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

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

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

asymptotic relative efficiencies of multistage tests corresp asymptotic relative efficiencies of two stage and multistage tests of a simple null hypothesis versus a simple location alternative are considered observations are taken in groups not necessarily of the same size and a test statistic is computed for comparison with thresholds in a two stage test if the test statistic of the first group of observations exceeds an upper threshold the alternative is accepted and if it crosses a lower threshold the null hypothesis is accepted otherwise a second group of samples is taken and a second test is performed two different classes of two stage tests are considered one of them computes the test statistic in the second stage from observations in the second group alone while the other uses both the first and the second groups of observations it is shown that these tests are asymptotically more efficient than fixed sample size tests but are less efficient than sequential probability ratio tests with proper choices of parameters the improvement over fixed sample size tests can be significant especially when the error probabilities are small however the complexity of two stage tests is comparable to that of fixed sample size tests making their use desirable the efficiency of k stage tests k 2 is also investigated with the conclusion that the behavior of a two stage test can be enhanced by adding stages up to a point beyond which the effect of adding stages diminishes

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

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

on the discretization of single input single output bilinear systems prompted by the observation that the parameters of a discrete bilinear model structure corresponding to a time invariant continuous bilinear model structure are input dependent quantities this paper deduces a correction factor that relates the continuous and discrete time models the correction factor that is obtained analytically is shown to provide an exact discretization an approximation to the correction factor is also included which produces a satisfactory discretization provided realistic bounds are placed on the choice of the sampling interval building on the developed approach for discretizing a first order bilinear system the procedure is extended to the case of higher order systems the new approach differs from existing schemes in that a discrete time bilinear model structure is retained with consideration given to a first order model of a high temperature furnace application it is shown that the resulting parameter variation is significantly reduced when a bilinear model structure is re

detecting small moving objects in image sequences using sequential hypothesis testing an algorithm is proposed for the solution of the class of multidimensional detection problems concerning the detection of small barely discernible moving objects of unknown position and velocity in a sequence of digital images a large number of candidate trajectories organized into a tree structure are hypothesized at each pixel in the sequence and tested sequentially for a shift in mean intensity the practicality of the algorithm is facilitated by the use of multistage hypothesis testing mht for simultaneous inference as well as the existence of exact closed form expressions for mht test performance in gaussian white noise gwn these expressions predict the algorithm s computation and memory requirements where it is shown theoretically that several orders of magnitude of processing are saved over a brute force approach based on fixed sample size tests the algorithm is applied to real data by using a robust preprocessing procedure to eliminate background structure and transform the image sequence into a residual representation modeled as gwn results are verified experimentally on a variety of video image sequences

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

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

a markov chain based numerical method for calculating network degree distributions this paper establishes a relation between scale free networks and markov chains and proposes a computation framework for degree distributions of scale free networks we first find that under the ba model the degree evolution of individual nodes in a scale free network follows some non homogeneous markov chains exploring the special structure of these markov chains we are able to develop an efficient algorithm to compute the degree distribution numerically the complexity of our algorithm is o t 2 where t is the number of time steps for adding new nodes we use three examples to demonstrate the computation procedure and compare the results with those from the existing methods pacs 84 35 i 64 60 fr 87 23 ge

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

a class of vertex edge growth small world network models having scale free self similar and hierarchical characters abstract the problem of uncovering the internal operating function of network models is intriguing demanded and attractive in researches of complex networks notice that in the past two decades a great number of artificial models are built to try to answer the above mentioned task based on the different growth ways these previous models can be divided into two categories one type possessing the preferential attachment follows a power law p k k 2 3 the other has exponential scaling feature p k k however there are no models containing above two kinds of growth ways to be presented even the study of interconnection between these two growth manners in the same model is lacking hence in this paper we construct a class of planar and self similar graphs motivated from a new attachment way vertex edge growth network operation more precisely the couple of both them we report that this model is sparse small world and hierarchical and then not only is scale free feature in our model but also lies the degree parameter 3 242 out the typical range note that we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power law parameter and the preferential attachment plays a dominate role on the development of networks over time at the end of this paper we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements

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

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

two stage wilcoxon detectors using conditional tests the idea of the wilcoxon detector using a conditional test is extended to two stage detectors which constitute a class of sequential detectors three different two stage detectors are considered using the wilcoxon statistic with conditional tests the three detectors differ in the usage of the samples of the first stage for computing the test statistic in the second stage in computing the test statistic in the second stage the first detector disregards all the samples of the first stage the second detector uses the value of the test statistic of the first stage and the third detector uses all the samples of the first stage the asymptotic relative efficiency improves from the first to the second detector comparisons of these detectors with fixed sample size fss detectors show that they are better than both the fss linear detector and the fss conditional wilcoxon detector under the same false alarm and detection probabilities

network formation determined by the diffusion process of random walkers we studied the diffusion process of random walkers in networks formed by their traces this model considers the rise and fall of links determined by the frequency of transports of random walkers in order to examine the relation between the formed network and the diffusion process a situation in which multiple random walkers start from the same vertex is investigated the difference in diffusion rate of random walkers according to the difference in dimension of the initial lattice is very important for determining the time evolution of the networks for example complete subgraphs can be formed on a one dimensional lattice while a graph with a power law vertex degree distribution is formed on a two dimensional lattice we derived some formulae for predicting network changes for the 1d case such as the time evolution of the size of nearly complete subgraphs and conditions for their collapse the networks formed on the 2d lattice are characterized by the existence of clusters of highly connected vertices and their life time as the life time of such clusters tends to be small the exponent of the power law distribution changes from 1 2 to 3

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

random models of scale free networks in this paper we study two models of network evolution and give more realistic descriptions of the local processes than barabasi albert model incorporating the addition of new nodes the addition of new links the rewiring and deleting of links to random networks model with single or double preferential attachment s we have proved that the two models are of scale free networks if the parameters are chosen properly and got the scaling exponent by the continuum theory

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

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

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

a family of small world network models built by complete graph and iteration function abstract small world networks are popular in real life complex systems in the past few decades researchers presented amounts of small world models in which some are stochastic and the rest are deterministic in comparison with random models it is not only convenient but also interesting to study the topological properties of deterministic models in some fields such as graph theory theorem computer sciences and so on as another concerned darling in current researches community structure modular topology is referred to as an useful statistical parameter to uncover the operating functions of network so building and studying such models with community structure and small world character will be a demanded task hence in this article we build a family of sparse network space n t which is different from those previous deterministic models even though our models are established in the same way as them iterative generation by randomly connecting manner in each time step every resulting member in n t has no absolutely self similar feature widely shared in a large number of previous models this makes our insight not into discussing a class certain model but into investigating a group various ones spanning a network space somewhat surprisingly our results prove all members of n t to possess some similar characters a sparsity b exponential scale feature p k k and c small world property here we must stress a very screming but intriguing phenomenon that the difference of average path length a p l between any two members in n t is quite small which indicates this random connecting way among members has no great effect on a p l at the end of this article as a new topological parameter correlated to reliability synchronization capability and diffusion properties of networks the number of spanning trees on a representative member n b t of n t is studied in detail then an exact analytical solution for its spanning trees entropy is also obtained

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

a weighted local world evolving network model with aging nodes abstract in this paper the dynamical behaviors of a class of weighted local world evolving networks with aging nodes are investigated as the network grows each newly added node is connected to some existing nodes through strength age preferential attachment each time step the newly added node with randomly determined initial degree is connected to some existing nodes through a local strength age preferential attachment by using tools from stochastic analysis and continuous approximation it is theoretically proved that the strength distribution of the generated network has a power law form with exponent depending nontrivially on a decay factor 0 1 in addition the clustering coefficient correlation and small world properties of this class of networks are examined via simulations it is shown that clustering coefficient is a monotone decreasing function of the decay factor and the assortative degree correlation and small world properties appear simultaneously finally the new model is used to characterize the internet topology as a typical application

the modeling of scale free networks abstract in order to explore further the mechanism responsible for scale free networks we introduce two extended models of the ba model the model a where the system incorporates the addition of new links between existing nodes a new node with new links and the rewiring of some links at every time step all sites are born with some initial attractiveness we calculate analytically the degree distribution the system self organizes into a scale free network the scaling exponent 2 the model b is a new model we consider that some old links are deleted with the anti preferential probability the result indicates that the system evolves itself into a scale free network the scaling exponent varies from 2 to 3

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

the emergence of scale free networks with a seceding mechanism in order to explore further the underlying mechanism of the scale free networks we study stochastic secession as a mechanism for the creation of complex networks in this evolution the network growth incorporates the addition of new links between existing nodes the deleting and rewiring of some existing links and the stochastic secession of nodes to random growing networks with preferential attachment the model yields scale free behavior for the degree distribution furthermore we get the analytical expression of the power law degree distribution with scaling exponent ranges from 1 1 to 9 the analytical expressions are in good agreement with the numerical simulation results

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

markov chains theory for scale free networks abstract this paper proposes a markov chain method to predict the growth dynamics of the individual nodes in scale free networks and uses this to calculate numerically the degree distribution we first find that the degree evolution of a node in the ba model is a nonhomogeneous markov chain an efficient algorithm to calculate the degree distribution is developed by the theory of markov chains the numerical results for the ba model are consistent with those of the analytical approach a directed network with the logarithmic growth is introduced the algorithm is applied to calculate the degree distribution for the model the numerical results show that the system self organizes into a scale free network

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

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

the relations between network operation and topological property in a scale free and small world network with community structure abstract it is always an open demanding and difficult task for generating available model to simulate dynamical functions and reveal inner principles from complex systems and networks in this article due to lots of real life and artificial networks are built from series of simple and small groups components we discuss some interesting and helpful network operation to generate more realistic network models in view of community structure modular topology we present a class of sparse network models n t m at the moment we capture the fact the n t 4 has not only scale free feature which means that the probability that a randomly selected vertex with degree k decays as a power law following p k k where is the degree exponent but also small world property which indicates that the typical distance between two uniform randomly chosen vertices grows proportionally to logarithm of the order of n t 4 namely relatively shorter diameter and lower average path length simultaneously displays higher clustering coefficient next as a new topological parameter correlating to reliability synchronization capability and diffusion properties of networks the number of spanning trees over a network is studied in more detail an exact analytical solution for the number of spanning trees of the n t 4 is obtained based on the network operation part hub vertex linking with each other will be helpful for structuring various network models and investigating the rules related with real life networks

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

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

time evolution of the degree distribution of model a of random attachment growing networks abstract for random growing networks barabas and albert proposed a kind of model in barabas et al physica a 272 1999 173 i e model a in this paper for model a we give the differential format of master equation of degree distribution and obtain its analytical solution the obtained result p k t is the time evolution of degree distribution p k t is composed of two terms at given finite time one term decays exponentially the other reflects size effect at infinite time the degree distribution is the same as that of barabas and albert in this paper we also discuss the normalization of degree distribution p k t in detail

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

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

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

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

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

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

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

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