Open AccessAdaptation in Stochastic Dynamic Systems—Survey and New Results III: Robust LQ Regulator Modification
Author(s) -
I. V. Semushin
Publication year - 2012
Publication title -
international journal of communications, network and system sciences/international journal of communications, network, and system sciences
Language(s) - English
Resource type - Journals
eISSN - 1913-3723
pISSN - 1913-3715
DOI - 10.4236/ijcns.2012.529071
Subject(s) - linear quadratic regulator , algebraic riccati equation , linear quadratic gaussian control , riccati equation , optimal control , computer science , mathematical optimization , mathematics , algorithm , differential equation , mathematical analysis
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