Accession Number : ADA192764

Title :   Strong Convergence and Convergence Rates of Approximating Solutions for Algebraic Riccati Equations in Hilbert Spaces.

Descriptive Note : Final rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Ito, Kazufumi

PDF Url : ADA192764

Report Date : May 1987

Pagination or Media Count : 21

Abstract : This paper considers the linear quadratic optimal control problem on infinite time interval for linear time invariant systems defined 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 to the Nth power of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi to the Nth power converges strongly to pi is obtained. Under this condition, we derive a formula which can be used to obtain a rate of convergence of pi to the Nth power to pi. The results are applied for the Galerkin approximation for parabolic systems and the averaging approximation for hereditary differential systems. Keywords: Distributed parameter systems, Algebraic Riccati equations, Galerkin approximation, Convergence rates.

Descriptors :   *HILBERT SPACE, *RICCATI EQUATION, ALGEBRA, APPROXIMATION(MATHEMATICS), CONTROL, CONVERGENCE, FINITE DIFFERENCE THEORY, INVARIANCE, LINEAR SYSTEMS, OPTIMIZATION, PARABOLAS, PARAMETERS, RATES, SOLUTIONS(GENERAL), TIME, TIME INTERVALS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE