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 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1987
- Accession Number
- ADA192764
Entities
People
- Kazufumi Ito