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A POD Projection Method for Large-Scale Algebraic Riccati Equations
Numerical Algebra, Control and Optimization
  • Boris Kramer
  • John R. Singler, Missouri University of Science and Technology
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.
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
Document Type
Article - Journal
Document Version
File Type
© 2016 American Institute of Mathematical Sciences, All rights reserved.
Publication Date
Citation Information
Boris Kramer and John R. Singler. "A POD Projection Method for Large-Scale Algebraic Riccati Equations" Numerical Algebra, Control and Optimization Vol. 6 Iss. 4 (2016) p. 413 - 435 ISSN: 21553289
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