Auxiliary model based parameter estimation for dual-rate output error systems with colored noise

The dual-rate sampled-data systems can offer better quality of control than the systems with single sampling rate in practice. However, the conventional identification methods run in the single-rate scheme. This paper focuses on the parameter estimation problems of the dual-rate output error systems with colored noises. Based on the dual-rate sampled and noise-contaminated data, two direct estimation algorithms are addressed: the auxiliary model based recursive extended least squares algorithm and the recursive prediction error method. The auxiliary model is employed to estimate the noise-free system output. An example is given to test and illustrate the proposed algorithms.     

Recursive computational formulas of the least squares criterion functions for scalar system identification

The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided.     

Maximum likelihood least squares identification for systems with autoregressive moving average noise

Maximum likelihood methods are important for system modeling and parameter estimation. This paper derives a recursive maximum likelihood least squares identification algorithm for systems with autoregressive moving average noises, based on the maximum likelihood principle. In this derivation, we prove that the maximum of the likelihood function is equivalent to minimizing the least squares cost function. The proposed algorithm is different from the corresponding generalized extended least squares algorithm. The simulation test shows that the proposed algorithm has a higher estimation accuracy than the recursive generalized extended least squares algorithm.     

Bias compensation methods for stochastic systems with colored noise

For ARX-like systems, this paper derives a bias compensation based recursive least squares identification algorithm by means of the prefilter idea and bias compensation principle. The proposed algorithm can give the unbiased estimates of the system model parameters in the presence of colored noises, and can be on-line implemented. Finally, the advantages of the proposed bias compensation recursive least squares algorithm are shown by simulation tests.     

Recursive prediction error identification of fractional order models

This paper deals with time domain identification of fractional order systems. A new identification technique is developed providing recursive parameters estimation of fractional order models. The identification model is defined by a generalized ARX structure obtained by discretization of a continuous fractional order differential equation. The parameters are then estimated using the recursive least squares and the recursive instrumental variable algorithms extended to fractional order cases. Finally, the quality of the proposed technique is illustrated and compared through the identification of simulated fractional order systems.     

Three-stage recursive least squares parameter estimation for controlled autoregressive autoregressive systems

A three-stage recursive least squares parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) systems. The basic idea is to decompose a CARAR system into three subsystems, one of which contains one parameter vector, and to identify the parameters of each subsystem one by one. Compared with the recursive generalized least squares algorithm, the dimensions of the involved covariance matrices in each subsystem become small and thus the proposed algorithm has a high computational efficiency. Finally, we verify the proposed algorithm with a simulation example.     

On consistency of recursive least squares identification algorithms for controlled auto-regression models

The recursive least squares (RLS) algorithms is a popular parameter estimation one. Its consistency has received much attention in the identification literature. This paper analyzes convergence of the RLS algorithms for controlled auto-regression models (CAR models), and gives the convergence theorems of the parameter estimation by the RLS algorithms, and derives the conditions that the parameter estimates consistently converge to the true parameters under noise time-varying variance and unbounded condition number. This relaxes the assumptions that the noise variance is constant and that high-order moments are existent. Finally, the proposed algorithms are tested with two example systems, including an experimental water-level system.     

A recursive identification algorithm for switched linear/affine models

In this work, a recursive procedure is derived for the identification of switched linear models from input–output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in terms of the prediction error (or the posterior error), appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares or any fast adaptive linear identifier. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. It has been also observed that by appropriately choosing the data assignment criterion, the proposed on-line method can be extended to deal also with the identification of piecewise affine models. Finally, performance is tested through some computer simulations and the modeling of an open channel system.     

Combined state and least squares parameter estimation algorithms for dynamic systems

The control theory and automation technology cast the glory of our era. Highly integrated computer chip and automation products are changing our lives. Mathematical models and parameter estimation are basic for automatic control. This paper discusses the parameter estimation algorithm of establishing the mathematical models for dynamic systems and presents an estimated states based recursive least squares algorithm, and the states of the system are computed through the Kalman filter using the estimated parameters. A numerical example is provided to confirm the effectiveness of the proposed algorithm.     

LPV identification of a turbocharged diesel engine

This work proposes a methodology of identifying linear parameter varying (LPV) models for nonlinear systems. First, linear local models in some operating points, by applying standard identifications procedures for linear systems in time domain, are obtained. Next, a LPV model with linear fractional dependence (LFR) with respect to measured variables is fitted with the condition of containing all the linear models identified in previous step (differential inclusion). The fit is carried out using nonlinear least squares algorithms. Finally, this identification methodology will then be applied to a nonlinear turbocharged diesel engine.     

Linear Versus Quadratic Estimators in Linearized Models

In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria for an ordering linear and quadratic estimators.     

Solution of linear least squares via the ABS algorithm

The ABS class for linear and nonlinear systems has been recently introduced by Abaffy, Broyden, Galantai and Spedicato. Here we consider various ways of applying these algorithms to the determination of the minimal euclidean norm solution of over-determined linear systems in the least squares sense. Extensive numerical experiments show that the proposed algorithms are efficient and that one of them usually gives better accuracy than standard implementations of the QR orthogonalization algorithm with Householder reflections.     

On the Convergence of the Generalized Linear Least Squares Algorithm

This paper considers the issue of parameter estimation for biomedical applications using nonuniformly sampled data. The generalized linear least squares (GLLS) algorithm, first introduced by Feng and Ho (1993), is used in the medical imaging community for removal of bias when the data defining the model are correlated. GLLS provides an efficient iterative linear algorithm for the solution of the non linear parameter estimation problem. This paper presents a theoretical discussion of GLLS and introduces use of both Gauss Newton and an alternating Gauss Newton for solution of the parameter estimation problem in nonlinear form. Numerical examples are presented to contrast the algorithms and emphasize aspects of the theoretical discussion. AMS subject classification (2000) 65F10.R. A. Renaut: This work was partially supported by the Arizona Center for Alzheimer’s Disease Research, by NIH grant EB 2553301 and for the second author by NSF CMG-02223.Received December 2003. Revised November 2004. Communicated by Lars Eldén.     

An implicit least squares algorithm for nonlinear rational model parameter estimation

In this study a new insight into least squares regression is identified and immediately applied to estimating the parameters of nonlinear rational models. From the beginning the ordinary explicit expression for linear in the parameters model is expanded into an implicit expression. Then a generic algorithm in terms of least squares error is developed for the model parameter estimation. It has been proved that a nonlinear rational model can be expressed as an implicit linear in the parameters model, therefore, the developed algorithm can be comfortably revised for estimating the parameters of the rational models. The major advancement of the generic algorithm is its conciseness and efficiency in dealing with the parameter estimation problems associated with nonlinear in the parameters models. Further, the algorithm can be used to deal with those regression terms which are subject to noise. The algorithm is reduced to an ordinary least square algorithm in the case of linear or linear in the parameters models. Three simulated examples plus a realistic case study are used to test and illustrate the performance of the algorithm.     

Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods

This paper studies the modelling and identification problems for multi-input single-output (MISO) systems with colored noises. In order to obtain the unbiased recursive estimates of the systems, this paper presents a recursive least squares (RLS) identification algorithm based on bias compensation technique. The basic idea is to eliminate the estimation bias by adding a correction term in the least squares (LS) estimates, a set of stable digital prefilters are suitably designed to preprocess the input sampled data from multi-input channels for the purpose of getting the bias term arisen by colored noises in LS estimates, and further to derive a bias compensation based RLS algorithm. The performance of the developed method is both analyzed theoretically and shown by means of simulation results.     

Auxiliary model identification method for multirate multi-input systems based on least squares

This paper derives state-space models for multirate multi-input sampled-data systems. Based on the corresponding transfer function models, an auxiliary model based recursive least squares algorithm is presented to identify the parameters of the multirate systems from the multirate input–output data. Further, convergence properties of the proposed algorithm are analyzed. Finally, an illustrative example is given.     

线性定常系统特征模型的特征参量辨识

说明线性定常系统特征模型的特征参量是一组由高阶线性定常系统的相关信息压缩而成,于是不能简单的作为与状态无关的慢时变参数来处理. 基于特征建模思想,建立了线性定常系统特征模型的特征参量与子空间方法之间的联系,给出了一种该特征模型的特征参量 的合成辨识算法.同时证明了在用于子空间辨识的样本量充分大和用于状态估计的时间充分长的情况下, 特征参量的估计值与真值之间的误差达到充分小. 最后,对于一个六阶的单输入单输出线性定常系统的仿真例子,对投影的带遗忘因子最小二乘算法和合成辨识算法进行了比较,验证了合成辨识算法的有效性.     

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

This article addresses the synchronization of nonlinear master–slave systems under input time‐delay and slope‐restricted input nonlinearity. The input nonlinearity is transformed into linear time‐varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple‐integral‐based Lyapunov–Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay‐range‐dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope‐restricted nonlinearity. Further, time‐delays are treated using an advanced delay‐range‐dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems. © 2015 Wiley Periodicals, Inc. Complexity 21: 220–233, 2016     

RECURSIVE SYSTEM IDENTIFICATION

Most of existing methods in system identification with possible exception of those for linear systems are off-line in nature, and hence are nonrecursive. This paper demonstrates the recent progress in recursive system identification. The recursive identification algorithms are presented not only for linear systems （multivariate ARMAX systems） but also for nonlinear systems such as the Hammerstein and Wiener systems, and the nonlinear ARX systems. The estimates generated by the algorithms are online updated and converge a.s. to the true values as time tends to infinity.