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

An accelerated technique for solving one type of discrete-time algebraic Riccati equations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

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

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier B.V.
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/j.cam.2018.02.004
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 15, 2018

References

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