LIAPOUNOV'S THEOREM ON THE RANGE OF A VECTOR MEASURE AND PONTRYAGIN'S MAXIMUM PRINCIPLE

Abstract

The necessary condition for the optimal control of a non-linear dynamical system is studied. The system under consideration is described by a canonical system of ordinary differential equations for the state variables. The differential equations depend also on certain parameters called control variables. The problem is to choose the value of these control variables, which can be time dependent, in order to satisfy given initialAND END POINTS CONDITIONS AND TO MAXIMIZE A GIVEN FUNCTIONAL. When there are no restrictions on the values which can be taken by the control variables the problem is relatively simple and equivalent to the Problem of Bolza of the calculus of variations. Such situation however is very unlikely to occur in practice because of the physical limitations of the control devices. (Autho )

Document Details

Document Type
Technical Report
Publication Date
May 07, 1962
Accession Number
AD0275944

Entities

People

  • Hubert Halkin

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Calculus
  • Calculus Of Variations
  • Differential Equations
  • Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research