The exact slow-fast decomposition of the algebraic riccati equation of singularly perturbed systems

Wu Chung Su; Zoran Gajic; Xue Min Shen

doi:10.1109/9.159592

The exact slow-fast decomposition of the algebraic riccati equation of singularly perturbed systems

Wu Chung Su, Zoran Gajic, Xue Min Shen

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

The algebraic Riccati equation of singularly perturbed control systems is completely and exactly decomposed into two reduced-order algebraic Riccati equations corresponding to the slow and fast time scales. The pure-slow and pure-fast algebraic Riccati equations are nonsymmetric ones, but their O(Ïµ) perturbations are symmetric. It is shown that the Newton method is very efficient for solving the obtained nonsymmetric algebraic Riccati equations. The presented method is very suitable for parallel computations. In addition, due to complete and exact decomposition of the Riccati equation, this procedure might produce a new insight in the two-time scale optimal filtering and control problems.

Original language	English (US)
Pages (from-to)	1456-1459
Number of pages	4
Journal	IEEE Transactions on Automatic Control
Volume	37
Issue number	9
DOIs	https://doi.org/10.1109/9.159592
State	Published - Sep 1992

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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abstract = "The algebraic Riccati equation of singularly perturbed control systems is completely and exactly decomposed into two reduced-order algebraic Riccati equations corresponding to the slow and fast time scales. The pure-slow and pure-fast algebraic Riccati equations are nonsymmetric ones, but their O({\"I}µ) perturbations are symmetric. It is shown that the Newton method is very efficient for solving the obtained nonsymmetric algebraic Riccati equations. The presented method is very suitable for parallel computations. In addition, due to complete and exact decomposition of the Riccati equation, this procedure might produce a new insight in the two-time scale optimal filtering and control problems.",

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