Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method

Alexander Lanzon; Yantao Feng; Brian D.O. Anderson; Michael Rotkowitz

doi:10.1109/TAC.2008.2006108

Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method

Alexander Lanzon^*, Yantao Feng, Brian D.O. Anderson, Michael Rotkowitz

^*Corresponding author for this work

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

78 Citations (Scopus)

Abstract

An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.

Original language	English
Pages (from-to)	2280-2291
Number of pages	12
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2008.2006108
Publication status	Published - 2008

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10.1109/TAC.2008.2006108

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title = "Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method",

abstract = "An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.",

keywords = "Algebraic Riccati equation (ARE), H Riccati equations, Indefinite quadratic term, Iterative algorithms",

author = "Alexander Lanzon and Yantao Feng and Anderson, {Brian D.O.} and Michael Rotkowitz",

year = "2008",

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AU - Feng, Yantao

AU - Anderson, Brian D.O.

AU - Rotkowitz, Michael

PY - 2008

Y1 - 2008

N2 - An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.

AB - An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.

KW - Algebraic Riccati equation (ARE)

KW - H Riccati equations

KW - Indefinite quadratic term

KW - Iterative algorithms

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U2 - 10.1109/TAC.2008.2006108

DO - 10.1109/TAC.2008.2006108

M3 - Article

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EP - 2291

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

ER -

Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method

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