APPLICATION OF DYNAMIC PROGRAMMING TO STOCHASTIC TIME OPTIMAL CONTROL,

Abstract

A non-linear control process is discussed where the control is bounded as absolute value. A random element (noise) that appears additively as part of the control variable is assumed. The performance criterion of driving the system back to equilibrium from its present perturbed state in minimum ''expected'' time, due to the presence of the random noise is used. The principle of optimality of dynamic programming to derive a novel partial differential equation in the minimum expected time is applied. Solutions of this equation yield the optimal control policy, which is bang bang. Specifically, far from the origin of the corresponding phase space, the control is set, once only, to drive the system into the linear region near the origin. In the linear region, the control switching sequence corresponding to Bushaw's theorem ensues. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 31, 1964
Accession Number
AD0431055

Entities

People

  • M. Ash

Organizations

  • System Development Corporation

Tags

DTIC Thesaurus Topics

  • Arrhenius Equation
  • Computer Programming
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Real Variables
  • Sequences
  • Switching

Readers

  • Control Systems Engineering.
  • Operations Research

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers