Accession Number : ADA186190

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

Corporate Author : BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS

Personal Author(s) : Ito, Kazufumi

PDF Url : ADA186190

Report Date : Apr 1987

Pagination or Media Count : 23

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)

Descriptors :   *CONVERGENCE, *GENETICS, *HILBERT SPACE, *RICCATI EQUATION, ALGEBRA, APPROXIMATION(MATHEMATICS), CONTROL, FINITE DIFFERENCE THEORY, INVARIANCE, OPTIMIZATION, PARABOLAS, RATES, SOLUTIONS(GENERAL), TIME, TIME INTERVALS, LINEAR ALGEBRAIC EQUATIONS, FEEDBACK, GAIN

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE