model quality evaluation in h sub 2 identification model quality evaluation in set membership identification is investigated in the recent literature two main approaches have been used to investigate this problem based on the concepts of n width and of radius of information in this paper it is shown that the n width is related to the asymptotic value of the conditional radius of information of the identification problem with noise free measurements upper and lower bounds of the conditional radius of information are derived for the h sub 2 identification of exponentially stable systems using approximating n dimensional models linear in the parameters in the presence of power bounded measurement errors the derived bounds are shown to be convergent to the radius for a large number of data and model dimensions moreover a formula for computing the worst case identification error for any linear algorithm is given in particular it is shown that the identification error of the least square algorithm may be increasing with respect to the model dimension peaking effect an almost optimal linear algorithm is presented that is not affected by this peaking effect and indeed is asymptotically optimal

non parametric nonlinear system identification a data driven orthogonal basis function approach in this paper a data driven orthogonal basis function approach is proposed for non parametric fir nonlinear system identification the basis functions are not fixed a priori and match the structure of the unknown system automatically this eliminates the problem of blindly choosing the basis functions without a priori structural information further based on the proposed basis functions approaches are proposed for model order determination and regressor selection along with their theoretical justifications

well posedness of h optimal control problems this paper considers the effect of perturbations of a nominal single input single output linear plant or a band of uncertainty on the solution to certain frequency domain optimal control problems weighted h infty sensitivity minimization mixed and robust sensitivity minimization will be considered along with problems of more general type a brief discussion of h p optimal control problems will also be given typical examples will be presented where optimal sensitivity does not depend continuously on the plant ill posedness and conditions for well posedness will be given it is demonstrated that similar discontinuities can occur for more general problems also suggested are ways of defining an optimization problem so that continuous dependence of the infimum is ensured

on slowly time varying systems abstract a characterization of stabilizing controllers for slowly time varying systems based on input output descriptions of the plant and the controller is presented this approach generalizes standard results on slowly time varying systems with finite dimensional state space representation and allows both the plant and the controller to be infinite dimensional the controller design will be based on frozen time versions of the plant obtained at equally spaced instances in time

identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors a procedure is developed for identification of probabilistic system uncertainty regions for a linear time invariant system with unknown dynamics on the basis of time sequences of input and output data the classical framework is handled in which the system output is contaminated by a realization of a stationary stochastic process given minor and verifiable prior information on the system and the noise process frequency response pulse response and step response confidence regions are constructed by explicitly evaluating the bias and variance errors of a linear regression estimate in the model parametrizations use is made of general forms of basis functions conservatism of the uncertainty regions is limited by focusing on direct computational solutions rather than on closed form expressions using an instrumental variable method for identification the procedure is suitable also for input output data obtained from closed loop experiments

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

a generalized orthonormal basis for linear dynamical systems in many areas of signal system and control theory orthogonal functions play an important role in issues of analysis and design in this paper it is shown that there exist orthogonal functions that in a natural way are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l sub 2sup n to this end use is made of balanced realizations of inner transfer functions the orthogonal functions can be considered as generalizations of for example the pulse functions laguerre functions and kautz functions and give rise to an alternative series expansion of rational transfer functions it is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion i e to obtain a good approximation by retaining only a finite number of expansion coefficients consequences for identification of expansion coefficients are analyzed and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

lipschitz continuity of inner outer factorization abstract conditions are provided under which inner and outer factor of h functions on the unit disk can be found which depend lipschitz continuously on data

extended ho kalman algorithm for systems represented in generalized orthonormal bases this paper considers the construction of minimal state space models of linear time invariant systems on the basis of system representations in terms of generalized orthogonal basis function expansions starting from the classical ho kalman algorithm that solves the problem using markov parameter expansions a generalization is obtained by analysing the matrix representations of the hankel operators in generalized orthonormal bases using the so called hambo domain techniques an efficient algorithm is given to implement the proposed method

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

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

rational basis functions for robust identification from frequency and time domain measurements this paper investigates the use of general bases with fixed poles for the purposes of robust estimation these bases which generalise the common fir laguerre and two parameter kautz ones are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied it is also shown that by using a min max criterion these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified the key idea facilitating this analysis is to re parameterise the chosen model structures into a new one with equivalent fixed poles but for which the basis functions are orthonormal in h 2 d

on line identification of time varying systems by nonparametric techniques a nonparametric algorithm based on orthogonal series is proposed for real time identification of nonstationary systems it is proved that the algorithm converges in the mean square sense the convergence conditions are closely related to those in dupac 2

h identification of soft uncertainty models abstract the paper investigates the problem of identifying uncertainty models of causal siso lti discrete time bibo stable unknown systems using frequency domain measurements corrupted by gaussian noise of known covariance additive uncertainty models are looked for consisting of a nominal model and an additive dynamic perturbation accounting for the modeling error the nominal model is chosen within a class of affinely parametrized models with transfer function of given possibly low order an estimate of the parameters minimizing the h modeling error is obtained by minimizing an upper bound of the worst case with respect to the modeling error second moment of the estimation error then a bound in the frequency domain guaranteeing to include with probability the frequency response error between the estimated nominal model and the unknown system is derived

frequency domain analysis of tracking and noise performance of adaptive algorithms in this paper an analysis of the tracking and noise performance of several adaptive algorithms is carried out for the case of model structures with fixed pole positions such structures have previously been proposed as an efficient generalization of the common fir model structure the focus of this work is to analyze the associated tradeoff between noise sensitivity and tracking ability in the frequency domain by illustrating how it is influenced by such things as input and noise spectral densities step size and in particular the choice of the fixed pole locations the latter influence is not described by preexisting analysis but is shown here to be amenable to attack by a particular class of orthonormal bases

optimal rejection of persistent and bounded disturbances continuity properties and adaptation continuity properties of the problem of optimal rejection of bounded persistent disturbances otherwise known as l sup 1 optimal control are furnished for discrete time single input single output systems it is shown that for any plant with no zeros on the unit circle the l sup 1 optimal design is continuous as a map from the plant to the optimal closed loop solution if the plant has a unique optimal solution in the case of nonuniqueness a superoptimal criterion is proposed that will always lead to a unique solution however it still fails to supply continuity a characterization of a general class of adaptive controllers in the presence of bounded disturbances is given using this characterization an adaptive robust scheme based on the l sup 1 design methodology is proposed and it is shown to be globally convergent

control of slowly varying linear systems state feedback control of slowly varying linear continuous time and discrete time systems with bounded coefficient matrices is studied in terms of the frozen time approach this study centers on pointwise stabilizable systems these are systems for which there exists a state feedback gain matrix placing the frozen time closed loop eigenvalues to the left of a line re s gamma

lipschitz continuity of h interpolation abstract optimal h interpolants may be infinitely sensitive to data however suboptimal interpolants of the aak central maximal entropy type are shown to satisfy a lipschitz condition with respect to data

brief paper on the asymptotic eigenvalue distribution of block toeplitz matrices related to the generalized orthonormal basis functions model in this paper we study the asymptotic distribution of the eigenvalues of a family of hermitian block toeplitz matrices generated by the internal signals of the so called generalized orthonormal basis functions models our results are a generalization of a well known theorem of szego which addresses only the case of hermitian toeplitz matrices

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

an optimal expansion of volterra models using independent kautz bases for each kernel dimension a new solution for the problem of selecting poles of the two parameter kautz functions in volterra models is proposed in general a large number of parameters are required to represent the volterra kernels although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions such as the kautz basis this representation has a wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non linear static mapping represented by the volterra series the resulting wiener volterra model can be truncated into fewer terms if the kautz functions are properly designed the underlying problem is how to select the arbitrary complex poles that fully parametrize these functions this problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion the present paper goes even further in that each multidimensional kernel is decomposed into a set of independent kautz bases each of which is parametrized by an individual pair of conjugate kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension an analytical solution for one of the kautz parameters valid for volterra models of any order is derived a simulated example is presented to illustrate these theoretical results the same approach is then used to model a real non linear magnetic levitation system with oscillatory behaviour

an ensemble approach to image matching using contextual features we propose a contextual framework for 2d image matching and registration using an ensemble feature our system is beneficial for registering image pairs that have captured the same scene but have large visual discrepancies between them it is common to encounter challenging visual variations in image sets with artistic rendering differences or in those collected over a period of time during which the lighting conditions and scene content may have changed differences between images may also be caused using a variety of cameras with different sensors focal lengths and exposure values local feature matching techniques cannot always handle these difficulties so we have developed an approach that builds on traditional methods to consider linear and histogram of gradient information over a larger more stable region we also present a technique for using linear features to estimate corner keypoints or pseudo corners that can be used for matching our pipeline follows this unique matching stage with homography refinement methods using edge and gradient information our goal is to increase the size of accurate keypoint match sets and align photographs containing a combination of man made and natural imagery we show that incorporating contextual information can provide complimentary information for scale invariant feature transform and boost local keypoint matching performance as well as be used to describe corner feature points

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

model quality evaluation in set membership identification abstract identification from corrupted input output measurements of systems that do not necessarily belong to the model class used is investigated this leads to a nonstandard set membership sm identification problem the goodness of different model classes is measured by the conditional radius of information a generalization of the radius in standard sm identification theory giving a measure of the minimal worst case modeling error upper and lower bounds on the radius are derived for linearly parameterized model classes specific formulas for the upper and lower bounds are given for the case of h 2 identification of exponentially stable systems in the presence of powerbounded noise the bounds are shown to coincide with the conditional radius when the model space dimension is equal to the number of output measurements an almost optimal identification algorithm is derived giving identification error within the range of the derived bounds

non asymptotic confidence regions for model parameters in the presence of unmodelled dynamics this paper deals with the problem of constructing confidence regions for the parameters of truncated series expansion models the models are represented using orthonormal basis functions and we extend the leave out sign dominant correlation regions lscr algorithm such that non asymptotic confidence regions for the parameters can be constructed in the presence of unmodelled dynamics the constructed regions have guaranteed probability of containing the true parameters for any finite number of data points the algorithm is first developed for fir models and then extended to models with generalized orthonormal basis functions the usefulness of the developed approach is demonstrated for fir and laguerre models in simulation examples

on worst case approximation of feasible system sets via orthonormal basis functions this note deals with the approximation of sets of linear time invariant systems via orthonormal basis functions this problem is relevant to conditional set membership identification where a set of feasible systems is available from observed data and a reduced complexity model must be estimated the basis of the model class is made of impulse responses of linear filters the objective of the note is to select the basis function poles according to a worst case optimality criterion suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

wiener system identification with generalized orthonormal basis functions many nonlinear systems can be described by a wiener schetzen model in this model the linear dynamics are formulated in terms of orthonormal basis functions obfs the nonlinearity is modeled by a multivariate polynomial in general an infinite number of obfs are needed for an exact representation of the system this paper considers the approximation of a wiener system with finite order infinite impulse response dynamics and a polynomial nonlinearity we propose to use a limited number of generalized obfs gobfs the pole locations needed to construct the gobfs are estimated via the best linear approximation of the system the coefficients of the multivariate polynomial are determined with a linear regression this paper provides a convergence analysis for the proposed identification scheme it is shown that the estimated output converges in probability to the exact output fast convergence rates in the order o p n f n r e p 2 can be achieved with n f the number of excited frequencies and n r e p the number of repetitions of the gobfs

an optimum time scale for discrete laguerre network any discrete time stable transfer function can be expressed by a discrete time laguerre series with a chosen time scale an optimum time scale such that an index is minimized is derived this index ensures that the coefficients of higher order laguerre functions go toward zero quickly the solution derived requires the knowledge of the impulse response of the discrete plant cases of first order plants second order underdamped plants and plants with multiunit delay are also discussed

state space representation for arbitrary orthogonal rational functions abstract we first give a brief summary of the arguments that lead to the conclusion that the use of orthogonal rational functions in system identification should not be restricted to the takenaka malmquist basis because there are important cases where orthogonality with respect to a certain nonnegative weight function is required the main result however is a generalization of known state space descriptions for the takenaka malmquist basis to the more general case this is important for control problems

identification of rational approximate models in h sup spl infin using generalized orthonormal basis robust identification with fir models fails to be successful when the number of coefficients to be estimated becomes large caused by lightly damped modes of the plant or poles very close to the unit circle the paper presents a two stage algorithm to obtain a low order approximate model in frequency domain in a generalized orthonormal basis with guaranteed h sup spl infin error bound for deterministic linear time invariant stable systems the first stage being an l sup spl infin rational approximation and the second nonlinear step being an h sup spl infin rational approximation

h sub spl infin identification and model quality evaluation set membership h sub spl infin identification is investigated using time domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors the problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error called radius of information is solved for classes of models affine in the parameters the radius of information is obtained as function of the h sub spl infin norm of the unmodeled dynamics a method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics thus allowing the actual evaluation of the radius of information the radius represents a measure of the predictive ability of the considered class of models and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part the effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given

orthogonal rational functions a transformation analysis finite impulse response fir models are among the most basic tools in control theory and signal processing and are routinely used in almost all fields of application the connections to orthogonal polynomials are well known however infinite impulse response iir models often provide much more compact descriptions and in many cases give improved performance the objective of this paper is to present a simple framework for the derivation and analysis of orthogonal iir transfer functions which are directly related to orthogonal rational functions orthogonality simplifies approximation analysis and leads to improved numerical properties the basic idea is to use a fractional transformation to map the problem to a new domain where an fir description is most appropriate this fir representation is then mapped back to the original domain to give an orthogonal iir representation it is then straightforward to extend many results for fir models to iir model structures with arbitrary stable poles i e prop

asymptotic properties of black box identification of transfer functions the problem of estimating the transfer function of a linear stochastic system is considered the transfer function is parametrized as a black box and no given order is chosen a priori this means that the model orders may increase to infinity when the number of observed data tends to infinity the consistency and convergence properties of the resulting transfer function estimates are investigated asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase it is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise to signal ratio at that frequency mulliplied by the model order to number of data points ratio