A POD Projection Method for Large-Scale Algebraic Riccati Equations

Abstract

The solution of large-scale matrix algebraic Riccati equations is important for instance in control design and model reduction and remains an active area of research. We consider a class of matrix algebraic Riccati equations (AREs) arising from a linear system along with a weighted inner product. This problem class often arises from a spatial discretization of a partial differential equation system. We propose a projection method to obtain low rank solutions of AREs based on simulations of linear systems coupled with proper orthogonal decomposition. The method can take advantage of existing (black box) simulation code to generate the projection matrices. We also develop new weighted norm residual computations and error bounds. We present numerical results demonstrating that the proposed approach can produce highly accurate approximate solutions. We also brie y discuss making the proposed approach completely data-based so that one can use existing simulation codes without accessing system matrices.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Algebraic Riccati Equations; Control Theory; Large-Scale; Proper Orthogonal Decomposition; Reduced-Order Modeling

International Standard Serial Number (ISSN)

2155-3289

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2016 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Dec 2016

Link to Full Text

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