bilinear system identification by volterra kernels estimation this note considers the identification of bilinear discrete time dynamic systems from sequences of input and noise corrupted output measurements in contrast to other approaches the proposed algorithm is simple and does not require knowledge of the noise statistics it is also shown that the obtained estimates are unbiased and consistent which is not shown in the previous papers

a cumulant based algorithm for the identification of input output quadratic systems the identification of a special class of polynomial models is pursued in this paper in particular a parameter estimation algorithm is developed for the identification of an input output quadratic model excited by a zero mean white gaussian input and with the output corrupted by additive measurement noise input output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms the output error method and a combination of the instrumental variables and the output error approach the proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator

strong consistency and convergence rate of parameter identification for bilinear systems this paper discusses the parameter identification problem of discrete time stochastic bilinear systems when the dynamic system noise is coloured and its variance function may be unbounded in time it will be proved under weak conditions that the extended least squares estimate of the system parameter has strong consistency and a fast convergence rate

a kinetic theory for quantum transport in aperiodic media transport theory is reinvestigated in a one particle model including dissipation mechanisms through a phenomenological time dependent part using the description of an aperiodic crystal in terms of noncommutative geometry it is then possible to rigorously derive kubo formulas for the electric conductivity within the framework of the relaxation time approximation a fractal analysis applied to the spectral measures entering in the kubo formula allows us to examine anomalous transport owing to quantum interferences this leads to anomalies in drude s formula

quantization of edge currents for continuous magnetic operators abstract for a magnetic hamiltonian on a half plane given by the sum of the landau operator with dirichlet boundary conditions and a random potential a quantization theorem for the edge currents is proven this shows that the concept of edge channels also makes sense in presence of disorder moreover gaussian bounds on the heat kernel and its covariant derivatives are obtained

explicit recursive and adaptive filtering in reproducing kernel hilbert spaces this brief presents a methodology to develop recursive filters in reproducing kernel hilbert spaces unlike previous approaches that exploit the kernel trick on filtered and then mapped samples we explicitly define the model recursivity in the hilbert space for that we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset we illustrate the feasibility of the methodology in the particular case of the gamma filter which is an infinite impulse response filter with controlled stability and memory depth different algorithmic formulations emerge from the signal model experiments in chaotic and electroencephalographic time series prediction complex nonlinear system identification and adaptive antenna array processing demonstrate the potential of the approach for scenarios where recursivity and nonlinearity have to be readily combined

optimal regularization parameter of the multichannel filtered x affine projection algorithm we discuss the optimal regularization parameter of the filtered affine projection fx ap algorithm suitable for feedforward active noise control while the original fx ap algorithm always provides a biased estimate of the minimum mean square solution we show that the optimal regularized fx ap algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual mse of the algorithm we derive some expressions for the optimal regularization parameter and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions

the quantum state diffusion model applied to open systems a model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation derived from a density operator equation such as the bloch equation and consistent with it the advantages of the numerical solution of these equations over the direct numerical solution of the density operator equations are described the method is applied to the nonlinear absorber cascades of quantum transitions second harmonic generation and a measurement reduction process the model provides graphic illustrations of these processes with statistical fluctuations that mimic those of experiments the stochastic differential equations originated from studies of the measurement problem in the foundations of quantum mechanics the model is compared with the quantum jump model of dalibard 1992 carmichael and others which originated among experimenters looking for intuitive pictures and rules of computation

identification of a class of stochastic bilinear systems abstract this paper considers the identification of a class of stochastic bilinear systems in which the transfer matrix in state equation is the sum of a constant matrix a and a random matrix s i and observation equation is linear estimations of covariance matrices of the random disturbances including the state noise observation noise and random part in transfer matrix associated with this system are also presented strong consistency of the estimations is also established

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

transient and steady state analysis of filtered x affine projection algorithms this paper provides an analysis of transient and steady state behavior of different filtered x affine projection algorithms algorithms suitable for single channel and for multichannel active noise controllers are treated within a unified framework very mild assumptions are posed on the active noise control system model which is only required to have a linear dependence of the output from the filter coefficients therefore the analysis applies not only to the linear finite impulse response models but also to nonlinear volterra filters i e polynomial filters and other nonlinear filter structures the convergence analysis presented in this paper relies on energy conservation arguments and does not apply the independence theory nor does it impose any restriction to the signal distributions it is shown in the paper that filtered x affine projection algorithms always provide a biased estimate of the minimum mean square solution nevertheless in many cases the bias is small and therefore these algorithms can be profitably applied to active noise control

recursive maximum likelihood identification of a non linear output affine model on line identification of the parameters in a non linear output affine model is considered the recursive maximum likelihood estimator which was originally derived for linear systems is extended to work for non linear systems which can be described by a stochastic form of sontag s output affine model some numerical implementation aspects are discussed a brief convergence analysis is given and a computer simulation study is included

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

extended generalized total least squares method for the identification of bilinear systems the extended generalized total least squares e gtls method that consider the special structure of the data matrix is proposed as one of the bilinear system parameters considering that the input is noise free and that bilinear system equation is linear with respect to the output we extend the gtls problem the extended gtls problem is reduced to an unconstrained minimization problem and is then solved by the newton raphson method we compare the gtls method and the extended gtls method as far as the accuracy of the estimated system parameters is concerned

nonlinear system identification an effective framework based on the karhunen loeve transform this paper proposes on the basis of a rigorous mathematical formulation a general framework that is able to define a large class of nonlinear system identifiers this framework exploits all those relationships that intrinsically characterize a limited set of realizations obtained by an ensemble of output signals and their parameterized inputs by means of the separation property of the karhunen loeve transform the generality and the flexibility of the approximating mappings ranging from traditional approximation techniques to multiresolution decompositions and neural networks allow the design of a large number of distinct identifiers each displaying a number of properties such as linearity with respect to the parameters noise rejection low computational complexity of the approximation procedure exhaustive experimentation on specific case studies reports high identification performance for four distinct identifiers based on polynomials splines wavelets and radial basis functions several comparisons show how these identifiers almost always have higher performance than that obtained by current best practices as well as very good accuracy optimal noise rejection and fast algorithmic elaboration as an example of a real application the identification of a voice communication channel comprising a digital enhanced cordless telecommunications dect cordless phone for wireless communications and a telephone line is reported and discussed

quantum return probability for substitution potentials we propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete schrodinger operators we compute it for some non periodic substitution potentials with different degrees of randomness and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves i e the more random the sequence the smaller such an exponent

robust combined estimation of states and parameters of bilinear systems abstract a robust bootstrap method is presented for estimating the states and parameters of bilinear systems based on huber s minimax principle robust statistics wiley new york 1981 the robust bootstrap algorithm is derived from the feasible canonical forms for the state space of bilinear systems a convergence theorem for the proposed algorithm is presented results of simulation provide a comparison with non robust bootstrap methods these show the advantages of the algorithm developed in this paper

identification of input output bilinear systems using cumulants this paper is concerned with the identification of a discrete input output bilinear system driven by an independent identically distributed i i d stochastic input and corrupted by measurement noise a novel algorithmic procedure for the direct computation of the unknown model parameters is developed based on crosscumulant information up to third order simulations and comparisons with a least squares type identification method are provided

mean square stability conditions for discrete stochastic bilinear systems necessary and sufficient conditions for mean square stability are proved for the following class of nonlinear dynamical systems finite dimensional bilinear models evolving in discrete time and driven by random sequences the stochastic environment under consideration is characterized only by independence wide sense stationarity and second order properties thus we do not assume random sequences to be gaussian zero mean or ergodic the probability distributions involved are allowed to be arbitrary and unknown limiting state moments are given in terms of the model parameters and disturbances moments

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

modified kolmogorov s neural network in the identification of hammerstein and wiener systems this brief deals with the possibilities of using the modified kolmogorov s neural network for the identification of non linear dynamic systems among them the wiener and hammerstein systems the algorithm of training the network is simple well convergent and with a small error of approximation the modified neural network is characterized by a simple computer algorithm it also omits complicated techniques of back propagation the simulation results are shown to illustrate the modified kolmogorov theorem

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

exact field driven interface dynamics in the two dimensional stochastic ising model with helicoidal boundary conditions abstract we investigate the interface dynamics of the two dimensional stochastic ising model in an external field under helicoidal boundary conditions at sufficiently low temperatures and fields the dynamics of the interface is described by an exactly solvable high spin asymmetric quantum hamiltonian that is the infinitesimal generator of the zero range process generally the critical dynamics of the interface fluctuations is in the kardar parisi zhang universality class of critical behavior we remark that a whole family of rsos interface models similar to the ising interface model investigated here can be described by exactly solvable restricted high spin quantum x x z type hamiltonians

on line parameter identification of bilinear systems in this correspondence an on line identification scheme for bilinear systems is presented this algorithm is a direct extension of the stochastic approximation algorithm proposed by saridis and stein to bilinear systems the properties of the algorithm are that it does not require knowledge of the noise statistics and that it converges to the true value of the parameters volterra kernals in the mean square sense

parameter estimation in bilinear systems by instrumental variable method estimation of parameters in discrete bilinear systems by the use of instrumental variables is considered in this paper through a simulation study it is shown that the method yields superior results compared to earlier methods

nonlinearity tests for bilinear systems abstract the purpose of this paper is to develop nonlinearity tests for open loop bilinear systems lagrange multiplier tests of linear systems against a bilinear alternative are proposed a simulation study is performed to check the validity of the asymptotic null distributions of the test statistics and to investigate the power characteristics of the tests two recent nonlinearity tests in the time series context are adapted to linear systems and compared with lagrange multiplier tests simulation results show that the proposed lagrange multiplier tests are more powerful than the other tests

a general framework for quadratic volterra filters for edge enhancement an inherent problem in most image enhancement schemes is the amplification of noise which due to weber s law is mostly visible in the darker portions of an image using a special class of quadratic volterra filters we can adapt the enhancement process in a computationally efficient way to the local image brightness because these filters are approximately equivalent to the product of a local mean estimator and a highpass filter we analyze and derive this subclass of quadratic volterra filters by investigating the 1 d case first and then we generalize the results to two dimensions an important property of these filters is that they map sinusoidal inputs to constant outputs which allows us to develop a new filter characterization that is more intuitive for our application than the 4 d frequency response this description finally leads to a novel least squares design methodology image enhancement results using our volterra filters are superior to those obtained with standard linear filters which we demonstrate both quantitatively and qualitatively

adaptive lattice bilinear filters two fast least squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented the lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem the computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods the first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs this method is conceptually very simple but results in biased system models in the presence of measurement noise the second is an approximate least squares output error solution the past samples of the output of the adaptive system itself are used to produce the filter output at the current time results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method

frisch scheme identification for dynamic diagonal bilinear models the article addresses the problem of dynamic system identification in the errors in variables framework for a class of discrete time time invariant input output bilinear models when subjected to a white input signal the proposed algorithm is based on an extension of the bias compensated least squares method and utilises the frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences the appropriateness of the approach is analysed and its performance evaluated when compared to other errors in variables identification techniques by means of a monte carlo simulation the results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed

maximum likelihood parameter estimation of bilinear systems this paper addresses the problem of estimating the parameters in a multivariable bilinear model on the basis of observed input output data the main contribution is to develop analyze and empirically study new techniques for computing a maximum likelihood based solution in particular the emphasis here is on developing practical methods that are illustrated to be numerically reliable robust to choice of initialization point and numerically efficient in terms of how computation and memory requirements scale relative to problem size this results in new methods that can be reliably deployed on systems of nontrivial state input and output dimension underlying these developments is a new approach in this context of employing the expectation maximization method as a means for robust and gradient free computation of the maximum likelihood solution

brief paper parameter identification for nonlinear systems guaranteed confidence regions through lscr in this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems the proposed method uses higher order statistics and extends the lscr leave out sign dominant correlation regions algorithm for linear systems introduced in campi and weyer 2005 guaranteed non asymptotic confidence regions in system identification automatica 41 10 1751 1764 extended version available at the confidence regions contain the true parameter value with a guaranteed probability for any finite number of data points moreover the confidence regions shrink around the true parameter value as the number of data points increases the usefulness of the proposed approach is illustrated on some simple examples

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

subspace identification of bilinear systems subject to white inputs the authors generalize linear subspace identification theory to an analog theory for the subspace identification of bilinear systems a major assumption they make is that the inputs of the system should be white and mutually independent it is shown that in that case most of the properties of linear subspace identification theory can be extended to similar properties for bilinear systems the link between the presented bilinear subspace method and kalman filter theory is made finally the practical relevance of the method is illustrated by making a direct comparison between linear and bilinear subspace identification methods when applied on data from a model of a distillation column

realization of bilinear stochastic systems this note considers the problem of realization of bilinear stochastic systems blsr first an explicit statement for the blsr problem is presented next a realization algorithm is developed in this algorithm the state vector is picked as a basis in the subspace obtained by projecting an appropriately defined past vector onto an appropriately defined future vector also the realization algorithm involves solving a matrix nonlinear equation which is akin to the algebraic riccati equation except for one additional term

identification of discrete time stochastic bilinear systems this paper considers the problem of identifying unknown parameters appearing in discrete time varying bilinear models the system is assumed to operate in a stochastic environment where the input disturbance and the noise observation have unknown probability distribution identifiability conditions are investigated in the light of a state covariance analysis for stochastic bilinear systems by assuming that the only accessible process is supplied by the noisy observation sequence a recursive identification procedure is proposed which is suitable for on line applications stochastic approximation algorithms are used for identifying time invariant bilinear systems

exclusion process and droplet shape we use a mathematical isomorphism between the one dimensional exclusion process and the two dimensional stochastic ising model in the low temperature limit to describe the typical instantaneous shape of a supercritical droplet we derive specifically the exact asymptotic distribution of the boundaries of a 1 spin region confined to z 2 and subjected to a positive magnetic field in an appropriate scaling the boundary distribution converges to a deterministic continuum limit

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

neural network approach to solving fuzzy nonlinear equations using z numbers in this article the fuzzy property is described by means of the z number as the coefficients and variables of the fuzzy equations this alteration for the fuzzy equation is appropriate for system modeling with z number parameters in this article the fuzzy equation with z number coefficients and variables is tended to be used as the models for the uncertain systems the modeling issue related to the uncertain system is to obtain the z number coefficients and variables of the fuzzy equation nevertheless it is extremely hard to get the z number coefficients of the fuzzy equations in this article in order to model the uncertain nonlinear systems a novel structure of the multilayer neural network is utilized in such a manner that it is able to obtain the z number coefficients of the fuzzy equation the suggested technique is validated by some examples with applications

self tuning control of non linear armax models a control weighted self tuning minimum variance controller with a non linear difference equation structure is described an extended recursive least squares estimation algorithm is employed to provide the adaptiveness performance analysis of the controller is discussed in terms of a cumulative loss function and high order correlation functions of the system input output and residual sequences simulation results from an experiment using a model identified from a real system are also provided

spl theta adaptive neural networks a new approach to parameter estimation a novel use of neural networks for parameter estimation in nonlinear systems is proposed the approximating ability of the neural network is used to identify the relation between system variables and parameters of a dynamic system two different algorithms a block estimation method and a recursive estimation method are proposed the block estimation method consists of the training of a neural network to approximate the mapping between the system response and the system parameters which in turn is used to identify the parameters of the nonlinear system in the second method the neural network is used to determine a recursive algorithm to update the parameter estimate both methods are useful for parameter estimation in systems where either the structure of the nonlinearities present are unknown or when the parameters occur nonlinearly analytical conditions under which successful estimation can be carried but and several illustrative examples verifying the behavior of the algorithms through simulations are presented

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

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

finite dimensional smoothers for map state estimation of bilinear systems in this paper we present two finite dimensional iterative algorithms for maximum a posteriori map state sequence estimation of bilinear systems bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems our iterative algorithms for state estimation are based on the expectation maximization em algorithm and outperform the widely used extended kalman smoother eks unlike the eks these em algorithms are optimal in the map sense finite dimensional solutions to the state sequence estimation problem for bilinear models we also present recursive on line versions of the two algorithms and show that they outperform the extended kalman filter ekf our main conclusion is that the em based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the ekf

a kinetic model of quantum jumps a new class of models describing the dissipative dynamics of an open quantum system s by means of random time evolutions of pure states in its hilbert space is considered the random evolutions are linear and defined by poisson processes at the random poissonian times the wavefunction experiences discontinuous changes quantum jumps these changes are implemented by some non unitary linear operators satisfying a locality condition if the hilbert space of s is infinite dimensional the models involve an infinite number of independent poisson processes and the total frequency of jumps may be infinite we show that the random evolutions in are then given by some almost surely defined unbounded random evolution operators obtained by a limit procedure the average evolution of the observables of s is given by a quantum dynamical semigroup its generator having the lindblad form 1 the relevance of the models in the field of electronic transport in anderson insulators is emphasised

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

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 stability condition for certain bilinear systems the authors derive a simple sufficient condition for the output of a discrete time time invariant bilinear system to be bounded whenever the input signal to the system is bounded by a finite constant

identification and control of a nonlinear discrete time system based on its linearization a unified framework this paper presents a unified theoretical framework for the identification and control of a nonlinear discrete time dynamical system in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a higher order function this representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system and reveals the role played by the linearized system in a more transparent form under the assumption that the linearized system is controllable and observable it is shown that 1 the nonlinear system is also controllable and observable in a local domain 2 a feedback law exists to stabilize the nonlinear system locally and 3 the nonlinear system can exactly track a constant or a periodic sequence locally if its linearized system can do so with some additional assumptions the nonlinear system is shown to have a well defined relative degree delay and zero dynamics if the zero dynamics of the linearized system is asymptotically stable so is that of the nonlinear one and in such a case a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly in a neighborhood of the equilibrium state the tracking can be achieved by using the state vector for feedback or by using only the input and the output in which case the nonlinear autoregressive moving average narma model is established and utilized these results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete time dynamical systems

a variational bayesian learning approach for nonlinear acoustic echo control in this work we present novel bayesian algorithms for acoustic echo cancellation and residual echo suppression in the presence of a memoryless loudspeaker nonlinearity the system nonlinearity is modeled using a basis generic nonlinear expansion this allows us to express the microphone observation in the dft domain in terms of the nonlinear expansion coefficients and the acoustic echo path we augment the observation model with first order markov models for the echo path vector and the nonlinear expansion coefficients to arrive at a composite state space model the echo path vector and each nonlinear expansion coefficient are designated as the unknown random variables in our bayesian model the posterior estimators for the random variables and the learning rules for the a priori unknown model parameters are then derived via the maximization of the variational lower bound on the log likelihood we further show that a bayesian post filter for residual echo suppression can be derived by optimizing a minimum mean square error mmse cost function subject to marginalization with respect to the posteriors estimated in the echo cancellation stage the effectiveness of the approach is supported by simulation results and an analysis using instrumental performance measures

recursive identification of bilinear systems methods of identifying bilinear systems from recorded input output data are discussed in this article a short survey of the existing literature on the topic is given standard methods from linear systems identification such as least squares extended least squares recursive prediction error and instrumental variable methods are transferred to bilinear input output model structures and tested in simulation special attention is paid to problems of stabilizing the model predictor and it is shown how a time varying kalman filter and associated parameter estimation algorithm can deal with this problem

recursive prediction error parameter estimator for non linear models abstract a recursive prediction error parameter estimation algorithm is derived for systems which can be represented by the narmax non linear armax model a convergence analysis is presented using the differential equation approach and the new concept of m invertibility is introduced the analysis shows that while a highly non linear process model may be used to capture the non linearity of the system it is advisable to fit a simple noise model the results of applying the algorithm to both simulated and real data are included

quadratic digital filters for image processing a class of nonlinear two dimensional filters is presented a matrix description is developed for such operators and some symmetry conditions are imposed which simplify and render more effective the filter structure a strategy for the design of filters capable of enhancing images having reduced contrast and degraded by noise is proposed

blind identification of bilinear systems this paper is concerned with the blind identification of a class of bilinear systems excited by non gaussian higher order white noise the matrix of coefficients of mixed input output terms of the bilinear system model is assumed to be triangular in this work under the additional assumption that the system output is corrupted by gaussian measurement noise we derive an exact parameter estimation procedure based on the output cumulants of orders up to four results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach

limits of infinite interaction radius dimensionality and the number of components for random operators with off diagonal randomness we consider random one body operators that are analogs of the statistical mechanics hamiltonians with a varying interaction radiusr the dimensionality of spaced and the number of the field components orbitals n we prove that all the moments of the green functions for nonreal energies of these operators converge asr d n to the products of the average green functions just as in the mean field approximation of statistical mechanics we find in particular the selfconsistent equation for the limiting integrated density of states and the limiting form of the conductivity which is nonzero on the whole support of the integrated density of states

on mott s formula for the ac conductivity in the anderson model we study the ac conductivity in linear response theory in the general framework of ergodic magnetic schrodinger operators for the anderson model if the fermi energy lies in the localization regime we prove that the ac conductivity is bounded from above by c 2 log 1 d 2 at small frequencies this is to be compared to mott s formula which predicts the leading term to be c 2 log 1 d 1

on the identification of bilinear systems from operating records in this paper the identification of a non linear system when the input output record is available is considered the system discussed is an open loop system it is assumed that the unobservable output x t at time t and the observable input w s s t are related by a bilinear model it is further assumed that only a contaminated version of the output is observed i e y t whore for each t y t x t z t and x t and z t are mutually independent the identification of the system is considered in the following cases i where the external noise z t is a gaussian white noise and ii where z t is a gaussian stationary time series satisfying an autoregressive moving average arma model of order g j the estimation procedures are illustrated with examples

quantum intermittency in almost periodic lattice systems derived from their spectral properties abstract hamiltonian tridiagonal matrices characterized by multi fractal spectral measures in the family of iterated function systems can be constructed by a recursive technique described here we prove that these hamiltonians are almost periodic they are suited to describe quantum lattice systems with nearest neighbours coupling as well as chains of linear classical oscillators and electrical transmission lines we investigate numerically and theoretically the time dynamics of the systems so constructed we derive a relation linking the long time power law behaviour of the moments of the position operator expressed by a scaling function of the moment order and spectral multi fractal dimensions dq via d1 we show cases in which this relation is exact and cases where it is only approximate unveiling the reasons for the discrepancies

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

comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models the estimation of the parameters of a transfer function model is considered relationships between the total least squares tls and instrumental variable iv approaches are outlined both methods

on discrete stochastic bilinear systems stability abstract mean square stability conditions for discrete time bilinear systems operating in a stochastic environment are given in this paper only independence and wide sense stationarity are required for the second order disturbance sequences involved thus dismissing ergodicity and zero mean assumptions stochastic stability conditions are derived by using a deterministic stability result for a class of separable nonlinear dynamical systems evolving in a banach space

linear response theory for magnetic schrodinger operators in disordered media abstract we justify the linear response theory for an ergodic schrodinger operator with magnetic field within the noninteracting particle approximation and derive a kubo formula for the electric conductivity tensor to achieve that we construct suitable normed spaces of measurable covariant operators where the liouville equation can be solved uniquely if the fermi level falls into a region of localization we recover the well known kubo str eda formula for the quantum hall conductivity at zero temperature

interface motion in a planar spin flip model derived from exclusion on the line we consider a two dimensional spin flip model which can be interpreted as the limit of the ising model at low temperature and a small nonzero external field in the hydrodynamic limit and for a special class of initial conditions the motion of the interface is governed by a nonlinear partial differential equation with a lattice distorted curvature term in our proofs we use results about the hydrodynamic behavior of the weakly asymmetric exclusion process on the integers and also on the nonnegative integers with a trap at the boundary

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples