An accelerated technique for solving one type of discrete-time algebraic Riccati equations

Matthew M. Lin, Chun Yueh Chiang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and H control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati equations. Our contribution is twofold. First, we present sufficient conditions for the existence of a unique positive definite solution. Second, we propose an accelerated algorithm to obtain the positive definite solution with the rate of convergence of any desired order. Numerical experiments strongly support that our approach performs extremely well even in the almost critical case. As a byproduct, we show that this method is capable of computing the unique negative definite solution, once it exists.

Original languageEnglish
Pages (from-to)91-110
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume338
DOIs
Publication statusPublished - 2018 Aug 15

Fingerprint

Positive Definite Solution
Algebraic Riccati Equation
Riccati equations
Discrete-time
Critical Case
Control theory
Control Theory
Byproducts
Rate of Convergence
Numerical Experiment
Engineering
Computing
Sufficient Conditions
Experiments

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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An accelerated technique for solving one type of discrete-time algebraic Riccati equations. / Lin, Matthew M.; Chiang, Chun Yueh.

In: Journal of Computational and Applied Mathematics, Vol. 338, 15.08.2018, p. 91-110.

Research output: Contribution to journalArticle

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