identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

cone constraints for solutions of homogeneous bilinear systems abstract sufficient conditions are derived under which all solutions of a homogeneous bilinear system remain within a cone for both the case where an initial state is prescribed and the case where the initial state lies within another prescribed cone this situation generalizes the classical uncontrolled case in which solutions of a linear system are constrained to lie in the cone consisting of the positive orthant the conditions are given in terms of an associated linear system originally utilized in realization theory and a particular representation of its inverse system in the case where the associated linear system has single input and output channels the conditions are also shown to be necessary

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

strong consistence of recursive identification for wiener systems the paper concerns identification of the wiener system consisting of a linear subsystem followed by a static nonlinearity f with no invertibility and structure assumption recursive estimates are given for coefficients of the linear subsystem and for the value f v at any fixed v the main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values this probably is the first strong consistency result for this kind of wiener systems a numerical example is given which justifies the theoretical analysis

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

on pseudo algebraically closed extensions of fields abstract the notion of pseudo algebraically closed pac extensions is a generalization of the classical notion of pac fields in this work we develop a basic machinery to study pac extensions this machinery is based on a generalization of embedding problems to field extensions the main goal is to prove that the galois closure of any proper separable algebraic pac extension is its separable closure as a result we get a classification of all finite pac extensions which in turn proves the bottom conjecture for finitely generated infinite fields the secondary goal of this work is to unify proofs of known results about pac extensions and to establish new basic properties of pac extensions e g transitiveness of pac extensions

recursive subspace identification of linear and non linear wiener state space models the moesp class of identification algorithms are made recursive on the basis of various updating schemes for subspace tracking

recursive identification for nonlinear arx systems based on stochastic approximation algorithm the nonparametric identification for nonlinear autoregressive systems with exogenous inputs narx described by yk 1 f yk yk 1 n0 uk uk 1 n0 ek 1 is considered first a condition on f is introduced to guarantee ergodicity and stationarity of yk then the kernel function based stochastic approximation algorithm with expanding truncations saawet is proposed to recursively estimate the value of f at any given y 1 y n0 u 1 u n0 r2n0 it is shown that the estimate converges to the true value with probability one in establishing the strong consistency of the estimate the properties of the markov chain associated with the narx system play an important role numerical examples are given which show that the simulation results are consistent with the theoretical analysis the intention of the paper is not only to present a concrete solution to the problem under consideration but also to profile a new analysis method for nonlinear systems the proposed method consisting in combining the markov chain properties with stochastic approximation algorithms may be of future potential although a restrictive condition has to be imposed on f that is the growth rate of f x should not be faster than linear with coefficient less than 1 as x tends to infinity

controllability aspects of quantum dynamics a unified approach for closed and open systems knowledge about to what extent quantum dynamical systems can be steered by coherent controls is indispensable for future developments in quantum technology the purpose of this paper is to analyze such controllability aspects for finite dimensional bilinear quantum control systems we use a unified approach based on lie algebraic methods from nonlinear control theory to revisit known and to establish new results for closed and open quantum systems in particular we provide a simplified characterization of different notions of controllability for closed quantum systems described by the liouville von neumann equation we derive new necessary and sufficient conditions for accessibility of open quantum systems modelled by the lindblad kossakowski master equation to this end we exploit a well studied topic of differential geometry namely the classification of all matrix lie groups which act transitively on the grassmann manifold or the punctured euclidean space for the special case of coupled spin 1 2 systems we obtain a remarkably simple characterization of accessibility these accessibility results correct and refine previous statements in the quantum control literature

parameter identification of wiener systems with discontinuous nonlinearities abstract the paper deals with modeling and parameter identification of wiener type nonlinear dynamic systems having discontinuous asymmetric piecewise linear characteristics with preloads and dead zones multiple application of a decomposition technique provides a special form of static nonlinearity description its incorporation into the wiener model leads to an input output equation where all the model parameters are separated and can be estimated iteratively using input output data and internal variable estimates more illustrative examples are included to demonstrate the feasibility of the proposed approach

maximum likelihood identification of wiener models the wiener model is a block oriented model having a linear dynamic system followed by a static nonlinearity the dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs we show that this will in general lead to biased estimates if there are other disturbances present than measurement noise the implications of bussgang s theorem in this context are also discussed for the case with general disturbances we derive the maximum likelihood method and show how it can be efficiently implemented comparisons between this new algorithm and the traditional approach confirm that the new method is unbiased and also has superior accuracy

efficient nonlinear wiener model identification using a complex valued simplicial canonical piecewise linear filter this paper proposes an efficient adaptive realization of the wiener model for the identification of complex valued nonlinear systems using a two dimensional simplicial canonical piecewise linear filter for the complex valued nonlinear mapping we derive a realization of the wiener model requiring fewer parameters than previous approaches an adaptive implementation of the proposed wiener model is derived and local convergence analysis for the updating algorithm is presented the tradeoff between computational complexity and modeling performance is discussed simulations of a system identification example show that the proposed algorithm can provide similar or better performance than other approaches in terms of computational complexity convergence speed and final mean squared error mse

adaptive laguerre lattice filters adaptive laguerre based filters provide an attractive alternative to adaptive fir filters in the sense that they require fewer parameters to model a linear time invariant system with a long impulse response we present an adaptive laguerre lattice structure that combines the desirable features of the laguerre structure i e guaranteed stability unique global minimum and small number of parameters m for a prescribed level of modeling error with the numerical robustness and low computational complexity of adaptive fir lattice structures the proposed configuration is based on an extension to the iir case of the fir lattice filter it is a cascade of identical sections but with a single pole all pass filter replacing the delay element used in the conventional fir lattice filter we utilize this structure to obtain computationally efficient adaptive algorithms o m computations per time instant our adaptive laguerre lattice filter is an extension of the gradient adaptive lattice gal technique and it demonstrates the same desirable properties namely 1 excellent steady state behavior 2 relatively fast initial convergence comparable with that of an rls algorithm for laguerre structure and good numerical stability simulation results indicate that for systems with poles close to the unit circle where an adaptive fir model of very high order would be required to meet a prescribed modeling error an adaptive laguerre lattice model of relatively low order achieves the prescribed bound after just a few updates of the recursions in the adaptive algorithm

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

adaptive control of a wiener type system application of a ph neutralization reactor in this paper the problem of on line identification and adaptive control of a wiener type non linear system is studied first a wiener model is defined whose linear and non linear parts are described using laguerre and piecewise linear basis functions respectively then an adaptive identification algorithm for this model is presented a local convergence analysis for the adaptive identification is performed the model obtained is used to adapt the parameters of a controller designed for the specific structure of the model the complete scheme is applied to a simulation of a ph neutralization reactor subject to several perturbations the results show the improved behaviour of the proposed scheme compared with other approaches found in the literature

brief estimation of an n l n hammerstein wiener model estimation of a single input single output block oriented model is studied the model consists of a linear block embedded between two static nonlinear gains hence it is called n l n hammerstein wiener model first the model structure is motivated and the disturbance model is discussed the paper then concentrates on parameter estimation a relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in parameters this leads to a simple algorithm which minimizes the original loss function the convergence and consistency of the algorithm are studied in order to reduce the variance error the obtained linear model is further reduced using frequency weighted model reduction simulation study will be used to illustrate the method

recursive identification method for piecewise arx models a sparse estimation approach this paper deals with the identification of nonlinear systems using piecewise linear models by means of a sparse overparameterization this challenging problem is turned into a convex optimization problem the proposed method uses a likelihood based methodology which adaptively penalizes model complexity and directly leads to a recursive implementation in this sparse estimation approach the tuning of user parameters is avoided and the computational complexity is kept linear in the number of data samples numerical examples with both simulated and experimental data are presented and the results are compared with previously published methods

adaptive discrete time sliding mode control of nonlinear systems described by wiener models abstractin this paper we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters the considered class of nonlinear systems is described by the block oriented models specifically the wiener models these models consist of dynamic linear blocks in series with static nonlinear blocks the proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete time sliding mode controller the parameters adaptation are performed using a new recursive parametric estimation algorithm this algorithm is developed using the adjustable model method and the least squares technique a recursive least squares rls algorithm is used to estimate the inverse nonlinear function a time varying gain is proposed in the discrete time sliding mode controller to reduce the chattering problem the stability of the closed loop nonlinear system with the proposed adaptive control scheme has been proved an application to a ph neutralisation

controllability properties for finite dimensional quantum markovian master equations various notions from geometric control theory are used to characterize the behavior of the markovian master equation for n level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states it is shown that the system can be accessible but neither small time controllable nor controllable in finite time in particular if the generators of quantum dynamical semigroups are unital then the reachable sets admit easy characterizations as they monotonically grow in time the two level case is treated in detail

a recursive local linear estimator for identification of nonlinear arx systems asymptotical convergence and applications in this paper we propose a recursive local linear estimator rlle for nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx first the rlle is introduced next the strong consistency as well as the asymptotical mean square error properties of the rlle are established and then an application of the rlle to an additive nonlinear system is discussed the rlle provides recursive estimates not only for the function values but also their gradients at fixed points a simulation example is provided to confirm the theoretical analysis

stochastic analysis of gradient adaptive identification of nonlinear systems with memory for gaussian data and noisy input and output measurements this paper investigates the statistical behavior of two gradient search adaptive algorithms for identifying an unknown nonlinear system comprised of a discrete time linear system h followed by a zero memory nonlinearity g spl middot the input and output of the unknown system are corrupted by additive independent noises gaussian models are used for all inputs two competing adaptation schemes are analyzed the first is a sequential adaptation scheme where the lms algorithm is first used to estimate the linear portion of the unknown system the lms algorithm is able to identify the linear portion of the unknown system to within a scale factor the weights are then frozen at the end of the first adaptation phase recursions are derived for the mean and fluctuation behavior of the lms algorithm which are in excellent agreement with monte carlo simulations when the nonlinearity is modeled by a scaled error function the second part of the sequential gradient identification scheme is shown to correctly learn the scale factor and the error function scale factor mean recursions for the scale factors show good agreement with monte carlo simulations for slow learning the stationary points of the gradient algorithm closely agree with the stationary points of the theoretical recursions the second adaptive scheme simultaneously learns both the linear and nonlinear portions of the unknown channel the mean recursions for the linear and nonlinear portions show good agreement with monte carlo simulations for slow learning the stationary points of the gradient algorithm also agree with the stationary points of the theoretical recursions

parametric and nonparametric curve fitting we are concerned with convergence issues in the identification of a static nonlinear function our investigation focuses on properties of the input signal that ensure convergence of the estimate both parametric and nonparametric approaches are considered in the parametric case we offer sufficient conditions under which the estimated parameters converge to their true values almost surely for the nonparametric case we offer necessary and sufficient conditions under which the estimated function converges almost surely to the true nonlinearity

adaptive control of weiner type nonlinear systems abstract this study is concerned with the problem of adaptive control of a wiener type nonlinear process it is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order with stable inverse followed by a known time delay the memoryless nonlinearity is one to one on a compact set and belongs to one of two classes 1 piecewise linear with known breakpoints or 2 smooth function in which case an approximation is made it is represented by linear splines the output signal from the linear part is not available for measurement the global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints otherwise there will be a residual tracking error which depends on the nonlinearity approximation error but the boundedness of all signals can be assured the proposed scheme is used for adaptive control of the ph process in a continuous flow reactor

nonparametric input density free estimation of the nonlinearity in wiener systems the nonlinear characteristic of a wiener system is estimated under nonparametric a priori information the probability density of the input signal is completely unknown and can be of any form the estimate is asymptotically biased but its bias can be made arbitrarily small results of computer simulations are presented

parameter bounds evaluation of wiener models with noninvertible polynomial nonlinearities in this paper a three stage procedure is presented for deriving parameters bounds of siso wiener models when the nonlinear block is modeled by a possibly noninvertible polynomial and the output measurement errors are bounded first using steady state input output data parameters of the nonlinear part are bounded by a tight orthotope then given the estimated uncertain nonlinearity and the output measurements collected exciting the system with an input dynamic signal bounds on the unmeasurable inner signal are computed finally such bounds together with noisy output measurements are used for bounding the parameters of the linear block

a fully adaptive normalized nonlinear gradient descent algorithm for complex valued nonlinear adaptive filters a fully adaptive normalized nonlinear complex valued gradient descent fanncgd learning algorithm for training nonlinear neural adaptive finite impulse response fir filters is derived first a normalized nonlinear complex valued gradient descent nncgd algorithm is introduced for rigour the remainder of the taylor series expansion of the instantaneous output error in the derivation of nncgd is made adaptive at every discrete time instant using a gradient based approach this results in the fully adaptive normalized nonlinear complex valued gradient descent learning algorithm that is suitable for nonlinear complex adaptive filtering with a general holomorphic activation function and is robust to the initial conditions convergence analysis of the proposed algorithm is provided both analytically and experimentally experimental results on the prediction of colored and nonlinear inputs show the fanncgd outperforming other algorithms of this kind

hard frequency domain model error bounds from least squares like identification techniques the problem of deriving so called hard error bounds for estimated transfer functions is addressed a hard bound is one that is sure to be satisfied i e the true system nyquist plot will be confined with certainty to a given region provided that the underlying assumptions are satisfied by blending a priori knowledge and information obtained from measured data it is shown how the uncertainty of transfer function estimates can be quantified the emphasis is on errors due to model mismatch the effects of unmodeled dynamics can be considered as bounded disturbances hence techniques from set membership identification can be applied to this problem the approach taken corresponds to weighted least squares estimation and provides hard frequency domain transfer function error bounds the main assumptions used in the current contribution are that the measurement errors are bounded that the true system is indeed linear with a certain degree of stability and that there is some knowledge about the shape of the true frequency response

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

stability analysis of closed loop algorithms for cancelling nonlinear memory effects in a nonlinear memory system using a nonlinear adaptive filter as a predistorter is an effective compensation technique predistorters based on closed loop algorithms typically exhibit better linearity than those based on indirect learning algorithms however the steady state of a closed loop algorithm may be affected by external noise or error signals in this paper the long term stability of a closed loop algorithm is analyzed using perturbation and iteration analyses it is shown that because of accumulation of historical errors it is difficult for typical closed loop algorithms to converge when the number of iterations becomes large to address this problem a modified closed loop algorithm is proposed by reducing the effect of accumulated historical errors the long term stability of the algorithm is largely improved as verified by numerical simulations

identification of certain time varying nonlinear wiener and hammerstein systems the problem of identification and tracking of time varying nonlinear systems is addressed in particular the wiener system that consists of a dynamic time varying linear part followed by a fixed nonlinearity and the hammerstein system in which the order of these two blocks is reversed are studied the extended kalman filter ekf algorithm is applied it is also shown that this algorithm can be reformulated in terms of a nonlinear minimization problem with a quadratic inequality constraint in order to ensure exponential stability resulting in the algorithm cekf as indicated by means of numerical examples this latter algorithm is less sensitive to the chosen initialization than the ekf the proposed algorithms depend on certain second order statistics that may be unknown in a typical scenario a method for estimation of these quantities is proposed it is demonstrated that the suggested algorithms can be successfully applied to the problem of acoustic echo cancelation

set membership identification of systems with parametric and nonparametric uncertainty a method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented in the disturbance free case the parameter set estimate is guaranteed to contain the parameter set of the true plant in the presence of stochastic disturbances the parameter set estimate obtained from finite data records is shown to have the property that it contains the true plant parameter set with probability one as the data length tends to infinity

on estimation of errors caused by non linear undermodelling in system identification the problem of quantifying errors due to non linear undermodelling is addressed in particular the wiener system which consists of a linear dynamic block followed by a static non linearity and the hammerstein system in which the order of these two blocks is reversed are studied in either case it is assumed that the objective is to identify the linear part of the system using a purely linear model these scenarios can be interpreted as linear identification applied to systems where non linearity errors may occur and hence need to be quantified the stochastic embedding approach is therefore applied to capture the on average properties of the undermodelling due to inadequate representation of the non linear effects as compared to previous methods the priors on the covariance matrix of the embedding parameters are reduced as a result an expression for the amplitude error bound of the estimated transfer function that does not require knowledge of the true system parameters is obtained the quality of t

singular trajectories and the contrast imaging problem in nuclear magnetic resonance in this article the contrast imaging problem in nuclear magnetic resonance is modeled as a mayer problem in optimal control whose solutions can be parameterized using pontryagin s maximum principle and analyzed using geometric optimal control in particular the optimal problem can be mainly reduced to the analysis of the hamiltonian dynamics describing the singular trajectories and encoding their optimality status

pac fields over finitely generated fields we prove the following theorem for a finitely generated field k let m be a galois extension of k which is not separably closed then m is not pac over k

robust model predictive control of wiener systems block oriented models boms have shown to be appealing and efficient as nonlinear representations for many applications they are at the same time valid and simple models in a more extensive region than time invariant linear models in this work wiener models are considered they are one of the most diffused boms and their structure consists in a linear dynamics in cascade with a nonlinear static block particularly the problem of control of these systems in the presence of uncertainty is treated the proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system this model is then employed to design a model predictive controller the mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities lmi theory the main feature of this approach is that it takes advantage of the static nature of the nonlinearity which allows to solve the control problem by focusing o

identification of iir wiener systems with spline nonlinearities that have variable knots an algorithm is developed for the identification of wiener systems linear dynamic elements followed by static nonlinearities in this case the linear element is modeled using a recursive digital filter while the static nonlinearity is represented by a spline of arbitrary but fixed degree the primary contribution in this note is the use of variable knot splines which allow for the use of splines with relatively few knot points in the context of wiener system identification the model output is shown to be nonlinear in the filter parameters and in the knot points but linear in the remaining spline parameters thus a separable least squares algorithm is used to estimate the model parameters monte carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities with a similar technique using polynomial nonlinearities

analysis of stochastic gradient tracking of time varying polynomial wiener systems this paper presents analytical and monte carlo results for a stochastic gradient adaptive scheme that tracks a time varying polynomial wiener 1958 system i e a linear time invariant lti filter with memory followed by a time varying memoryless polynomial nonlinearity the adaptive scheme consists of two phases 1 estimation of the lti memory using the lms algorithm and 2 tracking the time varying polynomial type nonlinearity using a second coupled gradient search for the polynomial coefficients the time varying polynomial nonlinearity causes a time varying scaling for the optimum wiener filter for phase 1 these time variations are removed for phase 2 using a novel coupling scheme to phase 1 the analysis for gaussian data includes recursions for the mean behavior of the lms algorithm for estimating and tracking the optimum wiener filter for phase 1 for several different time varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for phase 2 the polynomial coefficients are shown to be accurately tracked monte carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions

instrumental variable methods for identification of hammerstein systems abstract consistency conditions for instrumental variable methods applied to hammerstein models are derived and analysed it is necessary to have a model that is not over parametrized and an input that is strongly persistently exciting i e the inputs and their powers are jointly persistently exciting some specific choices of the instruments are proved to give consistency those instruments are formed as filtered inputs and powers of the input consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive real the vector of instruments is in general of larger dimension than the parameter vector it is shown then that a non singular linear transformation of the instruments gives a new and still consistent estimate some simulations using the iv variants proposed in this paper are also included

controllability of right invariant systems on real simple lie groups we deal with controllability of right invariant control systems on lie groups following the ideas of a series of papers by jurdjevic kupka gauthier bornard gauthier kupka sallet leite crouch el assoudi gauthier we obtain a generalization of these results in the general case of real semi simple lie groups

an analytic geometry approach to wiener system frequency identification this paper addresses the problem of wiener system identification the underlying linear subsystem is stable but not necessarily parametric the nonlinear element in turn is allowed to be nonparametric noninvertible and nonsmooth as wiener models are uniquely defined up to an uncertain multiplicative factor it makes sense to start the frequency identification process estimating the system phase which is common to all models to this end a consistent estimator is designed using analytic geometry tools accordingly the system frequency behavior is characterized by a family of lissajous curves interestingly all these curves are candidates to modelling the system nonlinearity but the most convenient one is the less spread of them finally the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates

quantifying the error in estimated transfer functions with application to model order selection previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics this prior information took the form of parameterized bounding functions or parameterized probability density functions in the time or frequency domain with known parameters it is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique this significantly reduces the prior information required to estimate transfer function error bounds the authors illustrate the usefulness of the method with a number of simulation examples how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under modeling is shown another simulation study compares the method to akaike s well known fpe and aic criteria

identification of piecewise affine systems via mixed integer programming this paper addresses the problem of identification of hybrid dynamical systems by focusing the attention on hinging hyperplanes and wiener piecewise affine autoregressive exogenous models in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron in particular we provide algorithms based on mixed integer linear or quadratic programming which are guaranteed to converge to a global optimum for the special case where the estimation data only seldom switches between the different submodels we also suggest a way of trading off between optimality and complexity by using a change detection approach

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

hinging hyperplanes for regression classification and function approximation a hinge function y h x consists of two hyperplanes continuously joined together at a hinge in regression prediction classification pattern recognition and noiseless function approximation use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters a simple and effective method for finding good hinges is presented

h control of a wiener type system a wiener system is a system which can be modelled as a linear dynamic followed by a static gain the goal of this paper is to develop a robust h compensator for controlling an siso wiener system the controller also takes the form of a wiener model the design approach consists of the approximation of the non linear gain using a piecewise linear pwl function and in using a linear controller for each sector obtained from this approximation therefore the general controller structure can be stated as a linear dynamic compensator in series with a pwl static gain as an illustrative case a neutralization ph reaction between a strong acid and a strong base in the presence of a buffer agent is dealt with computer simulations are developed for showing the performance of the proposed controller

statistical analysis of the single layer backpropagation algorithm i mean weight behavior the single layer backpropagation algorithm is a gradient descent method that adjusts the connection weights of a single layer perceptron to minimize the mean square error at the output it is similar to the standard least mean square al gorithm except the output of the linear combiner contains a differentiable nonlinearity in this paper we present a statis tical analysis of the mean weight behavior of the single layer backpropagation algorithm for gaussian input signals it is based on a nonlinear system identification model of the desired response which is capable of generating an arbitrary hyper plane decision boundary it is demonstrated that although the weights grow unbounded the algorithm on average quickly learns the correct hyperplane associated with the system iden tification model

gaussian approximation in recursive estimation of multiple state of nonlinear wiener systems abstract the paper concerns recursive state estimation in wiener systems where the output is a scalar weighted sum of multiple states a gaussian approximation to the computed conditional probability distribution for the scalar sum of states is shown to lead to a practicable numerical algorithm for estimating the multiple states this algorithm mimics the kalman filter simulations show the method giving good performance when the nonlinearity is severe quantization

adaptive precompensation of wiener systems this article presents an adaptive precompensation technique for the wiener system a class of nonlinear systems that can be represented by the interconnection of a linear dynamic subsystem and a memoryless nonlinear subsystem an adaptive algorithm for adjusting the parameters of the precompensator structured by a hammerstein model is derived using the stochastic gradient method the validity of the proposed algorithm is confirmed in a computer simulation by applying it to known wiener systems

fluctuation analysis of stochastic gradient identification of polynomial wiener systems this correspondence presents analytical results and monte carlo simulations for the fluctuation behavior of a stochastic gradient adaptive identification scheme this scheme identifies a polynomial wiener system linear fir filter followed by a static polynomial nonlinearity for noisy output observations the analysis includes 1 bounds and a recursion for the misadjustment matrix and 2 algorithm mean square stability regions a diagonal step size matrix for the adaptive coefficients is introduced to speed up convergence the theoretical predictions of the fluctuation analysis are supported by monte carlo simulations

towards identification of wiener systems with the least amount of a priori information iir cases in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non gaussian input case under the white noise input three types of a priori information are considered quadrant information point information and monotonic information in all three cases identifiability has been established and the corresponding nonparametric identification algorithms are developed along with their convergence proofs

design variables for bias distribution in transfer function estimation estimation of transfer functions of linear systems is one of the most common system identification problems several different design variables chosen by the user for the identification procedure affect the properties of the resulting estimate in this paper it is investigated how the choices of prefilters noise models sampling interval and prediction horizon i e the use of k step ahead prediction methods influence the estimate an important aspect is thai the true system is not assumed to be exactly represented within the chosen model set the estimate will thus be biased it is shown how the distribution of bias in the frequency domain is governed by a weighting function which emphasizes different frequency bands the weighting function in turn is a result of the previously listed design variables it is shown e g thai the common least squares method has a tendency to emphasize high frequencies and that this can be counteracted by prefiltering it is also shown that asymptotically it is only the prediction horizon itself and not how it is split up into sampling interval times number of predicted sampling instants that affects this weighting function

identification of block oriented nonlinear systems starting from linear approximations a survey abstract block oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use many different identification approaches were developed over the years to estimate the parameters of a wide range of block oriented nonlinear models one class of these approaches uses linear approximations to initialize the identification algorithm the best linear approximation framework and the approximation framework or equivalent frameworks allow the user to extract important information about the system guide the user in selecting good candidate model structures and orders and prove to be a good starting point for nonlinear system identification algorithms this paper gives an overview of the different block oriented nonlinear models that can be identified using linear approximations and of the identification algorithms that have been developed in the past a non exhaustive overview of the most important other block oriented nonlinear system identification approaches is also provided throughout this paper

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

identification of hammerstein wiener models this paper develops and illustrates a new maximum likelihood based method for the identification of hammerstein wiener model structures a central aspect is that a very general situation is considered wherein multivariable data non invertible hammerstein and wiener nonlinearities and colored stochastic disturbances both before and after the wiener nonlinearity are all catered for the method developed here addresses the blind wiener estimation problem as a special case

statistical analysis of the single layer backpropagation algorithm ii mse and classification performance for pt i see ibid p 583 91 1993 the analysis of pt i is extended to the evaluation of the mean square error and the probability of correct classification it is shown that the mean square error and the corresponding performance surface are such that the single layer perceptron is prevented from correctly classifying with probability one until the weights converge at infinity

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

brief paper initializing wiener hammerstein models based on partitioning of the best linear approximation this paper describes a new algorithm for initializing and estimating wiener hammerstein models which consist of two linear parts with a static nonlinearity in between the algorithm makes use of the best linear model of the system which is a consistent estimate of the systems dynamics for gaussian excitations the linear model is split in all possible ways into two sub models for all possible splits a wiener hammerstein model is initialized which means that a nonlinearity is introduced in between the two sub models the linear parameters of this nonlinearity can be estimated using least squares all initialized models can then be ranked depending on the fit typically one is only interested in the best one for which all parameters are fitted using prediction error minimization the paper explains the algorithm in detail and consistency of the initialization is proven computational aspects are investigated showing that in most realistic cases the number of splits of the initial linear model remains low enough to make the algorithm useful the algorithm is illustrated on an example where it is shown that the initialization is a tool to avoid many local minima

blind identification of simo wiener systems based on kernel canonical correlation analysis we consider the problem of blind identification and equalization of single input multiple output simo nonlinear channels specifically the nonlinear model consists of multiple single channel wiener systems that are excited by a common input signal the proposed approach is based on a well known blind identification technique for linear simo systems by transforming the output signals into a reproducing kernel hilbert space rkhs a linear identification problem is obtained which we propose to solve through an iterative procedure that alternates between canonical correlation analysis cca to estimate the linear parts and kernel canonical correlation kcca to estimate the memoryless nonlinearities the proposed algorithm is able to operate on systems with as few as two output channels on relatively small data sets and on colored signals simulations are included to demonstrate the effectiveness of the proposed technique

parameter identification of wiener systems with multisegment piecewise linear nonlinearities the paper deals with the identification of wiener systems having multisegment piecewise linear nonlinearities a special form of nonlinearity representation is used in the wiener system description the resulting output equation contains the least possible number of parameters required for the blocks of given system the proposed iterative method enables simultaneous estimation of both the linear block parameters and all the parameters characterizing the nonlinearity i e the slopes of linear segments and the constants determining the partition of domain limits for the constants are the only a priori knowledge required

on diophantine definability and decidability in some infinite totally real extensions of ℚ let m be a number field and w m a set of its non archimedean primes then let o m wm x m ord t x 0 t w m let p 1 p r be a finite set of prime numbers let f inf be the field generated by all the p j i th roots of unity as j and i 1 r let k inf be the largest totally real subfield of f inf then for any e 0 there exist a number field m k inf and a set w m of non archimedean primes of m such that w m has density greater than 1 e and z has a diophantine definition over the integral closure of o m w m in k inf

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

combined frequency prediction error identification approach for wiener systems with backlash and backlash inverse operators wiener systems identification is studied in the presence of possibly infinite order linear dynamics and memory nonlinear operators of backlash and backlash inverse types the latter is laterally bordered with polynomial lines of arbitrary shape it turns out that the borders are allowed to be noninvertible and crossing making possible to account within a unified theoretical framework for memory and memoryless nonlinearities moreover the prior knowledge of the nonlinearity type being backlash or backlash inverse or memoryless is not required using sine excitations and getting benefit from model plurality the initial complex identification problem is made equivalent to two tractable though still nonlinear prediction error problems these are coped with using linear and nonlinear least squares estimators which all are shown to be consistent