H. Dai and Z.-Z. Bai. “On Eigenvalue Bounds and Iteration Methods for Discrete Algebraic Riccati Equations,” Journal of Computational Mathematics, Vol. 29, No. 3, 2011, pp. 341-366. http://www.jcm.ac.cn/EN/10.4208/jcm.1010-m3258 http://www.jcm.ac.cn/EN/Y2011/V29/I3/341

has been cited by the following article:

• TITLE: Adaptation in Stochastic Dynamic Systems—Survey and New Results III: Robust LQ Regulator Modification

  AUTHORS: Innokentiy V. Semushin

  KEYWORDS: Adaptive Control; Factorization; Least Squares; Linear Systems; LQG Estimator; LQ Regulator; Orthogonalization; Receding Horizon Control; Scalarization

  JOURNAL NAME: International Journal of Communications, Network and System Sciences, Vol.5 No.9A, September 18, 2012

  ABSTRACT: The paper is intended to provide algorithmic and computational support for solving the frequently encountered linear-quadratic regulator (LQR) problems based on receding-horizon control methodology which is most applicable for adaptive and predictive control where Riccati iterations rather than solution of Algebraic Riccati Equations are needed. By extending the most efficient computational methods of LQG estimation to the LQR problems, some new algorithms are formulated and rigorously substantiated to prevent Riccati iterations divergence when cycled in computer implementation. Specifically developed for robust LQR implementation are the two-stage Riccati scalarized iteration algorithms belonging to one of three classes: 1) Potter style (square-root), 2) Bierman style (LDLT), and 3) Kailath style (array) algorithms. They are based on scalarization, factorization and orthogonalization techniques, which allow more reliable LQR computations. Algorithmic templates offer customization flexibility, together with the utmost brevity, to both users and application programmers, and to ensure the independence of a specific computer language.