CONTINUOUS CONTROL WITH STOCHASTIC SHOPPING TIME,

Abstract

The criterion for a continuous control process whose stopping time is a random variable of known cumulative probability distribution is expressed as a single improper integral. (Physical examples of interrupted control situations are: regulator component failure, catalyst deterioration, space vehicle midcourse guidance, and random waiting for a digital computer used in the control of several systems.) A necessary condition for an optimal trajectory is derived, shown to be time-invariant only for the exponential probability law, and related to reliability theory. The optimal feedback control law, optimal trajectory, and minimum expected cost are presented for time-invariant linear systems with quadratic cost and exponentially distributed stopping time. A simple condition on the feedback rule for time-varying linear systems with arbitrary stopping time probability distribution is derived. A connection with the deterministic theory is established via the limit as the variance approaches zero. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1966
Accession Number
AD0634831

Entities

People

  • Allen Klinger

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Computers
  • Digital Computers
  • Feedback
  • Guidance
  • Linear Systems
  • Midcourse Guidance
  • Probability
  • Probability Distributions
  • Random Variables
  • Spacecraft
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers