THE STRUCTURE OF ATTAINABLE SETS.

Abstract

The report contains a chronological listing of scientific publications and a summary of results, obtained under the grant. The major object of this study was the attainable set, i.e. the set of states attainable by all solutions, of a control system or more generally a generalized differential equation. The summary is divided into three sections: Existence of Solutions; Properites of Solutions and the attainable set; Techniques of approximation and calculation. A summary of all known results on the question of existence of solutions is given, with a description of how they overlap and fit together. Next, the known properties of the set of all solutions under various conditions, such as convexity of the right sides or Lipschitz continuity, etc. are listed, again with a discussion of their overlap and reference to where complete proofs can be found. Finally, the outline of approximation techniques is given. In short, this report summarizes the current state of knowledge in the theory of generalized differential equations and their attainable sets; many of the results being obtained under sponsorship of this grant. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1970
Accession Number
AD0712737

Entities

People

  • Henry Hermes

Organizations

  • University of Colorado Boulder

Tags

DTIC Thesaurus Topics

  • Continuity
  • Control Systems
  • Differential Equations
  • Equations

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research
  • Technical Research and Report Writing.