Optimal Stochastic Linear Systems with Exponential Performance Criteria and their Relation to Deterministic Differential Games

Abstract

In the report two stochastic optimal control problems are solved whose performance criteria are the expected values of exponential functions of quadratic forms. The optimal controller is linear in both cases but depends upon the covariance matrix of the additive process noise so that the Certainty Equivalence Principle does not hold. The controllers are shown to be equivalent to those obtained by solving a cooperative and a noncooperative quadratic (differential) game, and this leads to come interesting interpretations and observations. Some stability properties of the asymptotic controllers are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1972
Accession Number
AD0740377

Entities

People

  • D. H. Jacobson

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Control Systems
  • Covariance
  • Data Science
  • Difference Equations
  • Differential Equations
  • Engineering
  • Equations
  • Exponential Functions
  • Gaussian Noise
  • Linear Systems
  • Military Research
  • Noise
  • Physics
  • Random Variables
  • Steady State
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Robotics and Automation.
  • Statistical inference.