Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

Abstract

This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

A data-driven model-based shared control strategy considering drivers’ adaptive behavior in driver-automation interaction

“…To further validate the adaptive update capability of the Koopman driver model, we next quantificationally compare the performance of the Koopman driver model updated by WOEDMD in predicting driver’s adaptive behavior with the initial Koopman driver model identified by EDMD. Furthermore, the Multivariable Linear Regression (MLR) approach is also employed as a comparison, which is first trained by the least square method using the same driving data set as EDMD to obtain an initial model and then updated by the recursive least square algorithm 38 using the same driving data set as WOEDMD. Two error indicators, the mean absolute error (MAE) and the root-mean-square error (RMSE), are employed as the quantitative index, which are defined as…”

Recursive parameter estimation of exhaust gas oxygen sensors with input-dependent time delay and linear parameters

“…Hence, the gradient of the error criterion with respect to this time delay variable cannot be calculated explicitly but needs to be approximated. In Banyasz and Kevtczky (1994), Bedoui, Ltaief, and Abderrahim (2013a), Bedoui, Ltaief, and Abderrahim (2012a), Bedoui, Ltaief, and Abderrahim (2012b), Bedoui, Ltaief, and Abderrahim (2012c), Bedoui, Ltaief, and Abderrahim (2013b), Bedoui, Ltaief, and Abderrahim (2013c), Lim and Macleod (1995) a first-order approximation of the gradient with respect to the time delay variable using the corresponding difference quotient is used.…”

“…Amongst the time delay estimation approaches reviewed above, gradient-based approaches allow the straightest extension to the estimation problem at hand. This paper provides an extended reformulation of the known gradient-based, recursive estimation algorithms (Banyasz & Kevtczky, 1994;Bedoui et al, 2012aBedoui et al, , 2012bBedoui et al, , 2012cBedoui et al, , 2013aBedoui et al, , 2013bBedoui et al, , 2013cLim & Macleod, 1995), using first-order gradient approximations for the nonlinear parameters given by the variables describing the input-dependent time delay. The nature of these variables implies that the gradient with respect to them cannot be calculated analytically like for other nonlinear parameters, but has to be approximated.…”

Iterative identification of output error model for industrial processes with time delay subject to colored noise

“…In an earlier report [16] on an online identification algorithm for estimating all the model parameters and time delay in terms of a two-step procedure, the first step assumes a known time delay to estimate other model parameters, and the second step determines the optimal model parameters by minimizing the squared output error with respect to the assumed time delay. By constructing a generalized regression vector, a few RLS algorithms have been proposed [17][18][19] for simultaneously estimating all model parameters and time delay, assuming no load disturbance or white noise. In the presence of measurement noise, the standard RLS algorithm cannot guarantee consistent estimation.…”