Comparative Dynamics (Sensitivity Analysis) in Optimal Control Theory

Abstract

The paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative are given in the form of initial-value problems of linear differential equations. Possibility of discontinuous optimal controls is fully taken care of. The derivative of the maximized objective function with respect to the parameter is expressed in a simple form by using the auxiliary variables. An example of the comparative dynamics is given in terms of a model of optimal capital accumulation.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1972
Accession Number
AD0741708

Entities

People

  • Hajime Oniki

Organizations

  • Harvard University

Tags

Communities of Interest

  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Calculus Of Variations
  • Control Theory
  • Diagrams
  • Differential Equations
  • Dynamics
  • Economic Analysis
  • Economic Systems
  • Economics
  • Equations
  • Investments
  • Linear Differential Equations
  • Money
  • Phase Diagrams
  • United States
  • United States Government
  • Variational Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Operations Research