PONTRYAGIN'S MAXIMUM PRINCIPLE AND OPTIMAL CONTROL

Abstract

The mathematical formulation of the most general problem of Optimal Control can be considered as a problem of Mayer subjected to unilateral constraints, i.e., to certain restrictions expressible in terms of inequalities. Results of the classical calculus of variations in their usual forms cannot give a general solution to this problem because, among other things, the fundamental relation of the calculus of variations, i.e., the equation of Euler- Lagrange, is valid only in the case of points interior to the set of admissible points. The most general solution is given by the Maximum Principle of Pontryagin, but in its present form this principle cannot be applied in certain situations, and its validity has been proved in particular cases only. A derivation of this principle for the most general case is given.

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Document Details

Document Type
Technical Report
Publication Date
Sep 15, 1961
Accession Number
AD0267860

Entities

People

  • H. Halkin
  • I. Fluegge-lotz

Organizations

  • Stanford University

Tags

Communities of Interest

  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aeronautical Engineering
  • Aeronautical Laboratories
  • Air Force
  • Air Force Facilities
  • Calculus
  • Calculus Of Variations
  • Differential Equations
  • Electrical Engineering
  • Engineering
  • Equations
  • Fluid Mechanics
  • Mechanics
  • New Mexico
  • New York
  • Scientific Research
  • United States
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.