The Theory of Optimal Control and the Calculus of Variations

Abstract

The hamiltonian theory of the calculus of variations is formulated for a wide variety of problems in the theory of control. The hamiltonian function is constructed with the aid of the Minimum Principle, which is the counterpart of the same principle due to Pontryagin. The canonical differential equations of Hamilton are shown to imply Pontryagin's theorem. A number of concrete examples are included.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1960
Accession Number
AD0267577

Entities

People

  • R. E. Kalman

Organizations

  • Martin Marietta

Tags

Communities of Interest

  • Air Platforms
  • Autonomy

DTIC Thesaurus Topics

  • Air Force
  • Calculus
  • Calculus Of Variations
  • Computational Fluid Dynamics
  • Computational Science
  • Control Systems
  • Differential Equations
  • Dynamic Programming
  • Engineering
  • Equations
  • Euler Equations
  • Hamiltonian Functions
  • Law
  • Partial Differential Equations
  • Scalar Functions
  • Three Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.