CONTINUOUS TRANSFORMATIONS AND INTEGRAL MANIFOLDS.

Abstract

During the reporting the principal investigator and some of his collaborators completed seventeen research papers. This work is described. The major effort was devoted to problems of optimal control. Existence theorems were proved for lumped parameter control systems by a new type of analysis. A number of related conditions were analyzed with examples and applications. Existence theorems were proved for distributed parameter control systems by the use of Sobolev spaces technique and for partial differential equations written in the rather general form proposed by Dieudonne and Rashevski. A form of Pontryagin's principle were proved for these systems which is remarkably similar to a K. A. Lurie problem of magnetohydrodynamic channel flow. Further work concerns: measure theory, integration over a surface area, periodic solutions of nonlinear hyperbolic partial differential equations, in particular, nonlinear wave equations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1968
Accession Number
AD0681829

Entities

People

  • Lamberto Cesari

Organizations

  • University of Michigan

Tags

DTIC Thesaurus Topics

  • Channel Flow
  • Control Systems
  • Differential Equations
  • Electrical Solitons
  • Equations
  • Measure Theory
  • Partial Differential Equations
  • Theorems
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Systems Analysis and Design

Technology Areas

  • Space