Open AccessLinear quadratic Gaussian control for linear time‐delay systems
Author(s) -
Song Xinmin,
Yan Xuehua
Publication year - 2014
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2013.0400
Subject(s) - riccati equation , linear quadratic gaussian control , mathematics , control theory (sociology) , separation principle , algebraic riccati equation , estimator , controller (irrigation) , dimension (graph theory) , linear quadratic regulator , optimal control , linear system , gaussian , quadratic equation , mathematical optimization , control (management) , computer science , partial differential equation , nonlinear system , mathematical analysis , statistics , physics , geometry , quantum mechanics , artificial intelligence , pure mathematics , agronomy , state observer , biology
This study investigates a separation principle for the H 2 control of time‐delay systems with partial observations. The authors first consider the linear quadratic regulation problem for time‐delay systems. Based on the dynamic programming technique, the solution to the controller is given in terms of a backward partial difference Riccati equation. Then the estimation problem is investigated for linear discrete‐time systems in the presence of time‐delays. By employing the innovation analysis approach, the linear minimum‐mean‐square error (LMMSE) estimator is developed in terms of a forward partial difference Riccati equation. The Riccati equation is of the same dimension as the plant. Therefore compared with the conventional augmented approach, the presented approach greatly lessens the computational demand when the delay is large. Finally, they show that the separation principle holds in the following sense: an optimal controller can be obtained from two parts, one associated with the optimal control problem when state variable is available, and the other one associated with the LMMSE estimation problem.