thick points for planar brownian motion and the erdős taylor conjecture on random walk and conjectured that the limit exists and equals 1 tr a s the importance of determining the value of this limit is clarified in 1 3 below where this value appears in the power laws governing the local time of the walk the erd6s taylor conjecture was quoted in the book by r v sz 19 w but to the best of our knowledge the bounds in 1 1 were not improved prior to the present paper as it turns out an important step towards our solution of the erd6s taylor conjecture was the formulation by perkins and taylor 17 of an analogous problem on the maximal occupation measure that planar brownian motion run for unit time can

nonparametric system identification by kernel methods a new nonparametric estimate for nonlinear discrete time dynamic systems is considered the new algorithm is weakly consistent under a specific condition on the transition probability operator of a stationary markov process the estimate is applicable when a parametric state model of the system is difficult to choose

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

strong solutions of stochastic models for viscoelastic flows of oldroyd type abstract in this work we study stochastic oldroyd type models for viscoelastic fluids in r d d 2 3 we show existence and uniqueness of strong local maximal solutions when the initial data are in h s for s d 2 d 2 3 probabilistic estimate of the random time interval for the existence of a local solution is expressed in terms of expected values of the initial data

optimal control of deterministic systems via shifted legendre polynomials the synthesis of an optimal control function for deterministic systems described by integrodifferential equations is investigated by using the elegant operational properties of shifted legendre polynomials a direct computational algorithm for evaluating the optimal control and trajectory of deterministic systems is developed an example is given to illustrate the utility of this method

determining continuous time state equations from discrete time state equations via the principal q th root method fast computational methods are developed for finding the equivalent continuous time state equations from discrete time state equations the computational methods utilize the direct truncation method the matrix continued fraction method and the geometric series method in conjunction with the principal q th root of the discrete time system matrix for quick determination of the approximants of a matrix logarithm function it is shown that the use of the principal q th root of a matrix enables us to enlarge the convergence region of the expansion of a matrix logarithm function and to improve the accuracy of the approximants of the matrix logarithm function

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

a nonparametric polynomial identification algorithm for the hammerstein system almost all existing hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable to overcome this defect in this paper a new nonparametric polynomial identification algorithm for the hammerstein system is proposed which extends the idea in the author s previous work 1993 1994 on the hammerstein system identification to a more general and practical case where no functional value of the system nonlinearity is known a priori convergence and convergence rates in both uniform and global senses are established and simulation studies demonstrate the effectiveness and advantage of the new algorithm

analysis and parameter estimation of bilinear systems via block pulse functions problems of analysis and parameter estimation of bilinear systems via block pulse functions are discussed and recursive algorithms convenient for computers are presented compared with walsh function approaches the results are much simpler in form in this method any positive integer can be chosen as the number of sub intervals consequently much computing time and storage can be saved and the recursive algorithms developed also make it possible to identify on line the parameters of bilinear systems

iterative nonparametric estimation of a log optimal portfolio selection function let stock market vectors form a stationary ergodic sequence for fixed d spl isin n a log optimal portfolio selection function of the past d observed vectors is iteratively estimated on the basis of a training sequence by use of gradients and nonparametric regression strong consistency is obtained under a boundedness and spl alpha mixing condition without further assumptions on the distribution

analysis and parameter identification of bilinear systems via shifted legendre polynomials the problems of analysis and parameter identification of lime delay systems have been recently studied using rectangular functions such as walsh and block pulse functions in this paper the continuous shifted legendre polynomials are first used to solve the above mentioned problems the approach followed is that of converting the delay differential equation to an algebraic form through using the operational matrices of integration and delay the key point is the derivation of a delay operational matrix d which relates the coefficient vector x of the shifted legendre series of a given function x t with the coefficient vector x of its delay form x t in the form x dx where the elements of a are obtained from the initial function of x t two computational examples are given to illustrate the utility of the method the availability of recursive algorithms for constructing the delay operational matrix d makes the method particularly attractive to practise

stochastic landau lifshitz gilbert equation with anisotropy energy driven by pure jump noise abstract in this work we study a stochastic three dimensional landau lifshitz gilbert equation with non zero anisotropy energy which is drive by pure jump noise we show existence of weak martingale solutions taking values in a two dimensional sphere s 2 the construction of the solution is based on the classical faedo galerkin approximation the compactness method and the jakubowski version of the skorokhod theorem for nonmetric spaces

uniform measure results for the image of subsets under brownian motion the paper obtains bounds on the hausdorff and packing measures of the imagex e of a borel sete by a transient strictly stable processx t which a s hold for alle and for every measure function h beta gamma s s beta left log s right gamma star in some cases examples are constructed to show that the bounds are sharp

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

nonparametric identification of wiener systems by orthogonal series a wiener system i e a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade is identified both the input signal and disturbance are random white and gaussian the unknown nonlinear characteristic is strictly monotonous and differentiable and therefore the problem of its recovering from input output observations of the whole system is nonparametric it is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed the estimates apply the trigonometric legendre and hermite orthogonal functions pointwise consistency of all the algorithms is shown under some additional smoothness restrictions the rates of their convergence are examined and compared an algorithm to identify the impulse response of the linear subsystem is proposed

uniform consistency of kernel estimators of a regression function under generalized conditions abstract in this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data in addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous we consider the cases that some regressors are discrete and the data are either stationary mixing themselves or generated by a class of functions of one sided infinite stationary mixing sequences moreover we demonstrate the performance of the kernel estimation method under these generalized conditions by a numerical example

stochastic approximation in nonparametric identification of hammerstein systems derived from the idea of stochastic approximation recursive algorithms to identify a hammerstein system are presented two of them recover the characteristic of the nonlinear memoryless subsystem while the third one estimates the impulse response of the linear dynamic part the a priori information about both subsystems is nonparametric consistency in quadratic mean is shown and the convergence rate is examined results of numerical simulation are also presented

identification of a class of nonlinear continuous time systems using hartley modulating functions most of the existing approaches to identification of nonlinear dynamic systems involve matching a given input output behaviour with empirical discrete time approximations such as artificial neural networks kolmogorov gabor polynomials radial basis function networks etc techniques for dealing with physically based continuous time models are either applicable to only a restricted class of systems or are computationally very demanding in this paper a new methodology is presented that is applicable to a large class of nonlinear continuous time systems by defining a set of hartley modulating functions for characterizing the continuous process signals the advantages of this new class of modulating functions are that a set of algebraic equations with real coefficients results the formulations are free from boundary conditions and the computations can be made using fast algorithms for the discrete hartley transformation the resulting estimation scheme is applied to different categories of nonlinear syst

analysis and identification of non linear systems via shifted jacobi series based on shifted jacobi series algorithms have been established for the analysis and identification of non linear systems described by a hammerstein model consisting of a single valued non linearity followed by a linear plant moreover the parameter estimation of a certain non linear lumped system is also presented by using the shifted jacobi expansion for the analysis the solution of a non linear state equation is reduced to the solution of a linear algebraic matrix equation for the identification by expanding the measured input output data into the shifted jacobi series the unknown parameters of the non linear system are estimated through the least squares method examples are given to demonstrate the usefulness of this approach

linear systems identification from random threshold binary data a new identification problem of estimating parameters of linear dynamic systems from random threshold binary observations of its output and input is stated the only available data are collected as a result of checking whether a signal reached a randomly specified threshold at a randomly chosen instant of time the proposed estimation algorithm is based on the celebrated von neumann theorem which was earlier used mainly for generating random numbers strong consistency of parameters estimate from low cost output binary observations is proved assuming deterministic input signal of a finite duration possibilities of relaxing the assumption used in the theoretical part of the paper are considered by means of simulations

series expansion approach to the analysis and identification of discrete hammerstein systems in this paper a finite series expansion method is presented for the analysis and parameter identification of a discrete non linear system that is described by a hammerstein model consisting of a memoryless gain of polynomial form followed by a linear discrete system by expanding the system variables in discrete legendre orthogonal polynomials dlops and using the shift and product operational properties of dlops the hammerstein model is converted into a set of linear equations in the dlop coefficients of unknown output variables and in the system parameters this converted set of linear algebraic equations is convenient for finding the dlop coefficients of unknown variables also it allows one to determine the unknown system parameters using the least squares method when the system input and output data are available

random forests and kernel methods random forests are ensemble methods which grow trees as base learners and combine their predictions by averaging random forests are known for their good practical performance particularly in high dimensional settings on the theoretical side several studies highlight the potentially fruitful connection between the random forests and the kernel methods in this paper we work out this connection in detail in particular we show that by slightly modifying their definition random forests can be rewritten as kernel methods called kerf for kernel based on random forests which are more interpretable and easier to analyze explicit expressions of kerf estimates for some specific random forest models are given together with upper bounds on their rate of consistency we also show empirically that the kerf estimates compare favourably to the random forest estimates

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

large deviations and transitions between equilibria for stochastic landau lifshitz gilbert equation we study a stochastic landau lifshitz equation on a bounded interval and with finite dimensional noise we first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property next we prove the large deviations principle for the small noise asymptotic of solutions using the weak convergence method an essential ingredient of the proof is the compactness or weak to strong continuity of the solution map for a deterministic landau lifschitz equation when considered as a transformation of external fields we then apply this large deviations principle to show that small noise can cause magnetisation reversal we also show the importance of the shape anisotropy parameter for reducing the disturbance of the solution caused by small noise the problem is motivated by applications from ferromagnetic nanowires to the fabrication of magnetic memories

identification of non linear distributed systems via block pulse functions abstract a method using two dimension block pulse functions for estimating the parameters and initial and boundary conditions of a class of non linear distributed systems is presented compared with walsh function approaches it is more convenient for computer use and is simpler in form appropriate examples are included to illustrate the use of the proposed method

the shifted legend re approach to non linear system analysis and identification abstract applications of the shifted legendre polynomial expansion to the analysis and identification of the non linear system described by a hammerstein model which consists of a single valued non linearity followed by a linear plant are studied for the analysis by using the shifted legendre polynomial expansion the solution of a non linear state equation is reduced to the solution of a linear algebraic matrix equation for the identification through the shifted legendre expansions of the measured input output data the unknown parameters of both the linear plant and the characterization of the non linear element are estimated using the least squares method algorithms are presented numerical examples are given to illustrate the use of this approach

on identification of the controlled plants described by the hammerstein system a new polynomial identification method for the hammerstein system is proposed the method employs the results of nonparametric statistics and best approximation theory obtaining a polynomial form estimate of the nonlinearity in the system except continuity no conditions are imposed on the nonlinearity the uniform as well as global convergence of the method is established the rates of convergence in both cases are derived under mild conditions on the smoothness of the nonlinearity the method is especially suitable for identifying the controlled plants with the description of hammerstein systems

wong zakai approximation for the stochastic landau lifshitz gilbert equations abstract in this work we study stochastic landau lifshitz gilbert equations sllges in one dimension with non zero exchange energy only firstly by introducing a suitable transformation we convert the sllges to a highly nonlinear time dependent partial differential equation with random coefficients which is not fully parabolic we then prove that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property following regular approximation of the brownian motion and using reverse transformation we show existence of strong solution of sllges taking values in a two dimensional unit sphere s 2 in r 3 the construction of the solution and its corresponding convergence results are based on wong zakai approximation

packing and covering indices for a general levy process there has been substantial interest in the indices 0 2 defined by blumenthal and getoor determined by a general levy process in r d pruitt defined an index which determines the covering dimension and taylor showed that an index first considered by hendricks determines the packing dimension for the trajectory in the present paper we prove that b 2 min d and give examples to show that the whole range is attainable however we cannot completely determine the set of values of which can be attained as indices of some levy process

nonparametric estimation of nonlinear dynamic systems using semirecursive regression estimates abstract in the paper we apply semirecursive nonparametric estimation techniques for the estimation of dynamic systems we investigate in detail the estimation of hammerstein dynamic systems using kernel and partitioning regression estimates in particular we propose estimation algorithms and study their convergence for all distributions of the data

adaptive control for systems with bounded disturbances the authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum and nonminimum phase systems subject to bounded disturbances the parameter estimation scheme is a least squares algorithm with dead zone the dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates in the minimum phase case the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value the projection procedure can also be used to avoid pole zero cancellations in an adaptive pole placement algorithm

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

identification of time varying nonlinear systems using chebyshev polynomials abstract this paper is devoted to an identification of time varying nonlinear systems using chebyshev polynomials of the first kind for systems being linear relatively unknown functional parameters a method of approximate determination of these parameters has been worked out as the identification problems are ill posed to solve the obtained redefinite system of linear algebraic equations a regularization method is used

analysis and optimal control of time varying systems via chebyshev polynomials abstract the operational properties of the forward and backward integration and the product of chebyshev polynomials are derived these properties are applied to the analysis and optimal control of time varying linear systems by the approximation of time functions by truncated chebyshev series due to the unique property of the chebyshev polynomials excellent results are obtained as demonstrated by examples

neural network approach for identification of hammerstein systems in this paper four different on line gradient based learning algorithms for training neural network hammerstein models are presented in a unified framework these algorithms namely the backpropagation for series parallel models the backpropagation sensitivity method and truncated backpropagation through time algorithm bptt for parallel models are derived analysed and compared for the truncated bptt it is shown that determination of the number of unfolding time steps necessary to calculate the gradient with an assumed degree of accuracy can be made on the basis of impulse response functions of sensitivity models the algorithms are shown to differ in their computational complexity gradient approximation accuracy and convergence rates numerical examples are also included to compare the performance of the algorithms

wong zakai approximation for the stochastic landau lifshitz gilbert equations with anisotropy energy abstract the stochastic landau lifshitz gilbert equations sllges describe the behaviour of the magnetisation under the influence of the randomly fluctuating effective field in this work we consider the sllges in one space dimension in the presence of both the exchange energy and anisotropy energy and prove the existence of strong solution taking values in a two dimensional unit sphere s 2 in r 3 the key ingredients for the construction of the solution and its corresponding convergence results are the doss sussmann transformation maximal regularity property and the wong zakai approximation

graph laplacians and their convergence on random neighborhood graphs given a sample from a probability measure with support on a submanifold in euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold the graph laplacian of such a graph is used in several machine learning methods like semi supervised learning dimensionality reduction and clustering in this paper we determine the pointwise limit of three different graph laplacians used in the literature as the sample size increases and the neighborhood size approaches zero we show that for a uniform measure on the submanifold all graph laplacians have the same limit up to constants however in the case of a non uniform measure on the submanifold only the so called random walk graph laplacian converges to the weighted laplace beltrami operator

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

martingale solutions of nematic liquid crystals driven by pure jump noise in the marcus canonical form abstract in this work we consider a stochastic evolution equation which describes the system governing the nematic liquid crystals driven by a pure jump noise in the marcus canonical form the existence of a martingale solution is proved for both 2d and 3d cases the construction of the solution relies on a modified faedo galerkin method based on the littlewood paley decomposition compactness method and the jakubowski version of the skorokhod representation theorem for non metric spaces we prove that in the 2 d case the martingale solution is pathwise unique and hence deduce the existence of a strong solution

global identification of nonlinear hammerstein systems by recursive kernel approach abstract in this paper we discuss identification of hammerstein systems by the recursive kernel regression estimate we propose the identification algorithm and study its global convergence and the rate of convergence

measuring close approaches on a brownian path on obtient des tests integraux pour le taux d echappement uniforme d un mouvement brownien d dimensionnel

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

thick points for spatial brownian motion multifractal analysis of occupation measure let t x r denote the total occupation measure of the ball of radius r centered at x for brownian motion in ir we prove that sup x 1 t x r r log r 16 a s as r 0 thus solving a problem posed by taylor in 1974 furthermore for any a 0 16 the hausdorff dimension of the set of thick points x for which lim sup r 0 t x r r log r a is almost surely 2 a 8 this is the correct scaling to obtain a nondegenerate multifractal spectrum for brownian occupation measure analogous results hold for brownian motion in any dimension d 3 these results are related to the lil of ciesielski and taylor 1962 for the brownian occupation measure of small balls in the same way that levy s uniform modulus of continuity and the formula of orey and taylor 1974 for the dimension of fast points are related to the usual lil we also show that the lim inf scaling of t x r is quite different we exhibit non random c1 c2 0 such that c1 supx lim infr 0 t x r r 2 c2 a s in the course of our work we provide a general framework for obtaining lower bounds on the hausdorff dimension of random fractals of limsup type

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

nonparametric identification of a particular nonlinear time series system a nonlinear time series system is identified the system has a cascade structure that is it consists of a nonlinear memoryless element followed by a dynamic linear system given a gaussian input a hermite series based method for recovering the system nonlinearity is presented the proposed identification procedure is nonparametric since it is able to be consistent for a broad class of nonpolynomial characteristics the consistency and rate of convergence of the procedure are established also some data driven methods for selecting the optimal number of terms in the procedure are proposed the results are illustrated by a numerical example

thick points for intersections of planar sample paths let l x n x denote the number of visits to x z 2 of the simple planar random walk x up to step n let x be another simple planar random walk independent of x we show that for any 0 b 1 2 there are n 1 2 b o 1 points x e z 2 for which l x n x l x n x b 2 logn 4 this is the discrete counterpart of our main result that for any a 1 the hausdorff dimension of the set of thick intersection points x for which limsup r 0 i x r r 2 log r 4 a 2 is almost surely 2 2a here i x r is the projected intersection local time measure of the disc of radius r centered at x for two independent planar brownian motions run until time 1 the proofs rely on a multi scale refinement of the second moment method in addition we also consider analogous problems where we replace one of the brownian motions by a transient stable process or replace the disc of radius r centered at x by x rk for general sets k

global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation an improved exponential bound on the l sub 1 error for the recursive kernel regression estimates is derived it is shown using the martingale device that weak strong and complete l sub 1 consistencies are equivalent consequently the conditions on a certain smoothing sequence are necessary and sufficient for strong l sub 1 consistency of the recursive kernel regression estimate the rates of global convergence are also given obtained results are applied to recursive classification rules and to nonlinear time series estimation

computational algorithms for multiscale identification of nonlinearities in hammerstein systems with random inputs simple and efficient computational algorithms for nonparametric wavelet based identification of nonlinearities in hammerstein systems driven by random signals are proposed they exploit binary grid interpolations of compactly supported wavelet functions the main contribution consists in showing how to use the wavelet values from the binary grid together with the fast wavelet algorithms to obtain the practical counterparts of the wavelet based estimates for irregularly and randomly spaced data without any loss of the asymptotic accuracy the convergence and the rates of convergence are examined for the new algorithms and in particular conditions for the optimal convergence speed are presented efficiency of the algorithms for a finite number of data is also illustrated by means of the computer simulations

le comportement du mouvement brownien entre les deux instants ou il passe par un point double abstract a precise meaning is given to the following intuitive statement between the two times when it hits a double point a brownian motion behaves like a brownian bridge the main tool is the notion of intersection local time which provides a measure on the set of double points and hence a notion of properties of almost all double points results are applied to study points of infinite multiplicity of plane brownian paths

controller design oriented model identification method for hammerstein system abstract the paper proposes a new polynomial identification method for the hammerstein system by combining the results of parameter estimation theory and functions approximation theory the method circumvents many disadvantages of the earlier methods it is suitable for producing the controller design oriented model of hammerstein system consistency and convergency analysis are given for the obtained parameter estimates of the system s linear dynamics and approximating polynomial of its nonlinear memoryless element respectively simulation study verifies the effectiveness of the method