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Linear quadratic regulation for systems with time‐varying delay
Author(s) -
Zhang Huanshui,
Xie Lihua,
Wang Wei
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1427
Subject(s) - control theory (sociology) , smoothing , linear quadratic regulator , quadratic equation , controller (irrigation) , constant (computer programming) , upper and lower bounds , linear quadratic gaussian control , linear system , discrete time and continuous time , optimal control , elmore delay , channel (broadcasting) , computer science , mathematics , control (management) , mathematical optimization , propagation delay , telecommunications , mathematical analysis , programming language , statistics , geometry , agronomy , computer vision , biology , computer network , artificial intelligence , delay calculation
In this paper we study the linear quadratic regulation (LQR) problem for discrete‐time systems with time‐varying delay in the control input channel. We assume that the time‐varying delay is of a known upper bound, then the LQR problem is transformed into the optimal control problem for systems with multiple input channels, each of which has single constant delay. The optimal controller is derived by establishing a duality between the LQR and a smoothing estimation for an associated system with a multiple delayed measurement. Copyright © 2009 John Wiley & Sons, Ltd.