A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices

Chun Yueh Chiang; Hung Yuan Fan; Wen Wei Lin

doi:10.11650/twjm/1500405875

A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices

Chun Yueh Chiang^*
, Hung Yuan Fan
, Wen Wei Lin

^*Corresponding author for this work

Department of Mathematics

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

9 Citations (Scopus)

Abstract

In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

Original language	English
Pages (from-to)	933-954
Number of pages	22
Journal	Taiwanese Journal of Mathematics
Volume	14
Issue number	3 A
DOIs	https://doi.org/10.11650/twjm/1500405875
Publication status	Published - 2010 Jun

Keywords

Algebraic riccati equation
Invariant subspace
Singular
Structured doubling algorithm

ASJC Scopus subject areas

General Mathematics

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10.11650/twjm/1500405875

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abstract = "In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.",

keywords = "Algebraic riccati equation, Invariant subspace, Singular, Structured doubling algorithm",

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N2 - In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

AB - In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

KW - Algebraic riccati equation

KW - Invariant subspace

KW - Singular

KW - Structured doubling algorithm

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A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices

Abstract

Keywords

ASJC Scopus subject areas

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