variance expressions for spectra estimated using auto regressions an expression for the variance of the estimated spectrum based on auto regressions is developed this expression is asymptotic in the number of data but exact in the model order as the order tends to infinity it converges to the well known result that the variance is proportional to the model order times the square of the spectrum itself the exact expression gives insight into the character of this convergence its speed and its dependence on the poles of the underlying ar process

on the reproduction of closed loop experimental data by an lft perturbed model set this paper investigates the consistency between frequency domain closed loop experimental data and a model set with linear fractional unstructured uncertainties when the number of unstable poles of the transfer function matrices tfm in the model set are identical a necessary and sufficient condition is derived for the reproduction of experimental data this condition is expressed as the non positiveness of a quadratic form of the external disturbances and measurement errors together with a linear constraint in this derivation it is not required that all the tfms in the model set are internally stabilizable by the controller the condition is also not necessary for the closed loop system consisting of the nominal model and the controller to be internally stable it is believed that this condition is theoretically and computationally attractive in model set validation no matter whether a deterministic or stochastic framework is adopted

closed loop model set validation under a stochastic framework this paper deals with probabilistic model set validation it is assumed that the dynamics of a multi input multi output mimo plant is described by a model set with unstructured uncertainties and identification experiments are performed in closed loop a necessary and sufficient condition has been derived for the consistency of the model set with both the stabilizing controller and closed loop frequency domain experimental data fded in this condition only the euclidean norm of a complex vector is involved and this complex vector depends linearly on both the disturbances and the measurement errors based on this condition an analytic formula has been derived for the sample unfalsified probability sup of the model set some of the asymptotic statistical properties of the sup have also been briefly discussed a numerical example is included to illustrate the efficiency of the suggested method in model set quality evaluation

nonnegative matrix factorization and i divergence alternating minimization abstract in this paper we consider the nonnegative matrix factorization nmf problem given an elementwise nonnegative matrix v r m n find for assigned k nonnegative matrices w r m k and h r k n such that v wh exact nontrivial nonnegative factorizations do not always exist hence it is interesting to pose the approximate nmf problem the criterion which is commonly employed is i divergence between nonnegative matrices the problem becomes that of finding for assigned k the factorization wh closest to v in i divergence an iterative algorithm em like for the construction of the best pair w h has been proposed in the literature in this paper we interpret the algorithm as an alternating minimization procedure a la csiszar tusnady and investigate some of its stability properties nmf is widespreading as a data analysis method in applications for which the positivity constraint is relevant there are other data analysis methods which impose some form of nonnegativity we discuss here the connections between nmf and archetypal analysis

third order cumulants based methods for continuous time errors in variables model identification in this paper the problem of identifying stochastic linear continuous time systems from noisy input output data is addressed the input of the system is assumed to have a skewed probability density function whereas the noises contaminating the data are assumed to be symmetrically distributed the third order cumulants of the input output data are then asymptotically insensitive to the noises that can be coloured and or mutually correlated using this noise cancellation property two computationally simple estimators are proposed the usefulness of the proposed algorithms is assessed through a numerical simulation

quadric inclusion programs an lmi approach to mathcal h_ infty model identification practical application of mathcal h infty robust control relies on the system identification of a valid model set described by a linear system in feedback with a stable norm bounded uncertainty this model set should explain all possible or at least all previously measured behavior for the controlled plant such models can be viewed as norm bounded inclusions in the frequency domain this note introduces the quadric inclusion program that can identify inclusions from the input output data as a convex problem we prove several key properties of this algorithm and give a geometric interpretation for its behavior while we stress that the inclusion fitting is outlier sensitive by design we offer a method to mitigate the effect of measurement noise we apply this method to robustly approximate the simulated frequency domain data using orthonormal basis functions the result compares favorably with a least squares approach that satisfies the same data inclusion requirements

on some key issues in the windsurfer approach to adaptive robust control we examine a number of crucial questions that arise in the windsurfer approach to adaptive robust control considerations are limited to the case where the plant is stable and has no zeros on the imaginary axis the key conclusion is that given a strictly proper stable model of a strictly proper stable plant we can improve the performance robustness of the closed loop system through the windsurfer approach if the plant and the existing model have no unstable zeros within the designed closed loop bandwidth and if the deterioration in performance robustness caused by increasing the closed loop bandwidth results in a sufficiently high signal to noise ratio for a certain closed loop output error situations that may cause the iterative identification and control design process to terminate prematurely are identified a simulation example is used to illustrate the results discussed

global existence and regularity of solutions to a system of nonlinear maxwell equations abstract we consider the model that has been suggested by greenberg et al physica d 134 1999 362 383 for the ferroelectric behavior of materials in this model the usual linear maxwell s equations are supplemented with a constitutive relation in which the electric displacement equals a constant times the electric field plus an internal polarization variable which evolves according to an internal set of nonlinear maxwell s equations for such model we provide rigorous proofs of global existence uniqueness and regularity of solutions we also provide some preliminary results on the long time behavior of solutions the main difficulties in this study are due to the loss of compactness in the system of maxwell s equations these results generalize those of greenberg et al where only solutions with tm transverse magnetic symmetry were considered

covariance analysis in siso linear systems identification in this paper we analyze the asymptotic covariance of models of causal single input single output linear time invariant systems expressions for the asymptotic co variance of system properties es

variance error quantification for identified poles and zeros this paper deals with quantification of noise induced errors in identified discrete time models of causal linear time invariant systems where the model error is described by the asymptotic in data length variance of the estimated poles and zeros the main conclusion is that there is a fundamental difference in the accuracy of the estimates depending on whether the zeros and poles lie inside or outside the unit circle as the model order goes to infinity the asymptotic variance approaches a finite limit for estimates of zeros and poles having magnitude larger than one but for zeros and poles strictly inside the unit circle the asymptotic variance grows exponentially with the model order we analyze how the variance of poles and zeros is affected by model order model structure and input excitation we treat general black box model structures including armax and box jenkins models

probability matrices non negative rank and parameterization of mixture models abstract in this paper we parameterize non negative matrices of sum one and rank at most two using the least possible number of parameters we also show how this parameterization relates to a class of statistical models known in probability and statistics as mixture models for contingency tables in particular we show how to use this parameterization to make some optimization problems computationally easier

a bayesian approach to sparse dynamic network identification modeling and identification of high dimensional systems involving signals with many components poses severe challenges to off the shelf techniques for system identification this is particularly so when relatively small data sets as compared to the number signal components have to be used it is often the case that each component of the measured signal can be described in terms of a few other measured variables and these dependences can be encoded in a graphical way via so called dynamic bayesian networks the problem of finding the interconnection structure as well as estimating the dynamic models can be posed as a system identification problem which involves variable selection while this variable selection could be performed via standard selection techniques computational complexity may however be a critical issue being combinatorial in the number of inputs and outputs in this paper we introduce two new nonparametric techniques which borrow ideas from a recently introduced kernel estimator called stable spline as well as from sparsity inducing priors which use 1 type penalties numerical experiments regarding estimation of large scale sparse armax models show that this technique provides a definite advantage over a group lar algorithm and state of the art parametric identification techniques based on prediction error minimization

black box identification of multivariable transfer functions asymptotic properties and optimal input design abstract the problem of estimating the transfer function of a multivariable linear stochastic system is considered the transfer function is parametrized as a black box and no order is chosen a priori this means that the model order may increase to infinity as the number of observed data tends to infinity the asymptotic covariance of the transfer function estimate is calculated and is found to be independent of the noise model when the model order increases to infinity the derived expressions are also used to determine optimal unprejudiced input signals for the identification experiment

variance error quantifications that are exact for finite model order this paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order in the interests of improved accuracy this paper provides new expressions whose accuracy depends only on data length they are therefore exact for arbitrarily small true model order other authors have recognized the importance of such expressions and have derived them for the case of finite impulse response like model structures in which denominators are fixed at true values and only numerator terms are estimated this paper progresses beyond this situation to address the more general output error and box jenkins structures in which full dynamics models both numerator and denominator terms and noise models may be estimated a key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed

system identification with generalized orthonormal basis functions a least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function where the expansion is in terms of recently introduced generalized basis functions the basis functions are orthogonal in h2 and generalize the pulse laguerre and kautz bases one of their important properties is that when chosen properly they can substantially increase the speed of convergence of the series expansion this leads to accurate approximate models with only a few coefficients to be estimated explicit bounds are derived for the bias and variance errors that occur in parameter estimates as well as in the resulting transfer function estimates

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

closed loop subspace identification using the parity space it is known that many subspace algorithms give biased estimates for closed loop data due to the existence of feedback in this paper we present a new subspace identification method using the parity space employed in fault detection in the past the basic algorithm known as subspace identification method via principal component analysis simpca gives consistent estimation of the deterministic part and stochastic part of the system under closed loop column weighting for simpca is introduced which shows improved efficiency accuracy a simulation example is given to illustrate the performance of the proposed algorithm in closed loop identification and the effect of column weighting

elastic phase transitions a new model abstract in this note we consider a new model for one dimensional clastic phase transitions the model is described by two hyperbolic systems one which propagates information at speeds c and the other at speeds where c 0 the model supports slow moving under compressive shocks which connect separate phases of the material and microstructural equilibrium solutions similar to those predicted by viscosity capillarity theories for such materials our principal results are contained in section 3 and describe the long term behavior of the system section 4 presents numerical simulations for our model for a variety of initial and boundary conditions these results confirm the analysis of sections 2 and 3

frequency response estimation for ncfs of an mimo plant from closed loop time domain experimental data frequency response estimation from closed loop time domain experimental data is investigated in this paper for normalized coprime factors ncf of a multiple input multiple output mimo plant based on a linear fractional transformation lft representation for all the ncfs of plants internally stabilizable by a known controller this estimation problem is converted into the open loop nonparametric estimation of an inner transfer function matrix tfm an estimate is derived through constrained data matching it is proved that when the probing signals are periodic and the ncfs of the auxiliary plant are appropriately selected the estimate is asymptotically unbiased and with a normal complex normal distribution it has been made clear that the estimation bias and the estimation variance are always finite computationally tractable procedures are suggested for choosing the desirable auxiliary tfms

errors in variables identification in dynamic networks consistency results for an instrumental variable approach in this paper we consider the identification of a linear module that is embedded in a dynamic network using noisy measurements of the internal variables of the network this is an extension of the errors in variables eiv identification framework to the case of dynamic networks the consequence of measuring the variables with sensor noise is that some prediction error identification methods no longer result in consistent estimates the method developed in this paper is based on a combination of the instrumental variable philosophy and closed loop prediction error identification methods and leads to consistent estimates of modules in a dynamic network we consider a flexible choice of which internal variables need to be measured in order to identify the module of interest this allows for a flexible sensor placement scheme we also present a method that can be used to validate the identified model

closed loop identification of unstable systems using noncausal fir models abstractnoncausal finite impulse response fir models are used for closed loop identification of unstable multi input multi output plants these models are shown to approximate the laurent series inside the annulus between the asymptotically stable pole of the largest modulus and the unstable pole of the smallest modulus by delaying the measured output relative to the measured input the identified fir model is a noncausal approximation of the unstable plant we present examples to compare the accuracy of the identified model obtained using least squares instrumental variables methods and prediction error methods for both infinite impulse response iir and noncausal fir models under arbitrary noise that is fed back into the loop finally we reconstruct an iir model of the system from its stable and unstable parts using the eigensystem realisation algorithm

identification of systems with unknown inputs using indirect input measurements abstracta common issue with many system identification problems is that the true input to the system is unknown this paper extends a previously presented indirect modelling framework that deals with identification of systems where the input is partially or fully unknown in this framework unknown inputs are eliminated by using additional measurements that directly or indirectly contain information about the unknown inputs the resulting indirect predictor model is only dependent on known and measured signals and can be used to estimate the desired dynamics or properties since the input of the indirect model contains both known inputs and measurements that could all be correlated with the same disturbances as the output estimation of the indirect model has similar challenges as a closed loop estimation problem in fact due to the generality of the indirect modelling framework it unifies a number of already existing system identification problems that are contained as special cases for completeness

global convergence conditions in maximum likelihood estimation maximum likelihood estimation has been widely applied in system identification because of consistency its asymptotic efficiency and sufficiency however gradient based optimisation of the likelihood function might end up in local convergence in this article we derive various new non local minimum conditions in both open and closed loop system when the noise distribution is a gaussian process here we consider different model structures in particular ararmax bj and oe models

an indirect method for transfer function estimation from closed loop data abstract an indirect method is introduced that is able to estimate consistently the transfer function of a linear plant on the basis of data obtained from closed loop experiments even in the situation where the model of the noise disturbance on the data is not accurate moreover the method allows approximate identification of the open loop plant with an explicit and tunable expression for the bias distribution of the resulting model

quality evaluation for a coprime factor perturbed model set based on frequency domain data quality assessment is investigated under a probabilistic framework for a prescribed model set the results on unfalsified probability estimation are extended from additive modeling errors to normalized coprime factor perturbations an analytic formula has been derived for the sample unfalsified probability it is shown that with increasing the data length the sample unfalsified probability converges in probability to a number which is independent of experimental data numerical simulations show that the proposed sample unfalsified probability is appropriate in the evaluation of the quality of a model set

a general multirate approach for direct closed loop identification to the nyquist frequency and beyond without injecting any external persistently exciting signals a general multirate approach is proposed for direct closed loop identification first an extended least squares algorithm is designed to identify the mixed rate model after polynomial transformation next the identified mixed rate model is used to compute the fast rate model from which system dynamics to the nyquist frequency and beyond can be obtained identifiability is mathematically proven if the plant output sampling rate is non integer multiples of the controller sampling rate the effectiveness of the proposed approach is evaluated by both the simulation and experimental results in a hard disk drive

the asymptotic crlb for the spectrum of arma processes this paper addresses the issue of quantifying the frequency domain accuracy of autoregressive moving average arma spectral estimates as dictated by the cramer rao lower bound crlb classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity although they are commonly used in finite model order and finite data length settings as approximations more recent work has established quantifications that for ar models are exact for finite model order by employing new analysis methods based on rational orthonormal parameterizations together with the ideas of reproducing kernel hilbert spaces this paper develops quantifications that extend this previous work by being exact for finite model order in all of the ar ma and arma system cases these quantifications via their explicit dependence on poles and zeros of the underlying spectral factor reveal certain fundamental aspects of the accuracy achievable by spectral estimates of arma processes

an indirect prediction error method for system identification abstract a new form of prediction error method pem is developed it is applicable to the case where the model structure of interest can be imbedded in a larger model structure whose estimation is relatively easy an optimal way of reducing the larger model to the smaller model structure is presented and various interpretations of this reduction are given the proposed method will have the same asymptotic statistical properties as the standard pem but it can be implemented by a more efficient algorithm the properties of the method are illustrated by the means of some simulated examples

on a model of electromagnetic field propagation in ferroelectric media abstract the maxwell system in an anisotropic inhomogeneous medium with non linear memory effect produced by a maxwell type system for the polarization is investigated under low regularity assumptions on data and domain the particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by greenberg maccamy and coffman j m greenberg r c maccamy c v coffman on the long time behavior of ferroelectric systems phys d 134 1999 362 383 to avoid unnecessary regularity requirements the problem is approached as a system of space time operator equation in the framework of extrapolation spaces sobolev lattices a theoretical framework developed in r picard evolution equations as space time operator equations math anal appl 173 2 1993 436 458 r picard evolution equations as operator equations in lattices of hilbert spaces glasnik mat 35 2000 111 136 a solution theory for a large class of ferromagnetic materials confined to an arbitrary open set with suitably generalized boundary conditions is obtained

generalized fourier and toeplitz results for rational orthonormal bases this paper provides a generalization of certain classical fourier convergence and asymptotic toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one but rather a rational generalization which encompasses the trigonometric one as a special case these generalized fourier and toeplitz results have particular application in dynamic system estimation theory specifically the results allow a unified treatment of the accuracy of least squares system estimation using a range of model structures including those that allow the inclusion of prior knowledge of system dynamics via the specification of fixed pole or zero locations

on closed loop system identification using polyspectral analysis given noisy input output time domain data parametric models of linear systems operating in closed loop can be consistently identified from time domain noisy input output measurements using cumulant spectra without requiring parametric modeling of noise two algorithms are proposed and their asymptotic performance is analyzed

the variation of non parametric estimates in closed loop it is known that non parametric transfer function estimates in closed loop often have infinite variance we characterise the probability density function of such estimates under the assumption that the corresponding closed loop system estimate has complex normal distribution in the frequency domain the probability density function can be described as a horseshoe encircling the inverse of the controller with a global maximum on the line between the true value and the inverse of the controller the expected value of the absolute value of such estimates is finite and we propose it as a measure of variation we also derive and discuss new expressions for the variance when an exclusion zone is introduced around the singularity

on the convergence of multiplicative update algorithms for nonnegative matrix factorization nonnegative matrix factorization nmf is useful to find basis information of nonnegative data currently multiplicative updates are a simple and popular way to find the factorization however for the common nmf approach of minimizing the euclidean distance between approximate and true values no proof has shown that multiplicative updates converge to a stationary point of the nmf optimization problem stationarity is important as it is a necessary condition of a local minimum this paper discusses the difficulty of proving the convergence we propose slight modifications of existing updates and prove their convergence techniques invented in this paper may be applied to prove the convergence for other bound constrained optimization problems

asymptotic variance of closed loop subspace identification methods in this paper the asymptotic properties of a version of the innovation estimation algorithm by qin and ljung as well as of a version of the whitening filter based algorithm introduced by jansson are studied expressions for the asymptotic error as the sum of a bias term plus a variance term are given the analysis is performed under rather mild assumptions on the spectrum of the joint input output process however in order to avoid unnecessary complications the asymptotic variance formulas are computed explicitly only for finite memory systems i e of the arx type this assumption could be removed at the price of some technical complications the simulation results confirm that when the past horizon is large enough as compared to the predictor dynamics the asymptotic expressions provide a good approximation of the asymptotic variance also for armax systems

technical communique asymptotic variance expressions for closed loop identification asymptotic variance expressions are analyzed for models that are identified on the basis of closed loop data the considered methods comprise the classical direct method as well as the more recently developed indirect methods employing coprime factorized models dual youla kucera parametrizations and the two stage approach the variance expressions are compared with the open loop situation and evaluated in terms of their relevance for subsequent model based control design

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

on reduced rank nonnegative matrix factorization for symmetric nonnegative matrices abstract let v r m n be a nonnegative matrix the nonnegative matrix factorization nnmf problem consists of finding nonnegative matrix factors w r m r and h r r n such that v wh lee and seung proposed two algorithms one of which finds nonnegative w and h such that v wh f is minimized after examining the case in which r 1 about which a complete characterization of the solution is possible we consider the case in which m n and v is symmetric we focus on questions concerning when the best approximate factorization results in the product wh being symmetric and on cases in which the best approximation cannot be a symmetric matrix finally we show that the class of positive semidefinite symmetric nonnegative matrices v generated via a soules basis admit for every 1 r rank v a nonnegative factorization wh which coincides with the best approximation in the frobenius norm to v in r n n of rank not exceeding r an example of applications in which nnmf factorizations for nonnegative symmetric matrices v arise is video and other media summarization technology where v is obtained from a distance matrix

identification of unstable systems using output error and box jenkins model structures it is well known that the output error and box jenkins model structures cannot be used for prediction error identification of unstable systems the reason for this is that the predictors in this case generically will be unstable typically this problem is handled by projecting the parameter vector onto the region of stability which gives erroneous results when the underlying system is unstable the main contribution of this work is that we derive modified but asymptotically equivalent versions of these model structures that can also be applied in the case of unstable systems

a projection method for closed loop identification a new method for closed loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed just as the direct method this new method is applicable to systems with arbitrary feedback mechanisms this is in contrast to other methods such as the indirect method and the two stage method that assume linear feedback the finite sample behavior of the proposed method is illustrated in a simulation study

brief subspace identification of closed loop systems by the orthogonal decomposition method in this paper we consider a problem of identifying the deterministic part of a closed loop system by applying the stochastic realization technique of signal process 52 2 1996 145 in the framework of the joint input output approach using a preliminary orthogonal decomposition the problem is reduced to that of identifying the plant and controller based on the deterministic component of the joint input output process we discuss the role of input signals in closed loop identification and the realization method based on a finite data and then sketch a subspace method for identifying state space models of the plant and controller since the obtained models are of higher order a model reduction procedure should be applied for deriving lower order models some numerical results are included to show the applicability of the present technique

on the frequency domain accuracy of closed loop estimates it has been argued that the frequency domain accuracy of high model order estimates obtained on the basis of closed loop data is largely invariant to whether direct or indirect approaches are used the analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order and hence are approximations when either of these are finite however recent work has provided variance expressions that are exact for finite possibly low model order and hence can potentially deliver more accurate quantification of estimation accuracy this paper and a companion one revisits the study of identification from closed loop data in light of these new quantifications and establishes that under certain assumptions there can be significant differences in the accuracy of frequency response estimates these discrepencies are established here and in the companion paper to be dependent on what type of direct indirect or joint input output identification strategy is pursued

on the long time behavior of ferroelectric systems abstract this paper presents a new model for the ferroelectric behavior of materials the usual maxwell s equations are supplemented with a constitutive relation in which the electric displacement equals a constant times the electric field plus an internal polarization variable the latter evolves according to an internal set of maxwell equations this model is suggested by one presented by one of the authors for elastic behavior with phase change the model admits hysteretic behavior the asymptotic behavior with respect to time is studied and it is shown that the system tends to a steady state in which the polarization is governed by a nonlinear elliptic equation it is shown that this equation has multiple solutions which correspond to microstructure

structured nonnegative matrix factorization with applications to hidden markov realization and clustering abstract in this paper we study the structured nonnegative matrix factorization problem given a square nonnegative matrix p decompose it as p vav with v and a nonnegative matrices and with the dimension of a as small as possible we propose an iterative approach that minimizes the kullback leibler divergence between p and vav subject to the nonnegativity constraints on a and v with the dimension of a given the approximate structured decomposition p vav is closely related to the approximate symmetric decomposition p vv it is shown that the approach for finding an approximate structured decomposition can be adapted to solve the symmetric decomposition problem approximately finally we apply the nonnegative decomposition vav to the hidden markov realization problem and to the clustering of data vectors based on their distance matrix

estimation of transfer functions asymptotic theory and a bound of model uncertainty abstract the problem of transfer function estimation is considered we will discuss the problem in two related aspects firstly how to obtain a good black box transfer function model secondly how to derive a suitable description of the model uncertainty modelling errors we will emphasize the second point we shall discuss the asymptotic theory on the properties of transfer function estimates developed recently by ljung and yuan this new theory shows that the transfer function estimate is consistent the error of the estimate is asymptotically normal with a very simple expression for its variance their results will be extended here to cases where spectral analysis is used based on this theory we will propose the method for obtaining a low order nominal model of linear processes and define and estimate an upper bound of the model uncertainty an upper bound of the model uncertainty is a suitable description of the modelling errors for the robust controller design

parametric identification using weighted null space fitting in identification of dynamical systems the prediction error method with a quadratic cost function provides asymptotically efficient estimates under gaussian noise but in general it requires solving a nonconvex optimization problem which may imply convergence to nonglobal minima an alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest weighted null space fitting wnsf belongs to this class starting with the estimate of a nonparametric arx model with least squares then the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem which can be obtained with weighted least squares the method is suitable for both open and closed loop data and can be applied to many common parametric model structures including output error armax and box jenkins the price to pay is the increase of dimensionality in the nonparametric model which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold in this paper we conduct a rigorous analysis of these properties namely consistency and asymptotic efficiency also we perform a simulation study illustrating the performance of wnsf and identify scenarios where it can be particularly advantageous compared with state of the art methods

learning non linear functions with factor graphs we show how to use a discrete variable factor graph for learning non linear continuous functions from examples the paper proposes a scheme for embedding soft quantization in a probabilistic bayesian graph the quantized input variables are grouped into a compound variable that is mapped through a stochastic matrix into the discrete output distribution specific output values are then obtained through a process of de quantization the information flow carried by message propagation is bi directional and an algorithm for learning the factor graph parameters is explicitly derived the model that can easily merge discrete and continuous variables is demonstrated with examples and simulations

the fundamental role of general orthonormal bases in system identification the purpose of this paper is threefold firstly it is to establish that contrary to what might be expected the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure secondly it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros this is achieved by employing certain new results on generalized fourier series and the asymptotic properties of toeplitz like matrices in such a way that the new variance expressions presented here encompass pre existing ones as special cases via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification namely that orthonormal bases are much more than an implementational option offering improved numerical properties in fact they are an intrinsic part of estimation since as shown here orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them

brief paper an approach to closed loop subspace identification by orthogonal decomposition a method of identifying closed loop systems is developed by using the orthogonal decomposition ort method the idea is to project the input and output data onto the space of exogenous inputs by using the lq decomposition to obtain their deterministic components the ort based method is then applied to deterministic components like the direct approach in order to derive state space models of the plant we also show that the present method is a subspace version of the two stage method for transfer function estimation from closed loop data some simulation results are included to show the applicability of the present method

simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm this paper addresses the challenging problem of designing an adaptive feedback strategy for simultaneous identification and stabilization for a class of nonlinearly parameterized uncertain systems in discrete time the nonlinear least squares nls algorithm is applied to estimate the unknown parameters and it turns out to be the standard least squares ls algorithm whenever the model is linearly parameterized based on this algorithm both the strong consistency of the estimator and the global stability of the system are achieved with the output feedback design for the scalar parameter case

closed loop identification revisited identification of systems operating in closed loop has long been of prime interest in industrial applications the problem offers many possibilities and also some fallacies and a wide variety of approaches have been suggested many quite recently the purpose of the current contribution is to place most of these approaches in a coherent framework thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates the common framework is created by the basic prediction error method and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models the so called indirect methods e g are indeed direct methods employing noise models that contain the regulator the asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations we also study a new projection approach to closed loop identification with the advantage of allowing approximation of the open loop dynamics in a given and user chosen frequency domain norm even in the case of an unknown nonlinear regulator

a unifying construction of orthonormal bases for system identification this paper develops a general and very simple construction for complete orthonormal bases for system identification this construction provides a unifying formulation of many previously studied orthonormal bases since the common fir and recently popular laguerre and two parameter kautz model structures are restrictive special cases of the construction presented here however in contrast to these special cases the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided

non negative matrix factorization with fixed row and column sums in this short note we focus on the use of the generalized kullback leibler kl divergence in the problem of non negative matrix factorization nm f we will show that when using the generalized kl divergence as cost function for nivif the row sums and the column sums of the original matrix are preserved in the approximation we will use this special characteristic in several approximation problems c 2007 elsevier inc all rights reserved

asymptotic variance expressions for estimated frequency functions expressions for the variance of an estimated frequency function are necessary for many issues in model validation and experiment design a general result is that a simple expression for this variance can be obtained asymptotically as the model order tends to infinity this expression shows that the variance is inversely proportional to the signal to noise ratio frequency by frequency still for low order models the actual variance may be quite different we derive an exact expression for the variance which is not asymptotic in the model order this expression applies to a restricted class of models ar models as well as fixed pole models with a polynomial noise model it brings out the character of the simple approximation and the convergence rate to the limit as the model order increases it also provides nonasymptotic lower bounds for the general case the calculations are illustrated by numerical examples

global weak solutions of the fractional landau lifshitz maxwell equation abstract the fractional landau lifshitz maxwell equation is considered in this paper we show the global existence of suitable weak solutions by galerkin method and the vanishing viscosity method the main difficulties in this study are due to the loss of compactness of this system and the fact that the nonlinear term is nonlocal and of the same order of the equation to overcome these difficulties we introduce the commutator estimates and some cancellation properties to this equation which prove to be proper tools in the study of landau lifshitz type equations

a bias correction method for closed loop identification of linear parameter varying systems abstract due to safety constraints and unstable open loop dynamics system identification of many real world processes often requiresgathering data from closed loop experiments in this paper we present a bias correction scheme for closed loop identification of linear parameter varying input output lpv io models which aims at correcting the bias caused by the correlation between the input signal exciting the process and output noise the proposed identification algorithm provides a consistent estimate of the open loop model parameters when both the output signal and the scheduling variable are corrupted by measurement noise the effectiveness of the proposed methodology is tested in two simulation case studies

on the consistency between an lft described model set and frequency domain data the main objective of this technical note is to derive a simple necessary and sufficient condition for a linear fractional transformation lft perturbed model set being consistent with frequency domain plant input output data only discrete time models and unstructured modeling errors are dealt with compared with the available results in which the eigenvalues of a matrix are involved this condition is related only to the euclidean norms of two vectors moreover these vectors linearly depend on measurement errors some of its applications to model set validation have been briefly discussed based on this condition an almost analytic solution has been established for model set validation under a deterministic framework when the measurement errors are energy bounded numerical simulations show that this consistency condition can lead to a significant computation cost reduction

asymptotic variance expressions for identified black box transfer function models identification of black box transfer function models is considered it is assumed that the transfer function models possess a certain shift property which is satisfied for example by all polynomial type models expressions for the variances of the transfer function estimates are derived that are asymptotic both in the number of observed data and in the model orders the result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance respectively is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise the factor of proportionality is the ratio of model order to number of data this result is independent of the particular model structure used the result is applied to evaluate the performance degradation due to variance for a number of typical model uses some consequences for input design are also drawn

bounded error identification for closed loop systems this paper presents a scheme for the identification of a system which operates in closed loop and in the presence of bounded output disturbances two algorithms are proposed to solve this identification problem the first algorithm is an optimal bounding ellipsoid obe type algorithm this first algorithm is analyzed and sufficient conditions for stability and convergence are established relaxation of these conditions leads to a second identification algorithm the implementation of that second algorithm is realized in an iterative scheme a numerical example is provided to show the efficiency of the scheme

a unified framework for bias compensation based methods in correlated noise case this technical note presents a unified framework for bias compensation principle bcp based methods applied for identification of linear systems subject to correlated noise by introducing a non singular matrix and an auxiliary vector uncorrelated with the noise the unified framework is established since there are rich possibilities of the choices of the introduced matrix and vector the proposed unified framework is very flexible it can be verified that the existing bcp based methods are special cases of the achieved result it also shows that the unified framework can be used for deriving new or simplified versions of the bcp type methods

fundamental limitations on the variance of estimated parametric models in this technical note fundamental integral limitations are derived on the variance of estimated parametric models for both open and closed loop identification as an application of these results we show that for multisine inputs a well known asymptotic in model order variance expression provides upper bounds on the actual variance of the estimated models for finite model orders the fundamental limitations established here give rise to a dasiawater bedpsila effect which is illustrated in an example