input nonlinearity recovering in a class of systems a system in which a nonlinear memoryless part is followed by a nonlinear dynamic one is identified under nonparametric a priori information the input nonlinearity is recovered with the kernel regression estimate

a blind approach to hammerstein model identification this paper discusses the hammerstein model identification using a blind approach by fast sampling at the output it is shown that identification of the linear part can be achieved based only on the output measurements that makes the hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variables

hierarchical gradient parameter estimation algorithm for hammerstein nonlinear systems using the key term separation principle in this paper we use the hierarchical identification principle to decompose a hammerstein controlled autoregressive system into three subsystems apply the key term separation principle to express the system output as a linear combination of the system parameters and then derive a hierarchical gradient parameter estimation algorithm for identifying all subsystems finally a multi innovation stochastic gradient algorithm is presented to improve the estimation accuracy by making full of the identification innovation the simulation results show that the proposed algorithm is effective

hammerstein systems identification in presence of hard nonlinearities of preload and dead zone type hammerstein system identification is considered in presence of preload and dead zone nonlinearities the discontinuous feature of these nonlinearities makes it difficult to get a single system parameterization involving linearly all unknown parameters those of the linear subsystem and those of the nonlinearity therefore system identification has generally been dealt with using multiple stage schemes including different parametrizations and several data acquisition experiences however the consistency issue has only been solved under restrictive assumptions regarding the identified system in this paper a new identification scheme is designed and shown to be consistent under mild assumptions

brief paper convergence of the iterative algorithm for a general hammerstein system identification the convergence of the iterative identification algorithm for a general hammerstein system has been an open problem for a long time in this paper it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters

anomalous transport in external fields continuous time random walks and fractional diffusion equations extended the continuous time random walk ctrw in a homogeneous velocity field and in arbitrary force fields is studied within the extended ctrw scheme anomalous transport properties due to long tailed waiting time or jump length distributions are consistently introduced the connections with generalised diffusion equations in a potential field are discussed these equations being of fractional order in particular the problems of a constant and a hookean linear force i e of a linear and a parabolic potential are worked out

continuous time hammerstein system identification a continuous time hammerstein system i e a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one is identified the system is driven and disturbed by white random signals the a priori information about both subsystems is nonparametric which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown an algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown the impulse response of the dynamic part is recovered with a correlation method the algorithms are computationally independent results of a simulation example are given

adaptive digital control of hammerstein nonlinear systems with limited output sampling this paper is motivated by the practical control considerations that nonlinearity is abundant in industrial processes and output sampling rates are often limited due to hardware constraints in particular for a hammerstein nonlinear sampled data system in which the output sampling period is an integer multiple of the input updating period we derive by using a polynomial transformation technique a mathematical model which is suitable for parameter estimation with dual rate measurement data further we present an adaptive control scheme for such a dual rate nonlinear system the parameter estimation based adaptive algorithm can achieve virtually asymptotically optimal control and ensure that the closed loop system is stable and globally convergent the simulation results are included

time series modeling by a second order hammerstein system in this paper we discuss the modeling of an observed time series as the output of a second order hammerstein model driven by an independent and identically distributed i i d gaussian noise the modeling is discussed from the point of view of the hypothesis testing ht of statistical indexes derived from higher order statistics hos three points of view can be adopted in ht the more general approach is to not make any assumption on the index statistics notably on the variance and thus to use the t 2 hotelling test the second point of view involves calculating a theoretical variance in order to define normalized variables whose statistics are known the last approach is a mixed version of the others two these three approaches are applied to statistical indexes derived from linear combination of slices of spectra from the third order up the fifth order some subcases need to use the derivatives of the polyspectra since general relationships are null and cannot be used for the ht the second part of this paper is devoted to linear and quadratic kernel identification using the relationship defined for ht definition as for the ht several subcases have to be discussed using either the polyspectra or the derivatives of polyspectra

applications of inverse tempered stable subordinators abstract the inverse tempered stable subordinator is a stochastic process that models power law waiting times between particle movements with an exponential tempering that allows all moments to exist this paper shows that the probability density function of an inverse tempered stable subordinator solves a tempered time fractional diffusion equation and its folded density solves a tempered time fractional telegraph equation two explicit formulae for the density function are developed and applied to compute explicit solutions to tempered fractional cauchy problems where a tempered fractional derivative replaces the first derivative in time several examples are given including tempered fractional diffusion equations on bounded or unbounded domains and the probability distribution of a tempered fractional poisson process it is shown that solutions to the tempered fractional diffusion equation have a cusp at the origin

a new algorithm for the design of multifunctional observers this paper presents a general algorithm for low order multifunctional observer design with arbitrary eigenvalues the feature of this algorithm is that it can generate a functional observer with different orders which are no larger but usually much less than m v 1 where m is the number of functionals and v is the observability index of a c since the order needed for the observer varies with the functionals besides other system parameters this design approach should be practical the resulting observer system matrix is in its jordan form the key step of this algorithm is the generation of the basis for the transformation matrix which relates the system and observer states the computation of this algorithm is quite reliable it is based on the block observable lower hessenberg form of a c and all its initial and major computation involves only the orthogonal operations

iterative identification of block oriented nonlinear systems based on biconvex optimization abstract we investigate the identification of a class of block oriented nonlinear systems which is represented by a common model in this paper then identifying the common model is formulated as a biconvex optimization problem based on this a normalized alterative convex search nacs algorithm is proposed under a given arbitrary nonzero initial condition it is shown that we only need to find the unique partial optimum point of a biconvex cost function in order to obtain its global minimum point thus the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions by applying the results to hammerstein wiener systems with an invertible nonlinear function the long standing problem on the convergence of iteratively identifying such systems under arbitrary nonzero initial conditions is also now solved

parameter estimation error bounds for hammerstein nonlinear finite impulsive response models abstract this paper presents a parameter estimation algorithm for a class of hammerstein nonlinear systems input nonlinear fir finite impulse response models and studies in detail the convergence properties of the proposed identification algorithm in the stochastic framework and derives the upper and lower bounds of the parameter estimation errors pee from the available input output data the analysis indicates that the mean square pee upper and lower bounds of the algorithm approach zero as the data length increases a simulation example is given

subspace identification for non linear systems with measured input non linearities this paper uses subspace methods to identify a class of multi input multi output discrete time non linear time varying systems specifically we identify systems that are non linear in measured data and linear in unmeasured states numerical examples are presented to demonstrate the efficacy of the method

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

iterative identification of hammerstein systems the iterative method was first proposed to estimate hammerstein system in 9 it is a very simple and efficient algorithm in general the convergence of iterative algorithm can be a problem 12 it was recently shown that iterative algorithms with normalisation possess some global convergence properties in identification of hammerstein system with smooth nonlinearity and finite impulse response fir linear part 3 4 11 the convergence for an infinite impulse response iir system was however not solved in this chapter the results are extended to hammerstein systems with an iir linear part the global convergence for an iir system is established for the odd nonlinearities

modeling and parameter identification of systems with multisegment piecewise linear characteristics this paper deals with the modeling and parameter identification of nonlinear systems having multi segment piecewise linear characteristics the decomposition of the corresponding mapping provides a new form of multi segment nonlinearity representation leading to an output equation where all the parameters to be estimated are separated hence an iterative method with internal variable estimation can be applied for parameter identification using input output data records the only required a priori knowledge of the nonlinear characteristic represents the limits for the domain partition the proposed model of given static nonlinearity is also incorporated into the hammerstein model examples of parameter identification for static and dynamic systems with multi segment piecewise linear characteristics are presented

strong consistency of recursive identification for hammerstein systems with discontinuous piecewise linear memoryless block this note deals with identification of hammerstein systems with discontinuous piecewise linear memoryless block followed by a linear subsystem recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block by taking a sequence of iid random variables with uniform distribution to serve as the system input strong consistency is proved for all estimates given in the note the theoretical results are verified by computer simulation

anomalous diffusion and the first passage time problem we study the distribution of the first passage time fpt in levy type anomalous diffusion using the recently formulated fractional fokker planck equation we obtain three results 1 we derive an explicit expression for the fpt distribution in terms of fox or h functions when the diffusion has zero drift 2 for the nonzero drift case we obtain an analytical expression for the laplace transform of the fpt distribution 3 we express the fpt distribution in terms of a power series for the case of two absorbing barriers the known results for ordinary diffusion brownian motion are obtained as special cases of our more general results

decoupling the linear and nonlinear parts in hammerstein model identification the main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in hammerstein model identification therefore identification of the linear part for a hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

brief paper modeling and identification of systems with backlash a new analytic form of backlash characteristic description is introduced which uses appropriate switching functions and their complements the backlash parameters in the model equation are separated hence their estimation can be solved as a quasi linear problem using an iterative method with internal variable estimation also the identification of cascaded systems consisting of an input backlash followed by a linear dynamic system is presented simulation studies of backlash and cascaded systems identification are included

pathwise convergence of recursive identification algorithms for hammerstein systems this paper gives estimates for 1 coefficients contained in the linear part of the hammerstein system 2 the value of the nonlinear function f u in the hammerstein system at any u 3 ef u sub k and eu sub k f u sub k with u sub k denoting the system input no assumption is made on structure of f spl middot the estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one two numerical examples are given

a nonparametric kernel based approach to hammerstein system identification hammerstein systems are the series composition of a static nonlinear function and a linear dynamic system in this work we propose a nonparametric method for the identification of hammerstein systems we adopt a kernel based approach to model the two components of the system in particular we model the nonlinear function and the impulse response of the linear block as gaussian processes with suitable kernels the kernels can be chosen to encode prior information about the nonlinear function and the system following the empirical bayes approach we estimate the posterior mean of the impulse response using estimates of the nonlinear function of the hyperparameters and of the noise variance these estimates are found by maximizing the marginal likelihood of the data this maximization problem is solved using an iterative scheme based on the expectation conditional maximization which is a variation of the standard expectation maximization method for solving maximum likelihood problems we show the effectiveness of the proposed identification scheme in some simulation experiments

fixed point iteration in identifying bilinear models abstract inspired by fixed point theory an iterative algorithm is proposed to identify bilinear models recursively in this paper it is shown that the resulting iteration is a contraction mapping on a metric space when the number of input output data points approaches infinity this ensures the existence and uniqueness of a fixed point of the iterated function sequence and therefore the convergence of the iteration as an application one class of block oriented systems represented by a cascade of a dynamic linear l a static nonlinear n and a dynamic linear l subsystems is illustrated this gives a solution to the long standing convergence problem of iteratively identifying lnl winer hammerstein models in addition we extend the static nonlinear function n to a nonparametric model represented by using kernel machine

parameter estimation algorithms for multivariable hammerstein carma systems this paper considers parameter identification problems for multivariable hammerstein controlled autoregressive moving average carma systems we transform a multivariable hammerstein carma system into a new identification model which contains a set of bilinear parameter vectors i e two sets of parameter vectors to solve the difficulty of estimating the two sets of parameter vectors this paper constructs two different forms of the identification model in each of which the output is linear about one set of parameter vectors and presents an extended stochastic gradient algorithm to interactively estimate the two sets of parameter vectors by using the hierarchical identification principle the proposed hierarchical identification algorithm has a higher computational efficiency than the over parametrization model based stochastic gradient algorithm the simulation results indicate that the proposed algorithm is effective and an example of modeling a photovoltaic array system with the multivariable hammerstein model is given

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

finite model order accuracy in hammerstein model estimation hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems a static input nonlinearity followed by a linear dynamical part is an adequate way to model many real life systems this paper investigates the asymptotic in terms of sample size variance of hammerstein model estimates the work extends earlier results by ninness and gibson 2002 in the following ways not only frequency function estimation but estimation of general quantities is considered the expressions are not restricted to be valid asymptotically in the model order in addition the results cover model structures having noise models and allow for data generated under feedback the increase in variance due to the estimation of the input nonlinearity is characterized in particular under open loop operation white additive noise and the assumption of a separable process it is shown that the variance increase is exactly a term that was observed in ninness and gibson 2002 to result in good agreement with simulations this term vanishes in the formal asymptotic in model order analysis in ninness and gibson 2002

a new deterministic identification approach to hammerstein systems the deterministic identification of hammerstein systems is investigated in this paper based on the over sampling technique a new deterministic identification approach is presented which blindly identifies the linear dynamic part followed by the estimation of the nonlinear function the proposed method allows us to identify the hammerstein system using an over sampling rate smaller than the numerator polynomial s length of the linear dynamic part as required by other existing methods in addition it can obtain the true values of the system parameters in the noise free case and an asymptotically consistent estimate in the presence of noise the richness condition of the system input and the selection of the over sampling rate are studied for the identifiability of the hammerstein system simulation examples are given to show the performance of the proposed method

brief identification of linear systems with hard input nonlinearities of known structure this paper studies identification of systems with input nonlinearities of known structure for input nonlinearities parameterized by one parameter a deterministic approach is proposed based on the idea of separable least squares the identification problem is shown to be equivalent to an one dimensional minimization problem the method is very effective for several common static and nonstatic input nonlinearities for a general input nonlinearity a correlation analysis based identification algorithm is presented which is shown to be convergent

data filtering based recursive least squares algorithm for hammerstein systems using the key term separation principle this paper concerns parameter identification of hammerstein output error moving average systems with a two segment piecewise nonlinearity by combining the key term separation principle and the data filtering technique we transfer the hammerstein model into two regression identification models and present a data filtering based recursive least squares method to estimate the parameters of these two identification models the proposed algorithm achieves a higher computational efficiency than the standard approach by using covariance matrices of smaller dimensions from the two identification models instead of one identification model in the standard approach

discrete time adaptive control of linear dynamic systems with a two segment piecewise linear asymmetric nonlinearity in this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a two segment piecewise linear asymmetric nonlinearity followed by a linear system a switching gain sequence is introduced to make the parameter identification time invariant the algorithm will ensure that the closed loop system is globally convergent and stable for both the deterministic and stochastic cases

identification of iir nonlinear systems without prior structural information in this paper we propose a kernel method for identification of infinite impulse response iir nonlinear systems without prior structural information the main result of the paper is to establish the conditions for asymptotic convergence in terms of the input to output exponential stability the performance of the method is tested on real world applications and computer simulations the results obtained show the efficacy of the method

auxiliary model based least squares identification methods for hammerstein output error systems abstract the difficulty in identification of a hammerstein a linear dynamical block following a memoryless nonlinear block nonlinear output error model is that the information vector in the identification model contains unknown variables the noise free true outputs of the system in this paper an auxiliary model based least squares identification algorithm is developed the basic idea is to replace the unknown variables by the output of an auxiliary model convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition the simulation results show the effectiveness of the proposed algorithms

quasiconvexity analysis of the hammerstein model in this paper the hammerstein identification problem with correlated inputs is studied in a prediction error framework using separable least squares methods thus the identification is recast as an optimization over the parameters used to describe the nonlinearity a sufficient condition is derived that guarantees that the identification problem is quasiconvex with respect to the parameters that describe the nonlinearity simulations using both iid and correlated inputs are used to illustrate the result

recursive identification for wiener model with discontinuous piece wise linear function this paper deals with identification of wiener systems with nonlinearity being a discontinuous piece wise linear function recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid gaussian inputs the estimates are proved to converge to the corresponding true values with probability one a numerical example is given to justify the obtained theoretical results

technical communique generation of enhanced initial estimates for hammerstein systems hammerstein systems are nonlinear models that are used in many domains for their simplicity and physical meaning this paper presents a simple iterative method for generating good starting values which can be used to initialize the numerical nonlinear optimization of the cost function in the absence of model errors the presented method is proven to converge locally to the true model values in the noise less case

frequency domain identification of wiener models this paper proposes a frequency domain algorithm for wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity the convergence of the algorithm is established in the presence of white noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

bounding the parameters of linear systems with input backlash in this note we present a two stage procedure for deriving parameters bounds of linear systems with input backlash when the output measurement errors are bounded first using steady state input output data parameters of the nonlinear dynamic block are tightly bounded then given a suitable prbs input sequence we evaluate tight bounds on the unmeasurable inner signal which together with noisy output measurements are employed for bounding the parameters of the linear dynamic system

convergence of normalized iterative identification of hammerstein systems abstract an iterative identification algorithm of hammerstein systems needs a proper initial condition to guarantee its convergence in this paper we propose a new algorithm by fixing the norm of the parameter estimates the normalized algorithm ensures the convergence property under arbitrary nonzero initial conditions the proofs of the property also give a geometrical explanation on why the normalization guarantees the convergence an additional contribution is that the static function in the hammerstein system is extended to square integrable functions

nonlinear blind parameter estimation this note deals with parameter estimation of nonlinear continuous time models when the input signals of the corresponding system are not measured the contribution of the note is to show that with simple priors about the unknown input signals and using derivatives of the output signals one can perform the estimation procedure as an illustration we consider situations where the simple priors e g independence or gaussianity of the unknown inputs is assumed

a multi innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems this paper proposes a generalized extended stochastic gradient gesg algorithm for estimating the parameters of a class of wiener nonlinear autoregressive moving average systems using the gradient search in order to improve the convergence rates of the gesg algorithm a multi innovation gesg algorithm is derived the simulation results indicate that the proposed algorithms can effectively estimate the parameters of a class of output nonlinear systems

comment on fractional fokker planck equation with space and time dependent drift and diffusion the purpose of this paper is to correct errors presented recently in the paper lv et al j stat phys 149 619 628 2012 where the authors analyzed fractional fokker planck equation ffpe with space time dependent drift f x t f x f t and diffusion d x t d x tilde d t coefficients in the factorized form we show an important drawback in the derivation of the stochastic representation of ffpe presented in the aforementioned paper which makes the whole proof wrong moreover we present a correct proof of their result in even more general case when both drift and diffusion can have any not necessarily factorized form

analytic model for transient anomalous diffusion with highly persistent correlations in recent decades many stochastic processes have been proposed as models for real world time series data with anomalous spreading highly persistent correlations and transient distributional characteristics we introduce the higher order fractional tempered stable motion as the stochastic integral of the tempered stable motion with respect to a generalized higher order moving average kernel which provides an analytic model for stochastic processes possessing these characteristics this stochastic process provides a mathematical model for anomalous diffusion with a transient distribution resembling higher order fractional stable motion on short timescales and higher order fractional brownian motion in the long run the specifics of the crossover dynamics from the levy stable anomalous diffusion to the gaussian anomalous diffusion are controlled by explicit parameter values that correspond to physical attributes of the process it is well suited to modeling anomalous diffusion of any type sub super regular or hyperdiffusion under appropriate parametrizations due to its power law scaling of variance with respect to time it is also a useful model for position velocity acceleration triples due to its convenient path differentiability and integrability properties to highlight the potential physical relevance of this model for real world data we outline its key statistical properties including its covariance structure memory and second order self similarity we also give an easy to implement elementary method for sample path generation which may be used as a basis for simulation and monte carlo studies

cusping transport and variance of solutions to generalized fokker planck equations we study properties of solutions to generalized fokker planck equations through the lens of the probability density functions of anomalous diffusion processes in particular we examine solutions in terms of their cusping travelling wave behaviours and variance within the framework of stochastic representations of generalized fokker planck equations we give our analysis in the cases of anomalous diffusion driven by the inverses of the stable tempered stable and gamma subordinators demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model we also analyse the cases where the underlying anomalous diffusion contains a levy jump component in the parent process and when a diffusion process is time changed by an uninverted levy subordinator on the whole we present a combination of four criteria which serve as a theoretical basis for model selection statistical inference and predictions for physical experiments on anomalously diffusing systems we discuss possible applications in physical experiments including with reference to specific examples the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue

brief paper identification of hammerstein systems in presence of hysteresis backlash and hysteresis relay nonlinearities the problem of identifying hammerstein systems hamsys is addressed in presence of hysteresis backlash hb and hysteresis relay hr nonlinearities the memory feature makes it impossible to get a system parameterization involving linearly all unknown parameters therefore the linear subsystem and the nonlinear element are estimated separately the identification process involves appropriate system parameterizations and least squares like parameter estimators specific input signals are designed to guarantee persistent excitation pe and estimator consistency

on the convergence of an iterative algorithm used for hammerstein system identification an analytical counterexample to the general convergence of an interative algorithm used for identification of hammerstein systems is given numerical illustration is also included

parameter bounds for discrete time hammerstein models with bounded output errors in this note we present a two stage procedure for deriving parameters bounds in hammerstein models when the output measurement errors are bounded first using steady state input output data parameters of the nonlinear part are tightly bounded then for a given input transient sequence we evaluate tight bounds on the unmeasurable inner signal which together with noisy output measurements are used for bounding the parameters of the linear dynamic block

recursive identification of hammerstein systems with discontinuous nonlinearities containing dead zones this note deals with the recursive parameter identification of hammerstein systems with discontinuous nonlinearities i e two segment piecewise linear with dead zones and preloads a special form of the hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables the proposed method is illustrated by examples

fractional fokker planck equation with tempered α stable waiting times langevin picture and computer simulation in this paper we introduce a langevin type model of subdiffusion with tempered stable waiting times we consider the case of space dependent external force fields the model displays subdiffusive behavior for small times and it converges to standard gaussian diffusion for large time scales we derive general properties of tempered anomalous diffusion from the theory of tempered stable processes in particular we find the form of the fractional fokker planck equation corresponding to the tempered subdiffusion we also construct an algorithm of simulation of sample paths of the introduced process we apply the algorithm to approximate solutions of the fractional fokker planck equation and to study statistical properties of the tempered subdiffusion via monte carlo methods

frequency domain identification of hammerstein models discusses hammerstein model identification in the frequency domain using sampled input output data by exploring the fundamental frequency and harmonics generated by the unknown nonlinearity we propose a frequency domain approach and show its convergence for both the linear and nonlinear subsystems in the presence of noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

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

least squares solutions of bilinear equations abstract the problem of finding a least squares solution for a system of bilinear equations is investigated sufficient conditions to have a unique minimum are given in the case of random inputs three methods the normalized iterative method the over parameterization method and the numerical method are presented for solving the problem along with their convergence properties simulation examples are provided

brief paper discrete time adaptive control of linear systems with preload nonlinearity in this note a method is presented for doing discrete time adaptive control of a nonlinear system which is given by a cascade connection of a preload nonlinearity followed by a linear system it is shown that the algorithm will ensure that the closed loop system is globally convergent with a specific residue and stable for both the deterministic and stochastic cases

identification of a class of nonlinear autoregressive models with exogenous inputs based on kernel machines in this paper we propose a new approach to identify a new class of nonlinear autoregressive models with exogenous inputs narx based on kernel machine and space projection kmsp the well known hammerstein wiener model which includes blocks of nonlinear static functions in series with a linear dynamic block is a subset of the narx models considered in the kmsp based approach kernel machine is used to represent the functions and space projection to separate the represented functions we also discuss two possible ambiguities and give conditions to avoid such ambiguities the asymptotic behavior of the proposed approach is analyzed the performance of the proposed method is verified by simulation studies

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

parallel procedure for the design of observers in high order multivariable systems this paper considers the design of minimal order observers for reconstructing the state of high order multivariable systems the given system is first transformed to a lower block hessenberg form by means of orthogonal state coordinate transformations then the transformed system matrices along with certain assumed block forms for the observer matrices enable the constraint equations to be decomposed and solved effectively it is shown that a parallel procedure can be used to solve certain chain equations arising from this block decomposition

identification of nonlinear systems using a piecewise linear hammerstein model abstract in the paper a method for nonlinear system identification is proposed it is based on a piecewise linear hammerstein model which is linear in the parameters the model and the identification algorithm are adapted to allow the parameter identification in the presence of a special form of the excitation signal the identification method is derived from a recursive least squares algorithm which is properly adapted to take into account the proposed model structure and the properties of the identification signal the applicability of the approach is illustrated by an example in which a discontinuous nonlinear static function is connected to a dynamic block

parameter identification of discontinuous hammerstein systems the paper deals with the parameter identification of hammerstein systems having discontinuous asymmetric nonlinearities two segment piecewise linear with preload and dead zone application of a simple decomposition technique provides a special form of hammerstein model with a minimum number of parameters the identification is carried out with only one record of measured input output data despite the dead zone to demonstrate the feasibility of the identification method some illustrative examples are included

brief paper parameter identification of hammerstein systems containing backlash operators with arbitrary shape parametric borders a two stage parameter identification method is developed for hammerstein systems containing backlash nonlinearities bordered by parametric arbitrary shape lines in the first stage a persistently exciting input is designed so that the linear subsystem can be made decoupled from the nonlinear element therefore linear subsystem identification is coped with using a least squares estimator enjoying consistency due to input persistent excitation then the backlash parameters are estimated using appropriate periodic exciting signals and consistent parameter estimators

brief paper revisiting hammerstein system identification through the two stage algorithm for bilinear parameter estimation the two stage algorithm tsa has been extensively used and adapted for the identification of hammerstein systems it is essentially based on a particular formulation of hammerstein systems in the form of bilinearly parameterized linear regressions this paper has been motivated by a somewhat contradictory fact though the optimality of the tsa has been established by bai in 1998 only in the case of some special weighting matrices the unweighted tsa is usually used in practice it is shown in this paper that the unweighted tsa indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix this provides a theoretical justification of the unweighted tsa and also leads to a generalization of the obtained result to the case of colored noise with noise whitening numerical examples of identification of hammerstein systems are presented to validate the theoretical analysis

iterative algorithm for parameter identification of hammerstein systems with two segment nonlinearities this paper deals with parameter identification of hammerstein systems having two segment polynomial nonlinearities the application of a simple decomposition technique and using switching sequences provide a special form of a hammerstein model that is linear in parameters this model is used in an iterative algorithm enabling simultaneous estimation of all of the model parameters to demonstrate the feasibility of the identification method more illustrative examples are included

a blind approach to closed loop identification of hammerstein systems this paper is a continuing study of the blind approach for the hammerstein identification in sun et al 1999 and bai and fu 2002 in the framework of a closed loop sampled data system the output is sampled faster than the updating period of the input the parameters of the linear dynamics are consistently estimated from the information of the output only after which the unmeasurable inner signal is uniquely reconstructed the noise effect is explicitly considered in both the parameter and inner signal estimation the estimation of the system orders and time delay are studied on the basis of two groups of basic equations obtained by polyphase decomposition the proposed blind approach is validated and illustrated by a simulated numerical example

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed

comments on parallel procedure for the design of observers in high order multivariable systems shafai 1988 proposed a state observer design algorithm which is very slightly different from an earlier algorithm of tsui 1985 furthermore the change made by shafai severely worsens the parallel computation property the only key property of his algorithm claimed by shafai it is important to mention that this comment is obviously valid for the dual version of shafai s algorithm state feedback design for pole assignment which has appeared elsewhere several times recently

identification scheme for hammerstein output error models with bounded noise this technical note presents a method for the identification of hammerstein output error hoe models corrupted by bounded noise the method is based on an iterative scheme using two optimal bounding ellipsoid obe type algorithms the proposed approach allows the joint estimation of the linear part and of the nonlinear part with a low computational burden a numerical example is given so as to show the efficiency of the method