Open Loop Optimal Feedback Control for Continuous Linear Stochastic Systems.

Abstract

The control of a continuous time linear system with parameters and disturbance represented by stochastic processes is studied. The optimal open loop control is shown to be a linear function of the expected value of the initial condition vector and the function specifying the control, the control generation matrix, is shown to be the solution to a Fredholm integral equation. A computational procedure is derived for the solution to the control generation matrix based on results by Kagiwada and Kalaba for the solution to a Fredholm integral equation. A closed loop control law, the open loop optimal feedback (OLOF) control, is derived from the optimal open loop control and the control generation matrix shown to be the solution to a Volterra integral equation. The OLOF CONTROL GENERATION MATRIX FOR THE TIME-INVARIANT, INFINITE TIME SYSTEM IS SHOWN TO BE A CONSTANT MATRIX. Some examples are worked to demonstrate the OLOF control and to compare it with the optimal open loop control. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1970
Accession Number
AD0714131

Entities

People

  • Walter G. Murch

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Demographic Cohorts
  • Equations
  • Feedback
  • Integral Equations
  • Integrals
  • Linear Systems
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis