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

high order multivariable transfer function curve fitting algorithms sparse matrix methods and experimental results abstract this paper develops a computational approach to multivariable frequency domain curve fitting based on two norm minimization the algorithm is specifically tailored to the identification of complex systems having a large number of parameters and includes a sparse matrix method for reducing computation and memory requirements on large problems the algorithm is also well suited for identification of lightly damped systems such as flexible structures the overall approach is successfully demonstrated on a high order multivariable flexible structure experiment requiring the estimation of 780 parameters over a 100 hz band width

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

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

continuous location of dimensional structures abstract a natural extension of point facility location problems are those problems in which facilities are extensive i e those that cannot be represented by isolated points but as some dimensional structures such as straight lines line segments polygonal curves or circles in this paper a review of the existing work on the location of extensive facilities in continuous spaces is given gaps in the knowledge are identified and suggestions for further research are made

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

efficient algorithms for the weighted minimum circle problem the weighted minimum covering circle problem is a well known single facility location problem used in emergency facility models this paper introduces a classification scheme based on fundamental mathematical programming concepts for algorithms which solve both weighted and unweighted versions one result of this classification is proof that a recently developed method is identical to one developed in the nineteenth century also within the classification scheme efficient new algorithms are given for the weighted problem the results of some extensive computational tests identify the empirically fastest methods

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

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

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

quantification of uncertainty in transfer function estimation a mixed probabilistic worst case approach abstract in this paper an identification problem is solved which is directed towards the use of the identified model as a basis for robust control design a procedure is presented to identify on the basis of time domain measurement data a reduced order finite impulse response fir model together with an upper bound on the model error of the corresponding transfer function using only minor prior information we assume the measurement data to be contaminated with a stochastic noise disturbance with unknown spectral properties by applying a procedure similar to bartlett s procedure of periodogram averaging in conjunction with a periodic input signal the statistics of the model error asymptotically can be obtained from the data the model error consists of two parts a probabilistic part due to the stochastic noise disturbance and a worst case part due to the unmodelled dynamics the latter is explicitly bounded with a hard error bound while for the former a confidence interval can be specified asymptotically this enables an explicit trade off between undermodelling bias and variance terms the resulting error bound appears to be tight

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

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

accurate identification for control the necessity of an iterative scheme if approximate identification and model based control design are used to accomplish a high performance control system then the two procedures must be treated as a joint problem solving this joint problem by means of separate identification and control design procedures practically entails an iterative scheme a frequency response identification technique and a robust control design method are used to set up such an iterative scheme each identification step uses the previously designed controller to obtain new data from the plant the associated identification problem has been solved by means of a coprime factorization of the unknown plant the technique s utility is illustrated by an example

stability preserving maps and robust design in this paper we present the concept of a matrix stability preserving map and show its impact on the problem of robust controller design we develop a number of tests for checking whether a given matrix is a stability preserving map we show that the concept of a stability preserving map can be used to provide a different characterization of the existence of a fixed order controller that simultaneously stabilizes a finite number of plants we also demonstrate how it can be used to state conditions for the robust stabilization of families of plants with real parameter uncertainty in addition we show how stability preserving map tests lead to robust stabilization techniques and apply the methodology to a number of examples

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

continuous time control model validation using finite experimental data the application of robust control theory requires models containing unknown bounded perturbations and unknown bounded input signals model validation is a means of assessing the applicability of a given model with respect to experimental data this paper develops a theoretical framework and a computational solution for the model validation problem in the case where the model including unknown perturbations and signals is given in the continuous time domain yet the experimental datum is a finite sampled signal the continuous nature of the unknown components is treated directly with a sampled data lifting theory this gives results which are valid for any sample period and any datum length explicit calculation of whether sufficient data for invalidation has been obtained arises naturally in this framework a common class of robust control models is treated and leads to a convex matrix optimization problem a simulation example illustrates the approach

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

a globally optimal minimax solution for spectral overbounding and factorization in this paper an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified real valued nonparametric function of frequency this method has direct application to transforming nonparametric uncertainty bounds available from system identification experiments and or plant modeling into parametric representations required for modern robust control design software i e a minimum phase transfer function multiplied by a norm bounded perturbation

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

identification of dynamic models in complex networks with prediction error methods basic methods for consistent module estimates abstract the problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open loop or closed loop setting in this paper this problem is generalized to dynamical systems that operate in a complex interconnection structure and the objective is to consistently identify the dynamics of a particular module in the network for a known interconnection structure it is shown that the classical prediction error methods for closed loop identification can be generalized to provide consistent model estimates under specified experimental circumstances two classes of methods considered in this paper are the direct method and the joint io method that rely on consistent noise models and indirect methods that rely on external excitation signals like two stage and iv methods graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent module estimates

robust identification of strongly stabilizable systems for strongly stabilizable systems for which a strongly stabilizing controller is known approximately the authors consider system identification in the graph gap and chordal metrics using robust h sub infinity identification of the closed loop transfer function in the framework proposed by a j helmicki et al 1990 error bounds are derived showing that robust convergence is guaranteed and that the identification can be satisfactorily combined with a model reduction step two notions of robust identification of stable systems are compared and an alternative robust identification technique based on smoothing which can be used to yield polynomial models directly is developed

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

subspace based multivariable system identification from frequency response data two noniterative subspace based algorithms which identify linear time invariant mimo multi input multioutput systems from frequency response data are presented the algorithms are related to the recent time domain subspace identification techniques the first algorithm uses equidistantly in frequency spaced data and is strongly consistent under weak noise assumptions the second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure

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

non asymptotic model quality assessment of transfer functions at multiple frequency points in this paper we develop methods for evaluating uncertainties in the frequency response of a dynamical system based on finitely many input output data points we extend the leave out sign dominant correlation regions lscr algorithm to deliver confidence regions with a guaranteed probability for the frequency response at multiple frequencies and we introduce a computationally efficient scheme that enables the confidence regions to be constructed frequency by frequency simulation examples illustrating the usefulness of the developed algorithm are provided

preserving synchronization under matrix product modifications abstract in this article we present a methodology under which stability and synchronization of a dynamical master slave system configuration are preserved under modification through matrix multiplication the objective is to show that under a defined multiplicative group hyperbolic critical points are preserved along the stable and unstable manifolds the properties of this multiplicative group were determined through the use of simultaneous jordan decomposition it is also shown that a consequence of this approach is the preservation of the signature of the jacobian matrix associated with the dynamical system to illustrate the results we present several examples of different modified systems

using block norms for location modeling in formulating a continuous location model with facilities represented as points in rn e g typically in the plane one must characterize the distance between two points as a function of their coordinates two criteria in selecting a distance function are 1 to obtain good approximations of actual distances and 2 to obtain a mathematical model of the location problem that is easy to solve in this paper we show how a class of norms with polygonal contours called block norms can yield attractive choices as distance functions with respect to these criteria in particular we consider the following relevant properties of block norms they generalize the concepts of rectilinear or city block travel they are dense in the set of all norms they have interesting travel interpretations in the plane they can be expressed as a sum of the absolute values of linear functions they often give better approximations to actual highway distances than the most frequently used family of norms the lp norms and finally they yield linear programming formulations of certain facility location problems i e the weber problem and the rawls problem

instrumental variable methods for closed loop system identification in this paper several instrumental variable iv and instrumental variable related methods for closed loop system identification are considered and set in an extended iv framework extended iv methods require the appropriate choice of particular design variables as the number and type of instrumental signals data prefiltering and the choice of an appropriate norm of the extended iv criterion the optimal iv estimator achieves minimum variance but requires the exact knowledge of the noise model for the closed loop situation several iv methods are put in an extended iv framework and characterized by different choices of design variables their variance properties are considered and illustrated with a simulation example

estimating the circle closest to a set of points by maximum likelihood using the bhhh algorithm abstract the purpose of this paper is to exploit the idea that in linear models the least squares estimators and the maximum likelihood estimators based on the normality assumption are often identical in particular we wish to add the normality assumption to the problem of finding the best fitting circle the addition of the normality assumption will allow the use of the bhhh algorithm to estimate the model by maximum likelihood although the bhhh algorithm is not especially fast its virtue is that it only requires the first derivatives of the loglikelihood function and is therefore easier to program than the newton raphson algorithm as we will show the likelihood framework also allows for easy testing of several important hypotheses and construction of an r 2 measure from regression analysis

gbsss the generalized big square small square method for planar single facility location abstract big square small square is a geometrical branch and bound algorithm devised by p hansen et al or 33 1251 1265 for the solution of constrained planar minisum single facility location problems with l p norms and continuous non decreasing costfunctions the method basically works by splitting the studied planar region into squares and either rejecting or further processing these squares by the evaluation of a lower bound we present a modified version of this algorithm aimed at correcting a small failure to converge accelerating the calculations minimising the information to be stored and most importantly determining a region of near optimality furthermore the method is applicable to any planar single facility problem with distances measured by mixed norms and as an objective any continuous function of the distances this includes nearly all the models which have been proposed in the literature

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

bias of indirect non parametric transfer function estimates for plants in closed loop expressions for the bias of indirect non parametric estimates in closed loop are derived in terms of the experimental conditions application of the results to finite data experiments using both spectral estimates and empirical transfer function estimates are considered and illustrated with simulations

the minimax center estimation problem for automated roundness inspection abstract significant advances in computer technology sensing devices pattern recognition and image processing techniques have made the on line inspection of all production parts a feasible option in modern manufacturing systems this study is concerned with the development of efficient algorithms to determine the out of roundness error for automated inspection of circular production parts the out of roundness error is defined as the maximum deviation of a given sey of sample points taken from the boundary of the part from the so called minimax circle

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

statistical plant set estimation using schroeder phased multisinusoidal input design abstract in this paper a frequency domain method is developed for plant set estimation the estimation of a plant set rather than a point estimate is required to support many methods of modern robust control design the approach here is based on using a schroeder phased multisinusoid input design which has the special property of placing input energy only at the discrete frequency points used in the computation a detailed analysis of the statistical properties of the frequency domain estimator is given leading to exact expressions for the probability distribution of the estimation error and many important properties it is shown that for any nominal parametric plant estimate one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence the soft bound thus obtained can be used to replace hard bounds presently used in many robust control analysis and synthesis methods

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

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

a mean shift algorithm for large scale planar maximal covering location problems abstract the planar maximal covering location problem pmclp concerns the placement of a given number of facilities anywhere on a plane to maximize coverage solving pmclp requires identifying a candidate locations set cls on the plane before reducing it to the relatively simple maximal covering location problem mclp the techniques for identifying the cls have been mostly dominated by the well known circle intersect points set cips method in this paper we first review pmclp and then discuss the advantages and weaknesses of the cips approach we then present a mean shift based algorithm for treating large scale pmclps i e msmc we test the performance of msmc against the cips approach on randomly generated data sets that vary in size and distribution pattern the experimental results illustrate msmc s outstanding performance in tackling large scale pmclps

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

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

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

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 sufficient condition for simultaneous stabilization the condition under which it is possible to find a single controller that stabilizes k single input single output linear time invariant systems p sub i s i 1 k is investigated the concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable a method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example

locating objects in the plane using global optimization techniques we address the problem of locating objects in the plane such as segments arcs of circumferences arbitrary convex sets their complements or their boundaries given a set of points we seek the rotation and translation for such an object optimizing a very general performance measure which includes as a particular case the classical objectives in semi obnoxious facility location in general the above mentioned model yields a global optimization problem whose resolution is dealt with using difference of convex dc techniques such as outer approximation or branch and bound

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

relations between uncertainty structures in identification for robust control various techniques of system identification exist that provide a nominal model and an uncertainty bound an important question is what the implications are for the particular choice of the structure in which the uncertainty is described when dealing with robust stability performance analysis of a given controller and when dealing with robust synthesis it is shown that an amplitude bounded circular uncertainty set can equivalently be described in terms of an additive youla parameter and n gap uncertainty as a result the choice of structure does not matter provided that the identification methods deliver optimal uncertainty sets rather than an uncertainty bound around a prefixed nominal model frequency dependent closed loop performance functions based on the uncertainty sets are again bounded by circles in the frequency domain allowing for analytical expressions for worst case performance and for the evaluation of the consequences of uncertainty for robust design the results can be used to tune optimal experimental conditions in view of robust control design and in the further development of experiment based robust control design methods

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

algorithms for computerized inspection of rectangular and square shapes abstract vision systems are increasingly being considered and implemented as an alternative to manual inspection and manual gauging in manufacturing systems inspection for geometric shape and size is essential in automated quality monitoring the techniques used to perform this inspection need to be practical to satisfy time and equipment constraints and make the system cost effective this paper presents practical and useful techniques based on the euclidean least squares method to inspect production parts with rectangular and square shapes the techniques determine the optimal parameters of the straight lines that define the four edges of the object being inspected

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

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

a mixed integer formulation for maximal covering by inclined parallelograms abstract in this paper we introduce a zero one mixed integer formulation for a maximal covering problem where points are covered by inclined parallelograms in a plane the special case of covering rectangles with sides parallel to the axis is treated with a separate formulation finally an alternative algorithm for solving covering by inclined parallelograms is presented the formulations proposed can be easily adapted for other location and material cutting applications