "Line of Sight", "Parallel Pursuit", "Proportional N avigation" ,"Modified Pursuit" and others have been long and well known among engineers engaged in design of rocket and space technology. An abstract theory of dynamic game problems, in its turn, is based on the methods originated by R. Isaacs, L. S. Pontryagin, and N. N. Krasovskii, and on the approaches developed around these methods. 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 succesive pursuit.

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Editorial Reviews

Booknews
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

Preface. Introduction. 1. Auxiliary Mathematical Results. 2. The Method of Resolving Functions. 3. Group Pursuit. 4. Complete Conflict Controllability. 5. Successive Pursuit. 6. Interaction of Group of Controlled Objects. Bibliographic Commentary. References. Index.

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