Convergence of Galerkin Approximations for Operator Riccati Equations -- A Nonlinear Evolution Equation Approach

Abstract

An approximation and convergence theory is developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation is treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result is proved for quasi-autonomous nonlinear evolution accretive operators which is then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of these results are illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1988
Accession Number
ADA200256

Entities

People

  • I. G. Rosen

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Banach Space
  • Complex Variables
  • Convergence
  • Differential Equations
  • Equations
  • Hilbert Space
  • Hypotheses
  • Identities
  • Integral Equations
  • Integrals
  • Inverse Problems
  • Nonlinear Systems
  • Personal Information Managers
  • Real Numbers
  • Riccati Equation
  • Sequences
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space