from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

a bias correction method for identification of linear dynamic errors in variables models this paper considers the problem of identifying linear systems where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances an efficient method is developed which can perform unbiased parameter estimation without utilizing a prefilter the developed method is characterized by attractive features direct use of the observed data without prefiltering no need to evaluate autocorrelation functions for the input noise no need to identify a high order augmented system and provision of a direct unbiased estimate of the system parameters without parameter extraction computer simulations are presented to illustrate its superior performance including its significantly reduced computational complexity

identification of multivariable errors in variable models with dynamics this note considers the task of identifying a causal linear dynamic multivariable system excited by stationary zero mean noise of unknown spectrum and given measurements of the system inputs and outputs contaminated by independent additive noise also of unknown spectra although the solution is in general not unique finite dimensional parameterizations of the solution set are given even though the various spectra may not be rational

errors in variables identification using maximum likelihood estimation in the frequency domain this paper deals with the identification of errors in variables eiv models corrupted by additive and uncorrelated white gaussian noises when the noise free input is an arbitrary signal not required to be periodic in particular a frequency domain maximum likelihood ml estimator is proposed and analyzed in some detail as some other eiv estimators this method assumes that the ratio of the noise variances is known the estimation problem is formulated in the frequency domain it is shown that the parameter estimates are consistent an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived the possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed analyzed and illustrated

covariance matching for continuous time errors in variables problems a covariance matching approach for continuous time errors in variables problems is considered the noise free input signal is not explicitly modeled and is only assumed to be a stationary process it is described how three different systems of equations in the model parameters are obtained and how the parameters are estimated based on these systems of equations the approach is illustrated by some numerical studies

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

brief paper frequency domain maximum likelihood estimation of linear dynamic errors in variables models this paper studies the linear dynamic errors in variables problem for filtered white noise excitations first a frequency domain gaussian maximum likelihood ml estimator is constructed that can handle discrete time as well as continuous time models on a part s of the unit circle or imaginary axis next the ml estimates are calculated via a computationally simple and numerically stable gauss newton minimization scheme finally the cramer rao lower bound is derived

time analyticity and backward uniqueness of weak solutions of the navier stokes equations of multidimensional compressible flow abstract we prove that solutions of the navier stokes equations of three dimensional compressible flow restricted to fluid particle trajectories can be extended as analytic functions of complex time as consequences we derive backward uniqueness of solutions as well as sharp rates of smoothing for higher order lagrangean time derivatives the solutions under consideration are in a reasonably broad regularity class corresponding to small energy initial data with a small degree of regularity the latter being required for conversion to the lagrangean coordinate system in which the analysis is carried out

brief paper on the identifiability of errors in variables models with white measurement errors we discuss identifiability of dynamic siso errors in variables eiv models with white measurement errors although this class of models turns out to be generically identifiable it has been pointed out that in certain circumstances there may be two eiv models which are indistinguishable from external input output experiments this lack of global identifiability may be prejudicial to identification and needs better understanding the identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the rational transfer function of the ideal true system and the spectral density of the noiseless true input unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter we provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals namely their joint power spectral densities

comment on identification in the linear errors in variables model on considere un modele etudie par kapteyn et wansbeek 1983 et on presente des conditions necessaires et suffisantes d identification

on the accuracy of a covariance matching method for continuous time errors in variables identification on the accuracy of a covariance matching method for continuous time errors in variables identification

identification of the dynamic shock error model with autocorrelated errors abstract the paper gives necessary and sufficient conditions for the local identifiability of dynamic regression models with autocorrelated errors in the variables the conditions are simple counting rules combining the order parameters of a model and directly generalize the results of maravall and aigner a new method of identification is presented allowing a compact derivation of the results

hierarchical estimation algorithms for multivariable systems using measurement information abstract with the development of industry information technology many modelling methods have been focusing on the estimation problems of multivariable systems especially for the multivariable systems with output error autoregressive noises from input output measurement information since such a system includes both a parameter vector and a parameter matrix the conventional methods cannot be applied to parameter estimation and modelling in order to solve this difficulty a hierarchical least squares based iterative identification algorithm and a hierarchical generalized least squares identification algorithm are proposed the basic idea is to decompose the system into two fictitious subsystems to estimate the parameters of each subsystem and to coordinate the associated items between the two subsystems the simulation results indicate that the proposed algorithm is effective

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

dynamic errors in variables systems with three variables abstract errors in variables problems are considered for the case of three variables where the underlying relations among the noise free variables are linear and covariance information for the noisy variables is available the static problem where the variables are complex which can arise when narrowband filtering is used is analysed in detail some results are also presented for the case when the linear relations among the variables are defined by dynamic transfer functions

stochastic system identification with noisy input output measurements using polyspectra two new classes of parametric frequency domain approaches are proposed for estimation of the parameters of scalar linear errors in variables models i e linear systems where measurements of both input and output of the system are noise contaminated the first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross bispectrum or the integrated cross polyspectrum the system transfer function is first estimated at a number of frequencies exceeding one half the number of unknown parameters the estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations in the second class of approaches quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used the proposed parameter estimators are shown to be consistent in gaussian measurement noise when trispectral approaches are used

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

blind maximum likelihood identification of wiener systems this paper is about the identification of discrete time wiener systems from output measurements only blind identification assuming that the unobserved input is white gaussian noise that the static nonlinearity is invertible and that the output is observed without errors a gaussian maximum likelihood estimator is constructed its asymptotic properties are analyzed and the cramer rao lower bound is calculated a two step procedure for generating high quality initial estimates is presented as well the paper includes the illustration of the method on a simulation example

identification of dynamic errors in variables models this paper deals with the identifiability of scalar dynamic errors in variables models characterized by rational spectra the hypothesis of causality for the underlying dynamic system is taken into account by making use of stochastic realization theory and of the structural properties of state space representations it is shown that under mild assumptions the model is uniquely identified

estimation of quantized linear errors in variables models we present an estimation algorithm for dynamic shock error models dsem given 1 bit quantized noisy measurements of the input and output the algorithm is called the binary series estimation algorithm bsea bsea is computationally inexpensive since it involves counting the number of occurrences of particular patterns of zeros and ones in the input and output sequences it yields consistent parameter estimates that are asymptotically normal

semi global stabilizability of linear null controllable systems with input nonlinearities an h sub spl infin based lyapunov proof is provided for a result established by lin and saberi 1993 if a linear system is asymptotically null controllable with bounded controls then when subject to input saturation it is semi globally stabilizable by linear state feedback a new result is that if the system is also detectable then it is semi global stabilizable by completely linear output feedback further an extension which relaxes the requirements on the input characteristic is obtained

identifiability in multivariate dynamic linear errors in variables models abstract this article considers multivariate causal transfer function systems with latent stationary inputs and outputs their observation is assumed to be disturbed by errors in variables ev the main identification results for such models so far consist of structure theory derived are descriptions of classes of ev transfer function systems compatible with given covariance structures of the observed variables under various causality constraints the case of unique determination is treated only for one dimensional models the article derives a great variety of conditions under which a multivariate ev transfer function system is uniquely determined by the second order moments of the observed variables for this purpose it considers a general model class of nonparametric systems and subclasses of systems with some parameterized components having fixed order parameters if parametric the transfer function is a rational matrix parametric inputs or errors follow vector autoregressive moving average arma

the identification of multivariate linear dynamic errors in variables models abstract the paper establishes necessary and sufficient conditions for the local identifiability of multivariate linear time series models with measurement errors the models have a linear relation with rational transfer matrix function and variables specified by unrestricted vector arma processes of fixed orders or more general variables the identifiability conditions finally are simple counting rules combining the order parameters of a model the paper derives the results bydisplaying in detail a new identification method which is based on the factorization and the expansion into partial fractions of rational matrices

on line estimation of dynamic shock error models based on the kullback leibler information measure develops two sequential or on line estimation schemes in the time domain for dynamic shock error models which are special cases of errors in variables models the author s approach utilizes a state space representation of the model kalman filtering techniques and on line algorithms the first on line algorithm is based on the expectation maximization algorithm and uses a recursive gauss newton scheme to maximize the kullback leibler information measure the second on line algorithm the author proposes is a gradient based scheme and uses stochastic approximations to maximize the log likelihood in comparison to the off line maximum likelihood estimation scheme used in ghosh 1989 the author s on line algorithms have significantly reduced computational costs and negligible memory requirements simulations illustrate the satisfactory performance of the algorithms in estimating errors in variables systems with parameters that vary slowly with time or undergo infrequent jump changes

l 2 optimal identification of mimo errors in variables models from the v gap geometrical interpretation an l 2 optimal identification method is extended to cope with mimo errors in variables eiv model estimation based on a geometrical interpretation for the v gap metric the l 2 optimal approximate models are composed of system and noise models and characterised by a normalised right graph symbol nrgs and its complementary inner factor cif respectively this metric can be evaluated as the supreme of sine values of the maximal principal angles between nrgs frequency responses of two concerned models in order to make full use of the angular cosine formula for complex vectors to reduce computational loads a cif of the nrgs of the perturbed model is introduced and thus the system parameter optimisation can be efficiently solved by sequential quadratic programming methods with the estimated system model the associated noise model can be built by right multiplication of an inner matrix finally a simulation example demonstrates the effectiveness of the proposed identification method

global solutions of the navier stokes equations for multidimensional compressible flow with discontinuous initial data abstract we prove the global existence of weak solutions of the navier stokes equations for compressible isothermal flow in two and three space dimensions when the initial density is close to a constant in l 2 and l and the initial velocity is small in l 2 and bounded in l 2 n in two dimensions the l 2 norms must be weighted slightly a great deal of qualitative information about the solution is obtained for example we show that the velocity and vorticity are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a crucial role in the entire analysis particularly in closing the required energy estimates understanding rates of regularization near the initial layer and most important obtaining time independent pointwise bounds for the density

brief paper unifying some higher order statistic based methods for errors in variables model identification in this paper the problem of identifying linear discrete time systems from noisy input and output data is addressed several existing methods based on higher order statistics are presented it is shown that they stem from the same set of equations and can thus be united from the viewpoint of extended instrumental variable methods a numerical example is presented which confirms the theoretical results some possible extensions of the methods are then given

identification of continuous time systems using arbitrary signals abstract this paper presents a parametric frequencydomain identification algorithm for linear time invariant continuous time systems excited by arbitrary signals unlike the current available methods this approach allows accurate modeling in the complete frequency band from dc to nyquist

identification of multivariable stochastic linear systems via polyspectral analysis given noisy input output time domain data the paper considers the problem of identification of unknown parameters of multivariable linear errors invariables models attention is focused on frequency domain approaches where the integrated polyspectrum bispectrum or trispectrum of the input and the integrated cross polyspectrum respectively of the given time domain input output data are exploited two new classes of parametric frequency domain approaches are proposed and analyzed an integrated polyspectrum based persistence of excitation condition on system input is defined both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum based approaches are used the proposed parameter estimators are shown to be strongly consistent in gaussian measurement noise when integrated trispectrum based approaches are used the input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum

on time analyticity of weak solutions of the compressible navier stokes equations abstract we show that weak solutions of the compressible navier stokes equations are analytic as l 2 valued functions of time when pressure p is real analytic as a consequence there exist infinitely many effective viscous flux functions of higher orders

tracking control of nonlinear systems with bounded controls and control rates abstract the problem of tracking control of a class of nonlinear systems subject to control and control rate constraints is considered a continuous time predictive control approach is used to derive the nonlinear constrained control law asymptotically stable tracking is ensured in the absence of saturation the control and control rate constraints are guaranteed to be strictly satisfied by the control law an example is given to demonstrate the effectiveness of the method

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

the set of observationally equivalent errors in variables models abstract linear dynamic errors in variables or factor models with uncorrelated noise components are considered we give a description of the set of all noise spectra which are oberservationally equivalent with respect to the second moments of observations

a structure theory for linear dynamic errors in variables models we deal with problems connected with the identification of linear dynamic systems in situations when inputs and outputs may be contaminated by noise the case of uncorrelated noise components and the bounded noise case is considered if also the inputs may be contaminated by noise a number of additional complications in identification arise in particular the underlying system is not uniquely determined from the population second moments of the observations a description of classes of observationally equivalent systems is given continuity properties of mappings relating classes of observationally equivalent systems to the spectral densities of the observations are derived and the classes of spectral densities corresponding to a given maximum number of outputs are studied

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

principal information theoretic approaches 2000 principal information theoretic approaches journal of the american statistical association vol 95 no 452 pp 1349 1353

worst case identification of errors in variables models in closed loop a worst case identification method in frequency domain is proposed to cope with the identification of errors in variables models eivms in closed loop with a priori bound for the disturbing noises of an eivm in closed loop a frequency domain normalized coprime factor model ncfm with perturbation is derived and thus the identification of the eivm becomes that of the ncfm by employing the v gap metric as an optimization criterion the worst case error for an identified nominal ncfm is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities lmis during the parameter optimization the derivative of the nominal ncfm is constrained to some degree to reduce the effect of overfitting phenomenon different from other eivm identification methods we use v gap metric to characterize the disturbing noises and quantify the worst case error for the nominal ncfm as a result the identification result is not a deterministic model but a model set moreover this model set can be perfectly combined with the robust controller design finally a numerical simulation is presented to verify the proposed method

paper identification of scalar errors in variables models with dynamics the paper considers the task of identifying a causal linear dynamic system excited by stationary gaussian zero mean noise of unknown spectrum and given measurements of the system input and output contaminated by independent additive stationary noise signals of unknown spectra while the solution is normally not unique finite dimensional parameterizations of the solution set are given in some cases involving just one parameter even though the various spectra may not be rational

identification of invariants of over parameterized models finite sample results this paper shows that a certain class of estimates of invariants of over parameterized models are with probability one independent of the particular over parameterization chosen the result is nonasymptotic and the estimators considered minimize a cost function that is invariant with respect to the same parameter transformation as the overparameterized model

brief paper box jenkins identification revisited part iii part i of this series of three papers handles the identification of single input single output box jenkins models on arbitrary frequency grids in an open and closed loop setting part ii discusses the computational aspects and illustrates the theory on simulations and a real life problem this paper extends the results of parts i and ii to multiple input multiple output systems contrary to the classical time domain approach the presented technique does not require symbolic calculus for multiple output polynomial box jenkins models

box jenkins identification revisited part i theory in classical time domain box jenkins identification discrete time plant and noise models are estimated using sampled input output signals the frequency content of the input output samples covers uniformly the whole unit circle in a natural way even in case of prefiltering recently the classical time domain box jenkins framework has been extended to frequency domain data captured in open loop the proposed frequency domain maximum likelihood ml solution can handle i discrete time models using data that only covers a part of the unit circle and ii continuous time models part i of this series of two papers i generalizes the frequency domain ml solution to the closed loop case and ii proves the properties of the ml estimator under non standard conditions contrary to the classical time domain case it is shown that the controller should be either known or estimated the proposed ml estimators are applicable to frequency domain data as well as time domain data

the rank of reduced dispersion matrices psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements psychometricians concentrate on cases in which low rank can be attained preferably rank one the spearman case econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one the frisch case in this paper we give an extensive historial discussion of both fields we prove the two key results in a more satisfactory and uniform way we point out various small errors and misunderstandings and we present a methodological comparison of factor analysis and regression on the basis of our results

errors in variables identification of dynamic systems excited by arbitrary non white input abstract this work deals with the identification of dynamic systems from noisy input output observations where the noise free input is not parameterized the basic assumptions made are 1 the dynamic system can be modeled by a discrete or continuous time rational transfer function model 2 the temporal input output disturbances are mutually independent identically distributed noises and 3 the input power spectrum is non white not necessarily rational and is modeled nonparametrically the system identifiability is guaranteed by exploiting the non white spectrum property of the noise free input a frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input output noise variances the uncertainty bound of the estimates is calculated and compared to the cramer rao lower bound the efficiency of the proposed algorithm is illustrated on numerical examples

input saturation and global stabilization of nonlinear systems via state and output feedback for multi input multi output nonlinear systems whose free dynamics are lyapunov stable the author shows how the problem of global stabilization via dynamic output feedback can be solved by using the technique of input saturation the power of this technique is also illustrated by solving the problem of global stabilization via bounded state feedback for affine nonlinear systems with stable unforced dynamics analogous results are established for discrete time nonlinear systems

linear models based on noisy data and the frisch scheme we address the problem of identifying linear relations among variables based on noisy measurements this is a central question in the search for structure in large data sets often a key assumption is that measurement errors in each variable are independent this basic formulation has its roots in the work of charles spearman in 1904 and of ragnar frisch in the 1930s various topics such as errors in variables factor analysis and instrumental variables all refer to alternative viewpoints on this problem and on ways to account for the anticipated way that noise enters the data in the present paper we begin by describing certain fundamental contributions by the founders of the field and provide alternative modern proofs to certain key results we then go on to consider a modern viewpoint and novel numerical techniques to the problem the central theme is expressed by the frisch kalman dictum which calls for identifying a noise contribution that allows a maximal number of simultaneous linear relations a

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

global identification of the dynamic shock error model abstract the paper gives necessary and sufficient conditions for the global identifiability of dynamic regression models with errors in the variables the conditions are simple counting rules combining the order parameters of a model they are counterparts of conditions previously established for local identifiability in a series of papers