Accession Number : AD0712737

Title :   THE STRUCTURE OF ATTAINABLE SETS.

Descriptive Note : Final scientific rept. 1 Jan 67-31 Jul 70,

Corporate Author : COLORADO UNIV BOULDER DEPT OF MATHEMATICS

Personal Author(s) : Hermes,Henry

Report Date : SEP 1970

Pagination or Media Count : 17

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)

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), DIFFERENTIAL EQUATIONS, SET THEORY, TOPOLOGY, MAPPING(TRANSFORMATIONS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE