Strong Convergence and Convergence Rates of Approximating Solutions for Algebraic Riccati Equations in Hilbert Spaces,

Abstract

This paper considers the linear quadratic optimal control problem on infinite time interval for linear time-invariant systems define on Hilbert spaces. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sub n of finite dimensional approximations of the solution to ARE. A sufficient condition that shows N sub n converges strongly to pi is obtained. Under this condition, we derive a formula which can be used to obtain rate of convergence of N sub n to pi. We demonstrate and apply the results for the Galerkin approximation for parabolic systems and the averaging approximation for heredity differential systems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1987
Accession Number
ADA186190

Entities

People

  • Kazufumi Ito

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Classification
  • Contracts
  • Control Systems
  • Convergence
  • Engineering
  • Equations
  • Hilbert Space
  • Identification
  • Inequalities
  • Mathematics
  • Riccati Equation
  • Scientific Research
  • Security
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.

Technology Areas

  • Space