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arXiv · 2107.11708

Large-Scale Algebraic Riccati Equations with High-Rank Nonlinear Terms and Constant Terms

Bo Yu·Ning Dong
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Abstract

For large-scale discrete-time algebraic Riccati equations (DAREs) with high-rank nonlinear and constant terms, the stabilizing solutions are no longer numerically low-rank, resulting in the obstacle in the computation and storage. However, in some proper control problems such as power systems, the potential structure of the state matrix -- banded-plus-low-rank, might make the large-scale computation essentially workable. In this paper, a factorized structure-preserving doubling algorithm (FSDA) is developed under the frame of the banded inverse of nonlinear and constant terms. The detailed iterations format, as well as a deflation process of FSDA, are analyzed in detail. A partial truncation and compression technique is introduced to shrink the dimension of columns of low-rank factors as much as possible. The computation of residual, together with the termination condition of the structured version, is also redesigned.

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Bo Yu, Ning Dong. 2021-07-25. Large-Scale Algebraic Riccati Equations with High-Rank Nonlinear Terms and Constant Terms. https://arxiv.org/abs/2107.11708

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