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

a finite volume solution to the geophysical electromagnetic forward problem using unstructured grids abstractthe application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces we investigated the generalization of the standard yee s staggered scheme to unstructured tetrahedral voronoi grids using a finite volume approach we discretized the helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements to compute the electric and magnetic fields at the observation points an interpolation technique was employed which uses the edge vector interpolation functions of the tetrahedral elements to verify the presented scheme two examples were evaluated which revealed the computation of the total and secondary fields due to ele

model structure simplification of nonlinear systems via immersion this paper concerns the simplification of model structures of nonlinear systems while preserving their input output maps the basic technique is an immersion of a system which is a mapping of the initial state from the original system to another system of an identical input output map the necessary and sufficient conditions are presented for the immersibility of a given system into a state space representation of such particular structures as rational functions or polynomials with respect to the state the conditions are so mild that many types of nonlinear systems can be represented by rational or polynomial model structures moreover it is also shown that a polynomial state space representation can always be constructed to be at most quadratic with respect to the state

a bootstrap method for structure detection of narmax models many systems may be described by narmax models using only a few terms however depending on the order of the system the number of candidate terms can become very large selection of a subset of these candidate terms is necessary for an efficient system description this is an unresolved issue in system identification for over parameterized models therefore in this paper we develop a bootstrap structure detection bsd algorithm as a means of determining the structure of highly over parameterized models the performance of this bsd technique was evaluated by using it to estimate the structure of a 1 simple narmax model 2 moderately over parameterized narmax model and 3 highly over parameterized narmax model the results demonstrate that the bsd algorithm is a robust method for detecting the structure of narmax models this method provides accurate estimates of parameter statistics without relying on assumptions made by traditional procedures and yields a parsimonious description of the system

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

stable evaluation of green s functions in cylindrically stratified regions with uniaxial anisotropic layers we present a robust algorithm for the computation of electromagnetic fields radiated by point sources hertzian dipoles in cylindrically stratified media where each layer may exhibit material properties permittivity permeability and conductivity with uniaxial anisotropy analytical expressions are obtained based on the spectral representation of the tensor green s function based on cylindrical bessel and hankel eigenfunctions and extended for layered uniaxial media due to the poor scaling of these eigenfunctions for extreme arguments and or orders direct numerical evaluation of such expressions can produce numerical instability i e underflow overflow and or round off errors under finite precision arithmetic to circumvent these problems we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain to yield a robust algorithm for all parameter ranges numerical results are presented to illustrate the robustness of the formulation including cases of practical interest

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

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

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

minimal realization of nonlinear systems described by input output difference equations we consider a general class of nonlinear discrete time systems described by their input output i o relationship we first present the necessary and sufficient conditions for existence of a local observable state space realization of the system and an explicit algorithm for computing it in cases where the i o map and its resulting realization are nonminimal we formulate an algorithm for extracting its minimal realization whenever possible the developed theory and algorithms are illustrated by means of several examples

identification of multivariable bilinear state space systems based on subspace techniques and separable least squares optimization we discuss identification of discrete time bilinear state space systems with multiple inputs and multiple outputs subspace identification methods for bilinear systems suffer from the curse of dimensionality already for relatively low order systems the matrices involved become so large that the method cannot be used in practice we have modified the subspace algorithm such that it reduces the dimension of the matrices involved only the rows that have the largest influence on the model are selected the remaining rows are discarded this obviously leads to an approximation error the initial model that we get from the subspace method is optimized using the principle of separable least squares according to this principle we can first solve for the matrices that enter non linearly in the output error criterion and then obtain the others by solving a linear least squares problem

new spectral lanczos decomposition method for induction modeling in arbitrary 3 d geometry traditional resistivity tools are designed to function in vertical wells in horizontal well environments the interpretation of resistivity logs becomes much more difficult because of the nature of 3 d effects such as highly deviated bed boundaries and invasion the ability to model these 3 d effects numerically can greatly facilitate the understanding of tool response in different formation geometries three dimensional modeling of induction tools requires solving maxwell s equations in a discrete setting either finite element or finite difference the solutions of resulting discretized equations are computationally expensive typically on the order of 30 to 60 minutes per log point on a workstation this is unacceptable if the 3 d modeling code is to be used in interpreting induction logs in this paper we propose a new approach for solutions to maxwell s equations the new method is based on the spectral lanczos decomposition method sldm with krylov subspaces generated from the inverse powers of th

stabilizing predictive control of nonlinear arx models in this paper a predictive control algorithm for nonlinear discrete time systems is presented starting from a state space model conditions for the asymptotic tracking of constant reference signals in a neighbourhood of a given equilibrium are first derived then it is shown that the system under control can be locally described in terms of a suitable narx nonlinear arx model which in practice can be identified by means of well established techniques for the narx model a receding horizon predictive control algorithm is proposed which guarantees local stability and robust asymptotic tracking in the neighbourhood of the equilibrium conditions for local stability and tracking are given in terms of reachability observability and transmission zeros of the linearization of the original state space system around the equilibrium an example is reported to illustrate the effectiveness of the proposed method

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

output dead beat control for a class of planar polynomial systems output dead beat control for a class of nonlinear discrete time systems which are described by a single input output i o polynomial difference equation is considered the class of systems considered is restricted to systems with a two dimensional state space description it is assumed that the highest degree with which the present input appears in the equation is odd necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented we also design a minimum time output dead beat control algorithm feedback controller which yields stable zero dynamics whenever this is feasible a number of interesting phenomena are discussed and illustrated with examples

a proposed stepwise regression method for model structure identification this paper proposes a new methodology for constructing groundwater models the proposed methodology which determines simultaneously both model structure and model parameters is based on the following ideas 1 when solving the inverse problem different model structures always produce different model parameters 2 since the number of possible model structures of an aquifer is infinite the number of possible representative parameters is also infinite 3 to obtain a set of appropriate representative model parameters we must have an appropriate model structure and 4 an appropriate model structure should be determined not only by observation data and prior information but also by the accuracy requirements of model applications in this proposed methodology we start with a homogeneous model structure and step by step gradually increase the complexity of the model structure at each level of complexity we calculate not only the fitting residual of parameter identification but also the error of model structure to determine if a more complex model structure is needed the model structure error of using one model structure to replace another model structure is defined by a maximum minimum max min problem that is based on the distance between the two models and is measured in parameter observation and prediction or decision spaces this proposed methodology is used to solve a hypothetical remediation design problem in which the true hydraulic conductivity is a random field with a certain trend we have found that for the example problem virtually identical pumping policy is obtained when a five zone model with an optimized zonation pattern is used to represent the nonstationary random field we have also found that observation errors have minimum impact on management solution in comparison with structure errors to calculate the model structure error for this example the inverse solution is coupled with a management problem we have also developed an effective iteration method to handle nonlinear water quality constraints

smoothing data with local instabilities for the identification of chaotic systems chaotic systems are characterized by the local divergence of nearby orbits in state space this provokes a sensitive dependence on initial conditions and in turn drastically limits the accuracy of long term predictions this has important implications in the filtering of data generated by such systems in the present paper the use of global smoothers for chaotic data is investigated the ultimate objective is to be able to identify dynamically valid models from smoothed data when the identification from the original noisy data has completely failed the objective is to produce identified models that faithfully reproduce the dynamical invariants of the original system such as the geometry of the attractors in state space the largest lyapunov exponent fractal dimensions and poincare sections numerical examples are included which illustrate the main points of the paper

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

algebraic necessary and sufficient conditions for the controllability of conewise linear systems the problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable this paper focuses on conewise linear systems i e systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions for this class of systems we present algebraic necessary and sufficient conditions for controllability we also show that the classical results of controllability of linear systems and input constrained linear systems can be recovered from our main result our treatment employs tools both from geometric control theory and mathematical programming

a fast nonlinear model identification method the identification of nonlinear dynamic systems using linear in the parameters models is studied a fast recursive algorithm fra is proposed to select both the model structure and to estimate the model parameters unlike orthogonal least squares ols method fra solves the least squares problem recursively over the model order without requiring matrix decomposition the computational complexity of both algorithms is analyzed along with their numerical stability the new method is shown to require much less computational effort and is also numerically more stable than ols

inexact preconditioned conjugate gradient method with inner outer iteration an important variation of preconditioned conjugate gradient algorithms is inexact preconditioner implemented with inner outer iterations g h golub and m l overton numerical analysis lecture notes in math 912 springer berlin new york 1982 where the preconditioner is solved by an inner iteration to a prescribed precision in this paper we formulate an inexact preconditioned conjugate gradient algorithm for a symmetric positive definite system and analyze its convergence property we establish a linear convergence result using a local relation of residual norms we also analyze the algorithm using a global equation and show that the algorithm may have the superlinear convergence property when the inner iteration is solved to high accuracy the analysis is in agreement with observed numerical behavior of the algorithm in particular it suggests a heuristic choice of the stopping threshold for the inner iteration numerical examples are given to show the effectiveness of this choice and to compare the convergence bound

modelling and identification of non linear deterministic systems in the delta domain this paper provides a formulation for using the delta operator in the modelling of non linear systems it is shown that a unique representation of a deterministic non linear auto regressive with exogenous input narx model can be obtained for polynomial basis functions using the delta operator and expressions are derived to convert between the shift and delta domain a delta narx model is applied to the identification of a test problem a van der pol oscillator a comparison is made with the standard shift operator non linear model and it is demonstrated that the delta domain approach improves the numerical properties of structure detection leads to a parsimonious description and provides a model that is closely linked to the continuous time non linear system in terms of both parameters and structure

application of a least absolute shrinkage and selection operator to aeroelastic flight test data identification of non linear systems involves estimating unknown parameters and model regressor selection selection of a subset of candidate terms that best describes the observed output model selection is an important step in black box modelling of any observed process this procedure is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design in this study a least absolute shrinkage and selection operator lasso technique is investigated for computing efficient model descriptions of non linear aeroelastic systems the lasso minimises the residual sum of squares by the addition of an l1 penalty term on the parameter vector of the traditional l2 minimisation problem its use for model selection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and the

improved structure selection for nonlinear models based on term clustering in this paper the concepts of term clusters and cluster coefficients are defined and used in the context of system identification it is argued that if a certain type of term in a nonlinear model is spurious the respective cluster coefficient is small compared with the coefficients of the other clusters represented in the model once the spurious clusters have been detected the corresponding terms can be deleted from the set of candidate terms the consequences of doing this are i a drastic reduction in the size of the set of candidate terms and consequently a substantial gain in computation time is achieved ii the final estimated model is more likely to reproduce the dynamics of the original system and iii the final model is more robust to overparametrization numerical examples are included to illustrate the new procedure

on determining the structure of a non linear system abstract a method is presented for constructing a model of a non linear system from the input output data the structure of the system is assembled from a library of nonlinear terms that are possible suspects for inclusion in the model while each possible model structure is represented by a node in a tree it is shown that searching the tree for the optimal n term model structure can be done in n stages using an algorithm based on conjugate direction ideas the essential feature of the technique is that it generates a sequence of projection matrices such that the original vector valued functions become conjugate directions this leaves the original non linear terms intact and allows the structure for the optimal n term model to be assembled in n selections from the library examples are presented from regression analysis and non linear dynamic systems

brief paper structure detection and parameter estimation for narx models in a unified em framework in this paper we consider structure detection and parameter estimation of the nonlinear auto regressive with exogenous inputs narx model using the em expectation maximisation algorithm the parameter estimation step uses particle smoothing to obtain the necessary expectations in the e step and the parameters are then estimated in closed form in the m step the model structure detection is performed using an f test which makes use of the parameter information matrix inverse of the covariance matrix obtained from an augmentation of the em algorithm the steps for obtaining the information matrix are robust guaranteeing a positive semi definite information matrix to use in the structure detection step for the case of unknown model orders a method is proposed using the stochastic complexity sc information criterion for selecting between candidate models the sc is composed of the information matrix representing model complexity and a likelihood estimate representing model accuracy which are both generated as byproducts of the augmented em algorithm numerical results demonstrate that the em approach performs well in comparison to a standard alternative based on orthogonal least squares and also avoids the need to estimate a noise model for the case of measurement noise corrupted output signals

optimal experiment design for regression polynomial models identification in this paper the problem of optimal experimental design for parameter identification of static non linear blocks is addressed non linearities are assumed to be polynomial and represented according to the vandermonde base the optimality problem is formulated in a set membership context and the cost functions to be minimized are the worst case parameter uncertainties closed form optimal input sequences are derived when the input u is allowed to vary on a given interval u a u b since optimal input sequences are in general not invariant to base changes results and criteria for representing polymomials with different bases still preserving the optimal set of input levels derived from the vandermonde parameterization are introduced as well finally numerical results are reported showing the effectiveness of using optimal input sequences especially when identifying some block described dynamic models that include in their structure static non linearities such as hammerstein and lpv models in su

an implementation of the qmr method based on coupled two term recurrences recently we proposed a new krylov subspace iteration the quasi minimal residual algorithm qmr 1 for solving general nonsingular non hermitian systems of linear equations ax b 1

brief further results on localization based switching adaptive control we investigate a switching adaptive control scheme based on falsification which is conceptually different from existing switching adaptive control schemes a feature of the proposed localization method is its fast model falsification capability in the lti case this is manifested as the rapid convergence of the switching controller by analysing the geometry of localization we give a complete solution to the problem of optimal localization

a two stage algorithm for identification of nonlinear dynamic systems this paper investigates the two stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear in the parameters models and the model has to be built from a very large pool of basis functions or model terms the main objective is to improve the compactness of the model that is obtained by the forward stepwise methods while retaining the computational efficiency the proposed algorithm first generates an initial model using a forward stepwise procedure the significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced resulting in an optimised compact model with significantly improved performance the main contribution of this paper is that these two stages are performed within a well defined regression context leading to significantly reduced computational complexity the efficiency of the algorithm is confirmed by the computational complexity analysis and its effectiveness is demonstrated by the simulation results

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

a globally consistent nonlinear least squares estimator for identification of nonlinear rational systems this paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs despite its long history a globally consistent identification algorithm remains illusive this paper proposes a globally convergent identification algorithm for such nonlinear rational systems to the best of our knowledge this is the first globally convergent algorithm for the nonlinear rational systems the technique employed is a two step estimator though two step estimators are known to produce consistent nonlinear least squares estimates if a n consistent estimate can be determined in the first step how to find such a n consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two step estimators the technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step this is achieved by involving model transformation bias analysis noise variance estimation and bias compensation in the paper two simulation examples and a practical example are provided to verify the good performance of the proposed two step estimator

output deadbeat control of nonlinear discrete time systems with one dimensional zero dynamics global stability conditions output deadbeat control in one step is considered for a class of discrete time systems described by a nonlinear single input single output recursive representation global stability conditions are established for the particular subclass of systems with one dimensional zero dynamics the results are illustrated with applications to polynomial and neural dynamical systems

design of truncated maximum length ternary signals where their squared versions have uniform even harmonics the design of pseudo random maximum length prml ternary signals with properties suitable for identification of generalized quadratic hammerstein models is considered for such an application it is desirable for the signal to have odd harmonics uniform and even harmonics suppressed with its squared version having odd harmonics suppressed and even harmonics uniform to date the only class of signal known to possess such harmonic properties comprises of prml ternary signals based on galois field gf 3 and its extension fields in this note theoretical conditions for a prml signal to possess these properties are derived and imposed on the design of signals based on higher odd fields to generate truncated prml signals that fulfil the required specifications

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

identification of models for chaotic systems from noisy data implications for performance and nonlinear filtering abstract this paper investigates the identification of global models from chaotic data corrupted by additive noise it is verified that noise has a strong influence on the identification of chaotic systems in particular there seems to be a critical noise level beyond which the accurate estimation of polynomial models from chaotic data becomes very difficult similarities with the estimation of the largest lyapunov exponent from noisy data suggest that part of the problem might be related to the limited ability of predicting the data records when these are chaotic a nonlinear filtering scheme is suggested in order to reduce the noise in the data and thereby enable the estimation of good models this prediction based filtering incorporates a resetting mechanism which enables the filtering of chaotic data and which is also applicable to non chaotic data

a finite element based domain decomposition approach for plane wave 3d electromagnetic modeling we developed a novel parallel domain decomposition approach for 3d large scale electromagnetic induction modeling in the earth we used the edge based finite element method and unstructured meshes unstructured meshes were divided into sets of nonoverlapping subdomains we used the curl curl electric field equation to carry out the analysis in each subdomain the electric field was discretized by first order vector shape functions along the edges of tetrahedral elements the tangential components of the magnetic field on the interfaces of the subdomains were defined as a set of lagrange multipliers the unknown lagrange multipliers were solved from an interface problem defined on the interfaces of the subdomains with the availability of the lagrange multipliers the electric field values in each subdomain were solved independently three synthetic examples were evaluated to verify our code excellent agreement with previously published solutions was obtained synthetic examples revealed that our domain decomposition technique is scalable with respect to the number of subdomains and robust with regard to frequency and the heterogeneous distribution of material parameters i e electric conductivity electric permittivity and magnetic permeability

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

model quality in identification of nonlinear systems in this note the problem of the quality of identified models of nonlinear systems measured by the errors in simulating the system behavior for future inputs is investigated models identified by classical methods minimizing the prediction error do not necessary give small simulation error on future inputs and even boundedness of this error is not guaranteed in order to investigate the simulation error boundedness seb property of identified models a nonlinear set membership nsm method recently proposed by the authors is taken assuming that the nonlinear regression function representing the difference between the system to be identified and a linear approximation has gradient norm bounded by a constant spl gamma moreover the noise sequence is assumed unknown but bounded by a constant spl epsiv the nsm method allows to obtain validation conditions useful to derive validated regions within which to suitably choose the bounding constants spl gamma and spl epsiv moreover the method allows to derive an optimal estimate of the true system if the chosen linear approximation is asymptotically stable a necessary condition for the seb property in the present note a sufficient condition on spl gamma is derived guaranteeing that the identified optimal nsm model has the seb property if values of spl gamma in the validated region exist satisfying the sufficient condition the previous results can be used to give guidelines for choosing the bounding constants spl gamma and spl epsiv additional to the ones required for assumptions validation and useful for obtaining models with low simulation errors the numerical example representing a mass spring damper system with nonlinear damper and input saturation demonstrates the effectiveness of the presented approach

stabilizability and dead beat controllers for two classes of wiener hammerstein models two classes of block oriented models of the wiener hammerstein type are considered we prove that a generic condition is sufficient for a null controllable discrete time system of this form to have a stabilizing minimum time dead beat controller when the condition is violated we show how to design a nonminimum time stabilizing dynamic dead beat controller the result is used to obtain stabilizability conditions for these systems

spreading speed and traveling waves for a multi type sis epidemic model abstract the theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi type sis epidemic model to obtain the spreading speed c and the nonexistence of traveling waves with wave speed c c then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease free and endemic equilibria for c c this shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves we also give an affirmative answer to an open problem presented by rass and radcliffe l rass j radcliffe spatial deterministic epidemics math surveys monogr 102 amer math soc providence ri 2003

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

conservative modeling of 3 d electromagnetic fields part ii biconjugate gradient solution and an accelerator the preceding paper derives a staggered grid finite difference approximation applicable to electromagnetic induction in the earth the staggered grid finite difference approximation results in a linear system of equations ax b where a is symmetric but not hermitian this is solved using the biconjugate gradient method preconditioned with a modified partial cholesky decomposition of a this method takes advantage of the sparsity of a and converges much more quickly than methods used previously to solve the 3 d induction problem when simulating a conductivity model at a number of frequencies the rate of convergence slows as frequency approaches 0 the convergence rate at low frequencies can be improved by an order of magnitude by alternating the incomplete cholesky preconditioned biconjugate gradient method with a procedure designed to make the approximate solutions conserve current

output feedback stabilization of a class of wiener systems a globally stabilizing output feedback controller is designed for a class of continuous time wiener systems the wiener systems we consider consist of a linear dynamical block and an output polynomial nonlinearity connected in series the hybrid controller consists of three modes of operation which are periodically applied to the system the controller achieves a dead beat response of the closed loop system

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

a note on observability tests for general polynomial and simple wiener hammerstein systems we propose an algorithm based on symbolic computation packages for testing observability conditions of general polynomial systems which were formulated in sontag siam j control optim 17 1979 139 151 computational complexity of the observability test can be reduced and the test simplified for classes of polynomial systems we illustrate this by considering the class of simple wiener hammerstein systems which consist of a series of two linear dynamic blocks between which a static nonlinearity is sandwiched we consider the case when the nonlinearity is a monomial n q q 1 simple necessary and sufficient conditions for observability are given and they resemble but are subtly different from the well known result on observability for the series connection of two linear systems c 1998 elsevier science b v all rights reserved

treatment of singularity in the method of boundary integral equations for 2 5d electromagnetic modeling abstractfast and accurate simulation of responses of electromagnetic logging while drilling tools in 2d and 3d formations is important for further development of the proactive geosteering service which is currently based on the 1d layered model inversion in search of an optimal method of forward simulation we have developed boundary integral equations in a 2d formation model with planar boundaries a peculiarity of the method is that the number of grid nodes required for reaching a certain accuracy and hence the computation time increases as the transmitter approaches the boundary to retain efficiency in the case of transmitter boundary proximity we use the following modification of the method the main term of the calculated electromagnetic field namely the solution for the two layered model corresponding to the closest boundary is calculated by the well known explicit formulas whereas the anomalous field is found from the system of integral equations the modified method is implemented and tes

application of a general multi model approach for identification of highly nonlinear processes a case study an identification method for highly nonlinear processes is proposed based on a multi model approach and kolmogorov gabor polynomials owing to the large number of possible terms in this general model structure the significant terms are selected by several statistical test procedures leading automatically to a minimal order model realization the performance of this method is evaluated in an in depth case study using a simulated ph neutralization process the effects of important variables such as range of operating conditions signal noise ratio and data length are discussed

electromagnetic induction in a generalized 3d anisotropic earth part 2 the lin preconditioner a practical limitation in the use of generalized 3d forward modeling algorithms for inversion of electromagnetic data is the high computational cost of solving large ill conditioned systems of linear equations arising from the discretization of the governing maxwell equations to address this problem a new class of preconditioners has recently been proposed which is based on a helmholtz decomposition of the electric field in the low induction number lin regime this paper further develops that idea and introduces a lin preconditioner which can be applied to problems characterized by a fully generalized anisotropic medium included are sample calculations demonstrating a reduction by two orders of magnitude in the number of quasi minimal residual iterates and a speedup by a factor of approximately four in the solution time for one forward calculation also included are results previously unobtainable by standard jacobi preconditioning for simulating multicomponent induction sonde response in a horizo

nonlinear set membership prediction of river flow in the present paper a nonlinear set membership prediction method previously proposed by the authors is applied to a river flow prediction problem the method does not require the choice of the functional form of the model used for prediction but assumes a bound on the gradient norm of the regression function defining the model the method is used for the univariate prediction of the time series consisting of the mean daily discharges of the dora baltea river in northern italy taken from year 1941 to 1979 the obtained prediction performances are compared with those obtained by means of neural networks and of local linear approximation techniques used by other authors for this time series

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

set membership prediction of nonlinear time series in this paper a prediction method for nonlinear time series based on a set membership sm approach is proposed the method does not require the choice of the functional form of the model used for prediction but assumes a bound on the rate of variation of the regression function defining the model at the contrary most of the existing prediction methods need the choice of a functional form of the regression function or of state equations piecewise linear quadratic etc and this choice is usually the result of heuristic searches these searches may be quite time consuming and lead only to approximate model structures whose errors may be responsible of bad propagation of prediction errors especially for the multistep ahead prediction moreover the method proposed in this paper assumes only that the noise is bounded in contrast with statistical approaches which rely on noise assumptions such as stationarity ergodicity uncorrelation type of distribution etc the validity of these assumptions may be difficult to be reliably tested in many applications and is certainly lost in presence of approximate modeling in the present sm approach using a result developed in a previous paper the values of the bounds on the gradient of the regression function and on the noise can be suitably assessed to verify the validity tests two almost optimal prediction algorithms are then derived the second one having improved optimal properties over the first one at the expense of an increased computational complexity the method is tested and compared with other literature methods on the well known wolf sunspot numbers series widely used in the time series literature as a benchmark test and on the prediction of vertical dynamics of vehicles with controlled suspensions a simulation example is also presented to investigate how much conservative the sm approach may be in the most adverse situation where data are generated by a linear autoregressive ar model driven by i i d gaussian white noise and the sm prediction is compared with the optimal statistical predictor which makes use of the exact assumptions

controllability for a class of simple wiener hammerstein systems abstract controllability for a class of simple wiener hammerstein systems is considered necessary and sufficient conditions for dead beat and complete controllability for these systems are presented the controllability tests consist of two easy to check tests for the subsystems

identification of nonlinear systems in the presence of unknown but bounded disturbances this paper deals with recursive parameter estimation of nonlinear systems in the presence of unknown but bounded disturbances the proposed technique is performed by the use of a modified extended least squares algorithm so that the estimated parameters are consistent with the measurements and the noise constraints while local asymptotic convergence under very general conditions is assured one of the main features is to show from the stability analysis connection between some arbitrary factors and basin of attraction high performances from the design and implementation point of view will be shown through a numerical example under severe conditions

efficient 2 5d electromagnetic modeling using boundary integral equations abstractfast and accurate simulation of responses of logging while drilling lwd electromagnetic em tools in complex 2d and 3d formations is very important for reconstruction of the resistivity distribution in proactive geosteering currently real time interpretation is based on the 1d parametric inversion advances in fast simulation beyond the 1d model would open a way for real time 2d inversion we developed implemented numerically and tested an efficient method for simulation of lwd em tools in complex 2d formations with an arbitrary 3d position of the tool the method is based on the boundary integral equations for the tangential components of the field and the fourier transform which reduces the problem to a series of 1d integral equations computations are carried out simultaneously for the whole set of measurement points with the same matrix which provides a short computation time per point we verified the method by comparing our results with those obtained by the well known explicit 1d m

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

a suboptimal bootstrap method for structure detection of non linear output error models with application to human ankle dynamics identification of non linear systems involves estimating unknown parameters and structure detection selection of a subset of candidate terms that best describe the observed output this is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design for non linear systems simple output additive noise can generate multiplicative terms between the input output and noise the terms associated with noise need to be modelled to obtain unbiased parameter estimates significantly increasing the number of candidate terms to be estimated and considered in special cases it may be possible to use an output error oe model structure and the instrumental variable iv estimator to obtain unbiased parameters without modelling the noise this significantly reduces the dimensionality of the structure computation problem therefore in this paper we propose a suboptimal bootstrap structure detection sobsd algo

existence of traveling wavefronts in a cooperative systems with discrete delays in this paper we consider an important lotka volterra model describing a two species cooperative system with diffusive and discrete delays and investigate the existence of traveling wavefronts by some mathematics tools including the monotone iteration technique as well as the upper and lower solution method the results obtained can be seen as a generalization of previous results

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

unified set membership theory for identification prediction and filtering of nonlinear systems the problem of making inferences from data measured on nonlinear systems is investigated within a set membership sm framework and it is shown that identification prediction and filtering can be treated as specific instances of the general presented theory the sm framework presents an alternative view to the parametric statistical ps framework more widely used for studying the above specific problems in particular in the sm framework a bound only on the gradient of the model regression function is assumed at difference from ps methods which assume the choice of a parametric functional form of the regression function moreover the sm theory assumes only that the noise is bounded in contrast with ps approaches which rely on noise assumptions such as stationarity uncorrelation type of distribution etc the basic notions and results of the general inference making theory are presented moreover some of the main results that can be obtained for the specific inferences of identification prediction and filtering are reviewed concluding comments on the presented results are also reported focused on the discussion of two basic questions what may be gained in identification prediction and filtering of nonlinear systems by using the presented sm framework instead of the widely diffused ps framework why sm methods could provide stronger results than the ps methods requiring weaker assumptions on system and on noise

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

technical communique on an improved model reduction technique for nonlinear systems an algorithm is presented for reducing the number of terms in a nonlinear static system which can be modeled by a linear combination of nonlinear functions the method is an improvement over a previously presented algorithm desrochers and saridis 1980a the improvements now make it possible to perform all calculations from a single set of input and output data while in the original algorithm n sets of data were required where n is the number of terms retained in addition it is shown how the model error can be calculated at each iteration which relieves the arbitrariness of stopping the algorithm at a preselected value of n as was done originally then the insight gained from this improved technique is used to develop an optimal solution to the model reduction problem a major improvement over the original technique it is then conjectured that some structural concepts for such systems may exist in a matrix formed from the input and output data

a note on dead beat controllability of generalised hammerstein systems necessary and sufficient conditions for dead beat and complete controllability for a class of generalised hammerstein systems are presented since the system s structure is very close to linear only linear algebra is used for the controllability test the test is very simple and easy to use a closed loop minimum time dead beat controller can be designed for a subclass of generalised hammerstein systems using the grobner basis method

three dimensional induction logging problems part 2 a finite difference solution a 3 d finite difference solution is implemented for simulating induction log responses in the quasi static limit that include the wellbore and bedding that exhibits transverse anisotropy the finite difference code uses a staggered grid to approximate a vector equation for the electric field the resulting linear system of equations is solved to a predetermined error level using iterative krylov subspace methods to accelerate the solution at low induction numbers lins a new preconditioner is developed this new preconditioner splits the electric field into curl free and divergence free projections which allows for the construction of an approximate inverse operator test examples show up to an order of magnitude increase in speed compared to a simple jacobi preconditioner comparisons with analytical and mode matching solutions demonstrate the accuracy of the algorithm

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

regressor and structure selection in narx models using a structured anova approach regressor selection can be viewed as the first step in the system identification process the benefits of finding good regressors before estimating complex models are especially clear for nonlinear systems where the class of possible models is huge in this article a structured way of using the tool analysis of variance anova is presented and used for narx model nonlinear autoregressive model with exogenous input identification with many candidate regressors

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

efficient algorithms for volterra system identification in this paper nonlinear filtering and identification based on finite support volterra models are considered the volterra kernels are estimated via input output statistics or directly in terms of input output data it is shown that the normal equations for a finite support volterra system excited by zero mean gaussian input have a unique solution if and only if the power spectral process of the input signal is nonzero at least at m distinct frequencies where m is the memory of the system a multichannel embedding approach is introduced a set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format efficient algorithms for the estimation of the volterra parameters are derived for batch as well as for adaptive processing an efficient order recursive method is presented for the determination of the volterra model structure the proposed methods are illustrated by simulations

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

a comparison of three techniques using steady state data to identify non linear modal behavior of an externally excited cantilever beam non linear system identification is used to generate models of modes in physical structures analysis of the theoretical non linear model of a cantilevered beam is used to predict the inputs to the physical system that will produce responses suitable for enhanced parameter estimation thereby improving the model three identification techniques are described and applied to both numerical and experimental data the first is based on the continuous time differential equation model of the system the second uses relationships generated by the method of harmonic balance and the third is based on fitting steady state response data to the amplitude and phase modulation equations resulting from a multiple time scales analysis the performance of each method improves as the non linearities in the system become more pronounced the benefits and limitations of the methods are discussed

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

wiener hammerstein modeling of nonlinear effects in bilinear systems the modeling of nonlinear effects in bilinear systems using wiener hammerstein models is considered such models are chosen based on the block oriented structure of bilinear systems and the shapes of their volterra kernels theoretical analysis is given for first order bilinear systems and simulation results are presented for first and second order systems while the nonlinearity is only approximately wiener hammerstein the models are able to capture a significant part of the nonlinear dynamics in order to reduce the complexity of optimizing the model parameters the linear subsystems are estimated using the technique of linear interpolation in the frequency domain

on the relation between continuous and discrete nonlinear parametric models abstract actual applications of system identification and modeling utilize discrete time sampled data and yield discrete time models although the actual physical processes subserving the system may occur in continuous time in the case of nonlinear parametric models the physical interpretation of the estimated model parameters may change considerably between discrete time difference equation and continuous time differential equation representations furthermore a continuous time model may be desired although only discrete time data are available thus methods for defining the equivalence between these two forms of nonlinear parametric models are critically needed to assist in model development and interpretation this paper presents the kernel invariance method which is a conceptual extension of the impulse invariance method in linear system modeling as the means for defining the equivalence between continuous discrete nonlinear models