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# Accession Number:

## ADA200256

# Title:

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

# Descriptive Note:

## Final rept.

# Corporate Author:

## INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

# Report Date:

## 1988-08-01

# Pagination or Media Count:

##
30.0

# 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#