A POD projection method for large-scale algebraic Riccati equations
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A POD projection.pdf
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493.84 KB
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Author(s)
Singler, John
Kramer, Boris
Date Issued
September 2016
Journal
Numerical Algebra, Control and Optimization
Publisher
American Institute of Mathematical Sciences
Citation
Singler, John, and Boris Kramer. “A POD Projection Method for Large-Scale Algebraic Riccati Equations.” Numerical Algebra, Control and Optimization 6.4 (2016): 413–435.
Version
Final published version
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 briefly discuss making the proposed approach completely data-based so that one can use existing simulation codes without accessing system matrices
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.3934/naco.2016018
