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Title: Geometrical and topological methods in optimal control theory

Abstract

The present article will appear 30 years after Hermann`s report was published; in that report, the foundations of a new direction in optimal control theory, later called geometrical, were laid. The main purpose of this article is to present an overview of some of the basic results obtained in this direction. Each survey is subjective, and our work is no exception: the choice of themes and the degree of detail of their presentation are determined mainly by the author`s own interests (and by his own knowledge); the brief exposition, or, in general, the neglect of some aspects of the theory does not reflect their significance. As some compensation for these gaps (which refer mainly to discrete-time systems, to algebraic aspects of the theory, and, partially, to structural theory) there is a rather long reference list presented in the article (it goes up to 1993 and consists, basically, of papers reviewed in the review journal {open_quotes}Matematika{close_quotes} during last 30 years).

Authors:
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
161613
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 76; Journal Issue: 5; Other Information: PBD: 5 Oct 1995
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; CONTROL THEORY; DIFFERENTIAL TOPOLOGY; DIFFERENTIAL GEOMETRY; OPTIMIZATION

Citation Formats

Vakhrameev, S A. Geometrical and topological methods in optimal control theory. United States: N. p., 1995. Web. doi:10.1007/BF02362893.
Vakhrameev, S A. Geometrical and topological methods in optimal control theory. United States. https://doi.org/10.1007/BF02362893
Vakhrameev, S A. 1995. "Geometrical and topological methods in optimal control theory". United States. https://doi.org/10.1007/BF02362893.
@article{osti_161613,
title = {Geometrical and topological methods in optimal control theory},
author = {Vakhrameev, S A},
abstractNote = {The present article will appear 30 years after Hermann`s report was published; in that report, the foundations of a new direction in optimal control theory, later called geometrical, were laid. The main purpose of this article is to present an overview of some of the basic results obtained in this direction. Each survey is subjective, and our work is no exception: the choice of themes and the degree of detail of their presentation are determined mainly by the author`s own interests (and by his own knowledge); the brief exposition, or, in general, the neglect of some aspects of the theory does not reflect their significance. As some compensation for these gaps (which refer mainly to discrete-time systems, to algebraic aspects of the theory, and, partially, to structural theory) there is a rather long reference list presented in the article (it goes up to 1993 and consists, basically, of papers reviewed in the review journal {open_quotes}Matematika{close_quotes} during last 30 years).},
doi = {10.1007/BF02362893},
url = {https://www.osti.gov/biblio/161613}, journal = {Journal of Mathematical Sciences},
number = 5,
volume = 76,
place = {United States},
year = {Thu Oct 05 00:00:00 EDT 1995},
month = {Thu Oct 05 00:00:00 EDT 1995}
}