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The paper presents an online version of the identification method for estimating the impulse responses in the case of a two-input single-output linear empirical model of type 1 diabetes that allows us to adapt the model parameters due to the intra-subject time variability in real time. The method builds on and augments our original research by providing important enhancements concerning the online parameter estimation, recursive formulation of essential equations, improved regularization, and new effective approaches to numerically solve the estimation problem. Recursive equations are derived to update the covariance matrix of the sample cross-correlation function, as well as the inverse of this covariance matrix, where the customized Sherman-Morrison formula was considered. To efficiently update the parameter estimate at each sample while avoiding direct calculation of the Hessian matrix inverse, two alternative strategies are proposed to be applied instead. The first is based on the numeric minimization by the conjugate gradient method, whereas the second takes advantage of the Schulz method to approximate the inverse Hessian matrix. As a result, all steps of the identification algorithm were designed so that only basic linear operations are required. Features to robustify the estimate were also involved, as the optimal regularization strategies based on the inverse of the covariance matrix of the actual parameter distribution and the inter-sample parameter drift were applied. In the end of the paper, a series of simulation-based experiments was carried out to assess the effectiveness of the proposed method and to demonstrate all of its aspects and important characteristics. The documented results showed that the method can yield valid estimates of impulse responses and also effectively adapt parameters in real time under the influence of time-varying physiology.

This paper proposes a robust identification and control-based on a neural network method for a Twin Rotor Multivariable System (TRMS) using a recursive adaptive training algorithm. The algorithm is based on a recursive least squares approach with an additional steepest descent stage. An Adaline neural network is used for modeling the system, and a robust structure is selected based on a linear auto-regressive structure with exogenous inputs (ARX) related to the estimation error. The identification is performed online and the system is controlled under a polynomial structure by pole placement with a dead-beat strategy. The method is evaluated in terms of estimation and tracking error in the presence of external additive disturbances, parametric disturbances, and sinusoidal reference signals. The Root-Mean Square Error (RMSE) is used to evaluate the estimation performance and the Integral-Time Absolute Error (ITAE) is used to evaluate the tracking performance. As a result, a novel robust controller based on a neural network is designed where the best results are obtained for a training recursive least squares algorithm with an additional steepest descent stage. [ABSTRACT FROM AUTHOR]

Multi-rate systems exist widely in the field of computer process control. Research on the multi-rate issue of linear systems is relatively mature and is gradually turning to multi-rate issues of nonlinear systems. Concurrently, irregular process disturbances (impulse noise, outliers, non-zero mean noise) and varying transmission delay problems are often overlooked or considered alone, which is lacking generality. Thus, the main objective of this paper is to formulate and solve the identification problem of multi-rate nonlinear Wiener models with time-varying delay and irregular process disturbances simultaneously. The probability graph model of the Wiener process is constructed. Under the expectation–maximization (EM) framework, the Scale outlier model and Location outlier model (both based on Gaussian mixture distribution) are separately introduced to model the contaminated output data. The time-varying delay at each sampling instant is assumed as a uniform distribution. An auxiliary model is applied to acquire the unmeasured middle variable. Then, a robust EM identification algorithm is developed and its convergence is analyzed. The validity of the developed approach is illustrated through two numerical examples and a simulation of the continuous stirred tank reactor. • The parameter estimation of Wiener model under time-varying delay, multi-rate sampling and irregular interference (impulse noise, outliers) is studied for the first time. Under the expectation–maximization framework, the Scale outlier model is introduced to model the contaminated output data. The time-varying delay at each sampling instant is assume to obey the uniform distribution. The proposed method can estimate the model parameter and time varying delay simultaneously. • For the presence of non-zero mean noise, the Location outlier model is introduced to model the contaminated output data. The proposed method can further estimate the bias of non-zero noise. • The probability graph model of the Wiener process is constructed. The idea of an auxiliary model is applied to acquire the unmeasured middle variable. • The identification convergence of the proposed algorithm is analyzed. [ABSTRACT FROM AUTHOR]

Intensive research in the field of mathematical modeling of hydraulic servo systems has shown that their mathematical models have many important details which cannot be included in the model. Due to impossibility of direct measurement or calculation of dimensions of certain components, leakage coefficients or friction coefficients, it was supposed that parameters of the hydraulic servo system are random (stochastic nature). On the other side, it has been well known that the hydraulic servo cylinder can be approximated by a linear model with time-varying parameters. An estimation of states and time-varying parameters of linear state space models is of practical importance for fault diagnosis and fault tolerant control. Previous works on this topic consider estimation in Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of parameter-state robust estimation of linear state space models in presence of non-Gaussian noises. The case of robust estimation of states and parameters of linear systems with parameter faults is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithm. The good features of the proposed robust algorithm to identification of the hydraulic servo cylinder are illustrated by intensive simulations.

The robust identification problem of the linear parameter varying (LPV) systems with output data corrupted by outliers is considered in this paper. The local identification approach is used, and the LPV model is obtained by interpolating the local models with an exponential weighting function. In order to handle outliers that could occur in industrial processes, the corresponding probabilistic model is established with the process noise assumed to be mixture Laplace distributed, then the formulas to iteratively update the unknown model parameters and noise-free output are derived under the Variational Bayesian (VB) framework, which approximates the required posteriors and could avoid high dimensional integrals. One numerical example and a practical chemical process are employed to verify the efficacy of the developed algorithm. [ABSTRACT FROM AUTHOR]

The paper represents the main ideas of Robust Identification Theory, which was initiated by Ya.Z. Tzypkin in 80s of the past century. Here we demonstrate that the parallel application of both the "Whitening Procedure" and the recurrent min-max version of the "Maximum Likelihood Method" (MLLM), guarantees the property of Asymptotic Consistency of this procedure. The information Cramér–Rao inequality is also obtained and it is shown that this combined procedure attains this information bound. This means that for wide class of regular observations of ARX (auto regression with exogenous input) models, there does not exist any other identification algorithm, estimating asymptotically unknown parameters "quicker" then the procedure discussed here, if the distribution of the white noise at the input of the forming filter is known exactly. The main specific feature of this method consists in the possible consideration of external non-Gaussian white noise (defined on the given class of admissible distributions) in the input of the forming filter, making the noise sequence, affecting the input of ARX-dynamics, non-Gaussian, and correlated. The almost sure convergence as well as the Asymptotic Normality of the estimation error are formulated. If the information on the input of the forming filter is uncertain, that is, when the distribution belongs to a given class, then the Huber's approach is applied using the robust version of MLLM. [ABSTRACT FROM AUTHOR]

In this paper, a robust procedure for estimating of nominal hydrodynamic coefficients of an autonomous underwater vehicle (AUV) in presence of parameter uncertainties is proposed. Some parameters of the model of an AUV, such as its hydrodynamic coefficients, may perturb from their nominal values because of changes in its operating conditions and the surrounding environment. This paper presents two different filters for robust identification of the AUV parameters. The robust extended Kalman filter (REKF) and the extended H-infinity (EH ∞) filter are implemented to estimate the nominal hydrodynamic coefficients of the AUV. By using a model of a sample AUV and simulating the motion of the vehicle in the diving mode involving parameter perturbations, the performance of the filters is compared. The results show that the REKF outperforms the EH ∞ filter in this application. Also, the performance of these estimation algorithms is compared with the standard extended Kalman filter (EKF), using the data obtained from experimental test of a real AUV. It is observed that the model using the identified values of hydrodynamic coefficients of both filters can predict the actual trajectory of the vehicle and the robust filters are more accurate as compared to the standard EKF. • Hydrodynamic coefficients of an AUV are identified in presence of parameter uncertainties. • Two robust filters (REKF and EH ∞) filters are implemented to estimate the coefficients in the diving mode. • Both filters outperform the standard EKF in estimating the hydrodynamic coefficients. • The results show that REKF is the more accurate than EH ∞. [ABSTRACT FROM AUTHOR]

We develop an inverse method with the purpose of extracting elastic properties of materials in the framework of transient dynamics. To this end, we create a small linear system based on a set of well-chosen time-dependent virtual fields (VF) and measurement data. The parameters are the solutions of this system and can be quickly extracted. We compare this new method with the classical finite element model updating (FEMU) method for different case studies. In our study, the measurements are synthetic, i.e , they are calculated using a fine finite element (FE) model. Uniform white noise is added to model measurement uncertainties. Results, based on Monte Carlo simulations, show that our method is more robust and accurate than the FEMU method for an acceptable noise level. Our new method appears well-adapted to linear elasticity in transient dynamics. [ABSTRACT FROM AUTHOR]

Summary: This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm. [ABSTRACT FROM AUTHOR]

The aim of this paper is robust identification of smart foam, as an electroacoustic transducer, considering unmodeled dynamics due to nonlinearities in behaviour at low frequencies and measurement noise at high frequencies as existent uncertainties. Set membership estimation combined with model error modelling technique is used where the approach is based on worst case scenario with unknown but bounded uncertainties. The outcome is a robust identified model which consists of a nominal model with its uncertainty bounds that fits exactly the H_∞ robust control scheme which has been utilized in active noise control in recent years. While the nominal model has the desired physical characteristics as cut-off frequency and the anticipated slope and flatness before and after this frequency, respectively, it is maintained in the acceptably tight uncertainty upper and lower limits, thus validating the identification procedure. Looseness and tightness of uncertainty strip has also been discussed regarding nonlinearities and measurement noise in low and high frequency regions. Meanwhile the identified nominal model can also be utilized in non-robust noise control methods due to its lower order, reflecting the advantage of the applied identification approach.

Industrial data sets are often contaminated with outliers due to sensor malfunctions, signal interference, and other disturbances as well as interplay of various other factors. The effect of data abnormalities due to the outliers has to be systematically accounted while developing models that are resistant towards unforeseen effects of the outliers. The spectrum of methods that account for irregularities in process data while modeling are collectively known as robust identification methods. Even though, there are various non-probabilistic methods to tackle robust identification, few of them have considered the effect of outliers explicitly. In contrast to that, probabilistic identification methods ensure that these effects are given due attention. Despite these advantages, the probabilistic robust identification strategies have hardly been explored by practitioners. This review paper provides a general introduction to the probabilistic methods for robust identification, illustrates the main steps involved in the development of models, and reviews the related literature. Further, the paper contains two tutorial examples, including an industrial case study, to highlight various steps involved in the robust identification process. [ABSTRACT FROM AUTHOR]

Modeling of high dimensional dynamic process is considered as a challenging task. In this regard, probabilistic Slow Feature Analysis (PSFA), a dynamic latent variable model, is proven to be a useful tool which extracts temporally correlated dynamic features from the high-dimensional raw measurements. The extracted latent Slow Features (SFs) can capture process variations which are useful in developing dynamic models. Often times industrial data is affected by outliers, and modeling such data could result in inferior prediction performance. To deal with such scenarios, we propose a robust PSFA (RPSFA) based regression model that models outliers in the observation data using the Student's t-distribution. To estimate the parameters in RPSFA and to extract reduced dimension of SFs, we employ Expectation-Maximization (EM) algorithm under the Maximum Likelihood Estimation (MLE) framework considering SFs as hidden variables. To estimate the hidden SFs we propose a weighted gain Kalman filter based approach as the Normal distribution assumption of the observations is no longer valid. The validity and merits of the proposed approach are demonstrated though a simulated example, an industrial application and an experimental study. [ABSTRACT FROM AUTHOR]

In order to give a sufficient description of system characteristics, this paper proposes a Wiener model for nonlinear dynamic soft sensors. Based on the model, an improved swarm intelligent identification algorithm is proposed by combining the global cuckoo search (CS) and the local new Luus-Jaakola (NLJ) optimization. The Levy flight in the CS helps the search escape from local optima, and the NLJ search achieves the exploitation of local areas. Thus, a good balance is guaranteed between algorithmic exploration and exploitation. Because of the strong search ability of CS-NLJ algorithm, the approximation accuracy of identification can be improved in the presence of stochastic Gaussian or heavy-tailed noises. Further, the robust identification for dual-rate soft sensors is achieved by using the proposed model and the proposed identification algorithm. Finally, the simulation results verify the theoretical findings. [ABSTRACT FROM AUTHOR]

A novel automatic tuning strategy is proposed. It is based on an experiment of very short duration, followed by simultaneous identification of LTI model parameters and an estimate of their error covariance. The parametric uncertainty model is subsequently exploited to design linear controllers with magnitude bounds on some closed-loop transfer function of interest, such as the sensitivity function. The method is demonstrated through industrially relevant examples. Robustness is enforced through probabilistic constraints on the [ABSTRACT FROM AUTHOR]

The identification of ARX models with constrained output variance in the presence of non-Gaussian distribution of measurements is proposed in this paper. In the presence of non-Gaussian noise, the Masreliez–Martin filter (robust Kalman filter) is the natural frame for identification of model parameters. For the purpose of increasing the practical value of the filter, a heuristic modification is performed. Also, an optimal input is obtained by a minimum variance controller with a Gaussian reference signal. A fundamental issue in experiment design is that the optimal input in general depends on system parameters to be estimated. In order to realize obtained optimal input, authors have proposed a two-stage adaptive procedure, where one iterates between parameter estimation, on the one side, and experiment design using the current parameter estimates, on the other. The practical behavior of new approach to optimal input design for robust identification of ARX models is shown by intensive simulations. [ABSTRACT FROM AUTHOR]

This paper considers the nonlinear recursive algorithm for the identification of multivariable ARX models (autoregressive with exogenous input). It is assumed that the following a priori information is available: (a) a distribution class to which the stochastic disturbance belongs (b) a distribution class to which unknown parameters of ARX model belong A priori information (a) allows a description of outliers (large realizations of the stochastic process which are inconsistent with the largest part of population of observations) and introduces the nonlinear transformation of the prediction error in the recursive algorithm. A priori information (b) defines the initial conditions of the algorithm (for the vector of unknown parameters and the matrix gain) which increases the convergence speed in initial iterations. This intervention in the algorithm represents its regularization. Regularization problems are recently actualized thanks to statistical learning theory. Thanks to a priori information, the considered recursive algorithm is robust with respect to the uncertainty of statistical characteristics of disturbances and has the increased convergence speed in initial iterations. It is formulated theorem for convergence of estimated parameters with probability one. Simulation results illustrate the practical behavior of the algorithm. [ABSTRACT FROM AUTHOR]

The universal sequel to chronic kidney condition (CKD) is anemia. Patients of anemia have kidneys that are incapable of performing certain basic functions such as sensing of oxygen levels to secrete erythropoietin when red blood cell counts are low. Under such conditions, external administration of human recombinant erythropoietin (EPO) is administered as alternative to improve conditions of CKD patients by increasing their hemoglobin (Hb) levels to a given therapeutic range. Presently, EPO dosing strategies extensively depend on packet inserts and on “average” responses to the medication from previous patients. Clearly dosage strategies based on these approaches are, at best, nonoptimal to EPO medication and potentially dangerous to patients that do not adhere to the notion of expected “average” response. In this work, a technique called semi-blind robust identification is provided to uniquely identify models of the individual patients of anemia based on their actual Hb responses and EPO administration. Using the a priori information and the measured input-output data of the individual patients, the procedure identifies a unique model consisting of a nominal model and the associated model uncertainty for the patients. By incorporating the effects of unknown system initial conditions, considerably small measurement samples can be used in the modeling process. [ABSTRACT FROM AUTHOR]

A common assumption is that the model structure is known for modelling high performance aircraft. In practice, this is not the case. Actually, structure identification plays the most important role in the processing of nonlinear system modelling. The integration of mode structure identification and parameter estimation is an efficient method to construct the model for high performance aircraft, which is nonlinear and also contains uncertainties. This article presents an efficient method for identifying nonlinear model structure and estimating parameters for high-performance aircraft model, which contains uncertainties. The parameters associated with nonlinear terms are considered one after the other if they should be included in the nonlinear model until a stopping criterion is met, which is based on Akaike's information criterion. A numerically efficientU-Dfactorisation is presented to avoid complex computation of high-order matrices. The proposed method is applied to flight test data of a high-performance aircraft. The results demonstrate that the proposed method could obtain the good aircraft model with a reasonably good fidelity based on the comparison with flight test data. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the usual definition of Grünwald–Letnikov fractional derivative is first extended to interval derivatives in order to deal with uncertainties in the differentiation orders. The Laplace transform of interval derivatives is computed and its monotonicity is studied in the frequency domain. Next, the main objectives of this paper are presented as the implementation of three methods for set membership parameters estimation of fractional differentiation models based on complex frequency data. The first one uses a rectangular inclusion function with rectangle sides corresponding to real and imaginary parts of the complex frequency response; the second one uses a polar inclusion function and the gain/phase representation; the third one uses a circular inclusion function with disk representation. Each inclusion function introduces pessimism differently. It is shown that all three approaches are complementary and that the results can be merged to obtain a smaller feasible solution set. The proposed methods can be applied to estimate parameters of certain/uncertain linear time variant/invariant systems. [Copyright &y& Elsevier]

Abstract: Several approaches can be found in the literature to perform the identification of block oriented models (BOMs). In this sense, an important improvement is to achieve robust identification to cope with the presence of uncertainty. In this work, two special and widely used BOMs are considered: Hammerstein and Wiener models. The models herein treated are assumed to be described by parametric representations. The approach introduced in this work for the identification of the multiple input–multiple output (MIMO) uncertain model is performed in a single step. The uncertainty is described as a set of parameters which is found through the solution of an optimization problem. A distillation column simulation model is presented to illustrate the robust identification approach. This process is an interesting benchmark due to its well-known nonlinear dynamics. Both Hammerstein and Wiener models are used to represent this plant in the presence of uncertainty. A comparative study between these models is established. [Copyright &y& Elsevier]

The paper is oriented to EEG signal analysis, which is focused to quasi-stationarity hypothesis that the statistical properties of the channel signal fluctuate in time. Robust linear predictor is used for short segments of EEG as low-pass filter and the difference between the raw EEG and filter output was subject of statistical testing. Novelty is in the fluctuation measurement which enables to classify the Alzheimer's disease patients against controls. [ABSTRACT FROM AUTHOR]

Abstract: The paper introduces a novel method of adaptive robust identification of complex nonlinear dynamic plants including Box Jenkin, Mackey Glass and Sunspot series under the presence of strong outliers in the training samples. The identification model consists of a low complexity single layer functional link artificial neural network (FLANN) in the feed forward path and another on the feedback path. The connecting weights are iteratively adjusted by a population based particle swarm optimization technique so that a robust cost function (RCF) of the model-error is minimized. To demonstrate robust identification performance up to 50% random samples of the plant output is contaminated with strong outliers and are employed for training the model using PSO tool. Identification of wide varieties of benchmark complex static and dynamic plants is carried out through simulation study and the performance obtained are compared with those obtained from using standard squared error norm as CF. It is in general observed that, the Wilcoxon norm provides best identification performance compared to squared error and other RCFs based models. [Copyright &y& Elsevier]

Abstract: This paper describes a new kernel-based approach for linear system identification of stable systems. We model the impulse response as the realization of a Gaussian process whose statistics, differently from previously adopted priors, include information not only on smoothness but also on BIBO-stability. The associated autocovariance defines what we call a stable spline kernel. The corresponding minimum variance estimate belongs to a reproducing kernel Hilbert space which is spectrally characterized. Compared to parametric identification techniques, the impulse response of the system is searched for within an infinite-dimensional space, dense in the space of continuous functions. Overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization. The proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two-step procedure that projects the nonparametric estimate onto the space of nominal models. The continuous-time derivation immediately extends to the discrete-time case. On several continuous- and discrete-time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques. [Copyright &y& Elsevier]

Abstract: This work describes a new methodology for robust identification (RI), meaning the identification of the parameters of a model and the characterization of uncertainties. The alternative proposed handles non-linear models and can take into account the different properties demanded by the model. The indicator that leads the identification process is the identification error (IE), that is, the difference between experimental data and model response. In particular, the methodology obtains the feasible parameter set (FPS, set of parameter values which satisfy a bounded IE) and a nominal model in a non-linear identification problem. To impose different properties on the model, several norms of the IE are used and bounded simultaneously. This improves the model quality, but increases the problem complexity. The methodology proposes that the RI problem is transformed into a multimodal optimization problem with an infinite number of global minima which constitute the FPS. For the optimization task, a special genetic algorithm (-GA), inspired by Multiobjective Evolutionary Algorithms, is presented. This algorithm characterizes the FPS by means of a discrete set of models well distributed along the FPS. Finally, an application for a biomedical model which shows the blockage that a given drug produces on the ionic currents of a cardiac cell is presented to illustrate the methodology. [Copyright &y& Elsevier]

Abstract: In this paper, a systematic control-oriented robust identification procedure which produces a parametric/nonparametric set of models is applied to a duct, in order to design a feedback active noise control (ANC) based on robust analysis and control. In addition, practical problems encountered in applying such a robust identification and feedback control approaches to ANC are pointed out. These are mainly derived from the compromises between identification and control, performance and robustness, the inherent limitations of feedback when applied to ANC, model and controller order, and implementation issues. Theoretical and experimental results on a real duct are compared using two different noise sources, a speaker and a fan. [Copyright &y& Elsevier]

Abstract: A precursor to any advanced control solution is the step of obtaining an accurate model of the process. Suitable models can be obtained from phenomenological reasoning, analysis of plant data or a combination of both. Here, we will focus on the problem of estimating (or calibrating) models from plant data. A key goal is to achieve robust identification. By robust we mean that small errors in the hypotheses should lead to small errors in the estimated models. We argue that, in some circumstances, it is essential that special precautions, including discarding some part of the data, be taken to ensure that robustness is preserved. We present several practical case studies to illustrate the results. [Copyright &y& Elsevier]

Abstract: This paper presents the non-linear modelling, based on first principle equations, for a climatic model of a greenhouse and the estimation of the feasible parameter set (FPS) when the identification error is bounded simultaneously by several norms. The robust identification problem is transformed into a multimodal optimization problem with an infinite number of global minima that constitute the FPS. For the optimization task, a special evolutionary algorithm (-GA) is presented, which characterizes the FPS by means of a discrete set of models that are well distributed along the FPS. A procedure for determining the norm bounds, such that , is presented. [Copyright &y& Elsevier]

Abstract: One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a joint robust state feedback control/input design procedure which guarantees stability and prescribed closed-loop performance using models identified from experimental data. This means that given specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process. The condition takes the form of a linear matrix inequality. [Copyright &y& Elsevier]

Abstract: Fault diagnosis of multiprocessor systems gives the motivation for robust identifying codes. We provide robust identifying codes for the square and king grids. Often we are able to find optimal such codes. [Copyright &y& Elsevier]

Abstract: Robustness had become in past years a central issue in system and control theory, focusing the attention of researchers from the study of a single model to the investigation of a set of models, described by a set of perturbations of a “nominal” model. Such a set, often indicated as an uncertainty model set or model set for short, has to be suitably constructed to describe the inherent uncertainty about the system under consideration and to be used for analysis and design purposes. identification methods deliver uncertainty model sets in a suitable form to be used by well-established robust design techniques, based on or optimization methods. The literature on identification is now very extensive. In this paper, some of the most relevant contributions related to assumption validation, evaluation of bounds on unmodeled dynamics, convergence analysis and optimality properties of linear, two-stage and interpolatory algorithms are surveyed from a deterministic point of view. [Copyright &y& Elsevier]

Since it is difficult to fit measured parameters using the conventional traffic model, a new traffic density and average speed model is introduced in this paper. To determine traffic model structures accurately, a model identification method for uncertain nonlinear system is developed. To simplify uncertain nonlinear problem, this paper presents a new robust criterion to identify the multi-section traffic model structure of freeway efficiently. In the new model identification criterion, numerically efficient U-D factorization is used to avoid computing the determinant values of two complex matrices. By estimating the values of U-D factor of data matrix, both the upper and lower bounds of system uncertainties are described. Thus a model structure identification algorithm is proposed. Comparisons between identification outputs and simulation outputs of traffic states show that the traffic states can be accurately predicted by means of the new traffic models and the structure identification criterion. [ABSTRACT FROM AUTHOR]

This paper considers two robustly convergent algorithms for the identification of a linear system from (possibly) noisy frequency response data. Both algorithms are based on the same principle; obtaining a good worst case fit to the data under a smoothness constraint on the obtained model. However they differ in their notions of distance and smoothness. The first algorithm yields an FIR model of a stable system and is optimal, in a certain sense for a finite model order. The second algorithm may be used for modelling unstable plants and yields a real rational approximation in the L2-gap. Given a model and a controller stabilising the true plant, a procedure for winding number correction is also suggested. [Copyright &y& Elsevier]