variance mediated multifractal analysis of group participation in chasing a single dangerous prey abstract complexity of group participation in chasing a single dangerous prey is usually influenced by many factors such as the group size the physiological fitness of predator the hunting tactics and the running speed of prey the group members may take diversified roles and switch their roles in the process of group hunting in this paper we study group participation in lions pride hunting by using a minimal cheating pursuing model formulated in discrete time random walks predator s switching between cheating state and pursuing state is determined by a preset probability transition matrix which is regarded to be a product of the combination of various factors that influence group participation the physiological constraints of lions require that the measurement of complexity of group participation must be built for short time series on the basis of 300 simulated time steps numerical results show that our model reasonably reflects the common expectation that the pride groups tightly in chasing a single slow prey while in chasing a single fast prey it groups loosely we compute the distance between the group center and the center of the concerted pursuing for the quantification of group participation complexity embedded in short time series of these quantities is measured via a new method named variance mediated multifractal analysis this method is based on the partition function which is the weighted sum of probability measures of q th power the short time series is divided into non overlapping windows where the sample variance of each window is used to build the normalized probability measure a strategy one point indent for local past is designed to weigh the probability measures the singularity spectrum exhibits more multifractality in the simulated group participation in chasing a fast prey and far less such in chasing a slow one showing the potential applications of this method in studying short process of group hunting

brief paper adaptive hinging hyperplanes and its applications in dynamic system identification the model of adaptive hinging hyperplanes ahh is proposed in this paper it is based on multivariate adaptive regression splines mars and generalized hinging hyperplanes ghh and shares attractive properties of the two by making a modification to the basis function of mars ahh shows linear property in each subregion the ahh model is actually a special case of the ghh model which has a universal representation capability for continuous piecewise linear functions the approximation ability of the ahh model is proved the ahh algorithm is developed similar to the mars algorithm it is adaptive and can be executed efficiently hence has power and flexibility to model unknown relationships the ahh procedure is applied to identifying two dynamic systems and its potential is illustrated

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

brief paper identification of dynamic systems using piecewise affine basis function models piecewise affine pwa basis function autoregressive exogenous bpwarx models are proposed in this paper for nonlinear black box identification a bpwarx model is a weighted sum of pwa basis bpwa functions which are the minimum or maximum of n 1 affine functions in n dimensions since the bpwa functions have a universal representation capability for continuous pwa functions the bpwarx models provide better accuracy than the hinging hyperplane arx hharx models with the same number of parameters and the same order of computational complexity when using a modified gauss newton algorithm to build the models from input output data

an identification algorithm for polynomial narx models based on simulation error minimization classical prediction error approaches for the identification of non linear polynomial narx narmax models often yield unsatisfactory results for long range prediction or simulation purposes mainly due to incorrect or redundant model structure selection the paper discusses some limitations of the standard approach and suggests two modifications namely a new index based on the simulation error is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm the resulting algorithm is shown to be effective in the identification of compact and robust models generally yielding model structures closer to the correct ones computational issues are also discussed finally the identification algorithm is tested on a long range prediction benchmark application

parameter estimation problems with singular information matrices the case of a singular fisher information matrix fim represents a significant complication for the theory of the cramer rao lower bound crb that is usually handled by resorting to the pseudoinverse of the fisher matrix we take a different approach in which the crb is derived as the solution to an unconstrained quadratic maximization problem which enables us to handle the singular case in a simple yet rigorous manner when the fisher matrix is singular except under unusual circumstances any estimator having the specified bias derivatives that figure in the crb must have infinite variance

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

non parametric nonlinear system identification a data driven orthogonal basis function approach in this paper a data driven orthogonal basis function approach is proposed for non parametric fir nonlinear system identification the basis functions are not fixed a priori and match the structure of the unknown system automatically this eliminates the problem of blindly choosing the basis functions without a priori structural information further based on the proposed basis functions approaches are proposed for model order determination and regressor selection along with their theoretical justifications

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

adaptive inverse control of cable driven parallel system based on type 2 fuzzy logic systems this paper is concerned with the problem of type 2 fuzzy adaptive inverse control for a cable driven parallel system based on the heuristics and prior knowledge of the system the system is divided into six subsystems the proposed control scheme for each subsystem contains a forward model and a fuzzy adaptive inverse controller faic which are expressed by an interval type 2 fuzzy nonlinear autoregressive exogenous narx model respectively to construct the antecedents of the interval type 2 fuzzy narx forward models and faics the monotonic property of the fuzzy narx model is first proved and then their antecedent parameters can be determined by this property furthermore the consequent parameters of the forward models are computed offline via a constrained least squares algorithm and the consequent parameters of the faic are adjusted online via a recursive least squares algorithm experiment results are provided to show that the proposed type 2 fuzzy control scheme can realize the control objectives and achieve a good control performance

nonlinear system identification via direct weight optimization a general framework for estimating nonlinear functions and systems is described and analyzed in this paper identification of a system is seen as estimation of a predictor function the considered predictor function estimate at a particular point is defined to be affine in the observed outputs and the estimate is defined by the weights in this expression for each given point the maximal mean square error or an upper bound of the function estimate over a class of possible true functions is minimized with respect to the weights which is a convex optimization problem this gives different types of algorithms depending on the chosen function class it is shown how the classical linear least squares is obtained as a special case and how unknown but bounded disturbances can be handled most of the paper deals with the method applied to locally smooth predictor functions it is shown how this leads to local estimators with a finite bandwidth meaning that only observations in a neighborhood of the target point will be used in the estimate the size of this neighborhood the bandwidth is automatically computed and reflects the noise level in the data and the smoothness priors the approach is applied to a number of dynamical systems to illustrate its potential

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

an adaptive multi scale basis method for modelling discrete time nonlinear dynamical systems based on locally applicable autoregressive moving average with exogenous armax models this paper proposes two new adaptive modelling schemes for discrete time non linear dynamic systems based on the concept of a multiscale which originates in approximation theory a general result on the convergence of modelling based on the multiscale basis functions with a least square estimated is derived with the advantage of the multiresolution nature of the multiscale basis the new modelling scheme can be used to capture both the global and local characteristics of a non linear system over distinct scales the algorithms also provide a trade off between the model structure model size and the modelling error one of which emphasizes the modelling error with variable model structure whilst the other stresses a desired model size with better modelling error data based modelling examples are used to demonstrate the effectiveness of the multiscale modelling schemes with different multiscale basis

generalization of hinging hyperplanes the model of hinging hyperplanes hh can approximate a large class of nonlinear functions to arbitrary precision but represent only a small part of continuous piecewise linear cpwl functions in two or more dimensions in this correspondence the influence of this drawback for black box modeling is first illustrated by a simple example then it is shown that the above shortcoming can be amended by adding a sufficient number of linear functions to current hinges it is proven that any cpwl function of n variables can be represented by a sum of hinges containing at most n 1 linear functions hence the model of a sum of such expanded hinges is a general representation for all cpwl functions the structure of the novel general representation is much simpler than the existing generalized canonical representation that consists of nested absolute value functions this characteristic is very useful for black box modeling based on the new general representation an upper bound on the number of nestings of nested absolute value functions of a generalized canonical representation is established which is much smaller than the known result

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

an algorithm of uniform ultimate boundedness for a class of switched linear systems uniform ultimate boundedness of a class of switched linear systems is studied a switched linear system in this class consists of m subsystems and none of the individual subsystems need to be stabilizable the switched linear system is shown to be uniformly ultimately bounded for any pre given bound if the union of individual controllable subspaces covers the entire state space an algorithm for guaranteeing uniform ultimate boundedness is given to provide the design of continuous controllers and the switching strategy

diffusive corrections to asymptotics of a strong field quantum transport equation abstract the asymptotic analysis of a linear high field wigner bgk equation is developed by a modified chapman enskog procedure by an expansion of the unknown wigner function in powers of the knudsen number evolution equations are derived for the terms of zeroth and first order in in particular a quantum drift diffusion equation for the position density of electrons with an order correction on the field terms is obtained well posedness and regularity of the approximate problems are established and a rigorous proof that the difference between exact and asymptotic solutions is of order 2 uniformly in time and for arbitrary initial data is given

adaptive learning control for finite interval tracking based on constructive function approximation and wavelet using a constructive function approximation network an adaptive learning control alc approach is proposed for finite interval tracking problems the constructive function approximation network consists of a set of bases and the number of bases can evolve when learning repeats the nature of the basis allows the continuous adaptive learning of parameters when the network undergoes any structural changes and consequently offers the flexibility in tuning the network structure the expandability of the bases guarantees precision of the function approximation and avoids the trial and error procedure in structure selection for any fixed structure network two classes of unknown nonlinear functions namely either global l2 or local l2 with a known bounding function are taken into consideration using the lyapunov method the existence of solution and the convergence property of the proposed alc system are discussed in a rigorous manner by virtue of the celebrated orthonormal and multiresolution properties wavelet network is used as the universal function approximator with the weights tuned by the proposed adaptive learning mechanism

multiobjective parameter estimation for non linear systems affine information and least squares formulation this paper defines a class of system information affine information that includes both the dynamic residuals and some types of auxiliary information that can be used in system parameter estimation as special cases the types of information that can be cast under the affine information format give rise to quadratic functions that measure the extent to which a model fits such information and that can be aggregated in a single weighted quadratic cost functional this allows the definition of a multiobjective methodology for parameter estimation in non linear system identification which allows taking into account any type of affine information the results are presented in terms of a set of efficient solutions of the multiobjective estimation problem such a solution set is more meaningful than a single model since any affine information leads to a convex quadratic functional the whole set of efficient solutions is exactly accessible via the minimization of the quadratic functional with different weighti

efficient nonlinear wiener model identification using a complex valued simplicial canonical piecewise linear filter this paper proposes an efficient adaptive realization of the wiener model for the identification of complex valued nonlinear systems using a two dimensional simplicial canonical piecewise linear filter for the complex valued nonlinear mapping we derive a realization of the wiener model requiring fewer parameters than previous approaches an adaptive implementation of the proposed wiener model is derived and local convergence analysis for the updating algorithm is presented the tradeoff between computational complexity and modeling performance is discussed simulations of a system identification example show that the proposed algorithm can provide similar or better performance than other approaches in terms of computational complexity convergence speed and final mean squared error mse

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

sparse system identification for stochastic systems with general observation sequences abstract focusing on identification this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system with general observation sequences including stationary time series and feedback control for which the current input may depend on the past inputs and outputs system noises as well as exogenous dithers first a sparse parameter identification algorithm is introduced based on l 2 norm with l 1 regularization where the adaptive weights are adopted in the optimization variables of l 1 term second estimates generated by the algorithm are shown to have both set and parameter convergence that is sets of the zero and nonzero elements in the parameter can be correctly identified with probability one using a finite number of observations and further estimates of the nonzero elements converge to the true values almost surely third it is shown that the results are applicable to a large number of applications including variable selection open loop identification and closed loop control of stochastic systems finally numerical examples are given to support the theoretical analysis

fuzzy instrumental variable approach for nonlinear discrete time systems identification in a noisy environment nonlinear discrete time systems identification based on instrumental variable iv method and takagi sugeno ts fuzzy model is proposed in this paper the ivs statistically uncorrelated with noise are adequately chosen and mapped to fuzzy sets partitioning the input space of the nonlinear plant in subregions for unbiased estimates of the ts fuzzy model consequent parameters in a noisy environment the fuzzy instrumental variable fiv concept is proposed so that consistency and unbias properties of the fiv algorithm are derived from lemmas and theorem simulation results show the efficiency of the fiv algorithm for nonlinear system identification in a noisy environment and its application for modeling of an aluminium beam with free free configuration which is commonly used for active vibration control design in aircrafts and aerospace vehicles

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

detecting and interpreting distortions in hierarchical organization of complex time series hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept for model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric using selected time series representing such diverse phenomena as price changes and intertransaction times in financial markets sentence length variability in narrative texts missouri river discharge and sunspot number variability as examples we show that the resulting singularity spectra appear strongly asymmetric more often left sided but in some cases also right sided we present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying the composition of the time series one particularly intriguing case of this latter kind of asymmetry is detected in the daily reported sunspot number variability this signals that either the commonly used famous wolf formula distorts the real dynamics in expressing the largest sunspot numbers or if not that their dynamics is governed by a somewhat different mechanism

a recursive local linear estimator for identification of nonlinear arx systems asymptotical convergence and applications in this paper we propose a recursive local linear estimator rlle for nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx first the rlle is introduced next the strong consistency as well as the asymptotical mean square error properties of the rlle are established and then an application of the rlle to an additive nonlinear system is discussed the rlle provides recursive estimates not only for the function values but also their gradients at fixed points a simulation example is provided to confirm the theoretical analysis

path integral approach to quantum brownian motion abstract we apply the influence functional method of feynman and vernon to the study of brownian motion at arbitrary temperature by choosing a specific model for the dissipative interaction of the system of interest with its environment we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient we show that in the limit h 0 the results obtained from the influence functional formalism reduce to the classical fokker planck equation in the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature we obtain an explicit expression for the time evolution of the complete density matrix x x t when the system starts in a particular kind of pure state we compare our results with those of other approaches to the problem of dissipation in quantum mechanics

an analysis of the wigner poisson problem with inflow boundary conditions abstract we present a study of the wigner poisson problem in a bounded spatial domain with non homogeneous and time dependent inflow boundary conditions this system of nonlinearly coupled equations is a mathematical model for quantum transport of charges in a semiconductor with external contacts we prove well posedness of the linearized n dimensional problem as well as existence and uniqueness of a global in time regular solution of the one dimensional nonlinear problem

asymptotic properties of least squares estimates of hammerstein wiener models this paper investigates the asymptotic properties of least squares estimates of hammerstein wiener model structures and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process the inputs and the static non linearities in relation to the asymptotic distributional results a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided a key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting in this respect the hammerstein wiener model structure serves as a demonstration example a simulation study complements the theoretical findings

nonparametric direct mapping of rainfall runoff relationships an alternative approach to data analysis and modeling we present a new approach for the analysis and modeling of catchment rainfall runoff relationships that uses as predictor variables input history summary variables only the latter are defined as linear combinations of inputs at a given number of previous time steps this transforms the dynamic identification problem into a static one as the identification algorithm we use regression trees which act as a nonlinear nonparametric model the original algorithm is adapted to account for serial correlation in variables the new method is applied to two subcatchments of the u s department of agriculture forest service andrews experimental forest watershed oregon united states simple and interpretable tree models explain more than 80 of the initial deviance of the observations in both calibration and validation this suggests that the selected variables have a good predictive power and that further modeling attempts using them are warranted the models show a distinct pattern of the selected explanatory variables applications of the method include data quality control comparative analysis assessment of hydrological change and multicriterion evaluation of parametric hydrological models

accuracy analysis for wavelet approximations constructive wavelet networks are investigated as a universal tool for function approximation the parameters of such networks are obtained via some direct monte carlo procedures approximation bounds are given typically it is shown that such networks with one layer of wavelons achieve an l sub 2 error of order o n sup spl rhod where n is the number of nodes d is the problem dimension and spl rho is the number of summable derivatives of the approximated function an algorithm is also proposed to estimate this approximation based on noisy input output data observed from the function under consideration unlike neural network training this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated backpropagation and it completely avoids the problem of poor convergence or undesirable local minima

an interactive term approach to non parametric fir nonlinear system identification in this technical note a framework for designing specially structured input sequences for non parametric nonlinear system identification is presented so that interaction terms which describe interactions among variables can be identified separately in a sense the approach decomposes a general difficult nonlinear identification problem into a number of problems that are of lower orders corresponding identification algorithms are proposed

irredundant lattice representations of continuous piecewise affine functions in this paper we revisit the full lattice representation of continuous piecewise affine pwa functions and give a formal proof of its representation ability based on this we derive the irredundant lattice pwa representations through removal of redundant terms and literals necessary and sufficient conditions for irredundancy are proposed besides we explain how to remove terms and literals in order to ensure irredundancy an algorithm is given to obtain an irredundant lattice pwa representation in the worked examples the irredundant lattice pwa representations are used to express the optimal solution of explicit model predictive control problems and the results turn out to be much more compact than those given by a state of the art algorithm

identification of structured nonlinear systems this paper is concerned with the identification of static nonlinear components in a complex interconnected system these nonlinear components are treated nonparametrically in the sense that no natural parameterization is assumed to be available

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

term and variable selection for non linear system identification the purpose of variable selection is to pre select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection it is required that the selected significant variables alone should sufficiently represent the system generally not all the model terms which are produced by combining different variables make an equal contribution to the system output and terms which make little contribution can be omitted a parsimonious representation which contains only the significant terms can often be obtained without the loss of representational accuracy by eliminating the redundant terms based on these observations a new variable and term selection algorithm is proposed in this paper the term detection algorithm can be applied to the general class of non linear modelling problems which can be expressed as a linear in the parameters form the variable selection procedure is based on locally linea

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

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

a measurement fusion method for nonlinear system identification using a cooperative learning algorithm identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article a measurement fusion method for the predictor function estimate is proposed in the proposed scheme observed data are first fused by using an optimal fusion technique and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine ls svm a cooperative learning algorithm is proposed to implement the proposed measurement fusion method compared with related identification methods the proposed method can minimize both the approximation error and the noise error the performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the ls svm function estimate moreover the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate finally the proposed measurement fusion method is applied to arma signal and spatial temporal signal modeling experimental results show that the proposed measurement fusion method can provide a more accurate model

hinging hyperplanes for regression classification and function approximation a hinge function y h x consists of two hyperplanes continuously joined together at a hinge in regression prediction classification pattern recognition and noiseless function approximation use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters a simple and effective method for finding good hinges is presented

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

an iv qr algorithm for neuro fuzzy multivariable online identification in this paper a new algorithm for neuro fuzzy identification of multivariable discrete time nonlinear dynamic systems more specifically applied to consequent parameters estimation of the neuro fuzzy inference system is proposed based on a decomposed form as a set of coupled multiple input and single output miso takagi sugeno ts neuro fuzzy networks an on line scheme is formulated for modeling a nonlinear autoregressive with exogenous input narx recurrent neuro fuzzy structure from input output samples of a multivariable nonlinear dynamic system in a noisy environment the adaptive weighted instrumental variable wiv algorithm by qr factorization based on the numerically robust orthogonal householder transformation is developed to modify the consequent parameters of the ts multivariable neuro fuzzy network

consistent identification of narx models via regularization networks generalization networks are nonparametric estimators obtained from the application of tychonov regularization or bayes estimation to the hypersurface reconstruction problem under symmetry assumptions they are a particular type of radial basis function neural network in this correspondence it is shown that such networks guarantee consistent identification of a very general infinite dimensional class of narx models the proofs are based on the theory of reproducing kernel hilbert spaces and the notion of frequency of time probability by means of which it is not necessary to assume that the input is sampled from a stochastic process

on the input output representation of piecewise affine state space models this paper addresses the conversion of discrete time piecewise affine pwa state space models into input output form necessary and sufficient conditions for the existence of equivalent input output representations of a given pwa state space model are derived connections to the observability properties of pwa models are investigated under a technical assumption it is shown that every finite time observable pwa model admits an equivalent input output representation when an equivalent input output model exists a constructive procedure is presented to derive its equations several examples illustrate the proposed results

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

a quasi armax approach to modelling of non linear systems this paper proposes a class of quasi armax models for non linear systems similar to ordinary non linear armax models the quasi armax models are flexible black box models but they have various linearity properties similar to those of linear armax models a modelling scheme is introduced to construct models consisting of two parts a macro part and a kernel part by using taylor expansion and other mathematical transformation techniques it is first constructed as a class of quasi armax interfaces macro parts that have various linearity properties but contain some complicated coefficients mimo neurofuzzy models kernel parts are then introduced to represent the complicated coefficients it is shown that the proposed quasi armax models have both good approximation ability and some easy to use properties the proposed models have been successfully applied to prediction fault detection and adaptive control of non linear systems

on the three dimensional wigner poisson problem with inflow boundary conditions abstract we study the wigner poisson problem in a bounded spatial domain with non homogeneous and time dependent inflow boundary conditions this system is a quantum model of charge transport in a semiconductor device coupled with reservoirs in presence of a self consistent potential and of an external one we state a local in time well posedness result for the problem the main difficulty is proving in the three dimensional case that the non linear potential term is a lipschitz perturbation of the affine streaming operator in an appropriately weighted l 2 space

identification of stable models in subspace identification by using regularization in subspace identification methods the system matrices are usually estimated by least squares based on estimated kalman filter state sequences and the observed inputs and outputs for a finite number of data points the estimated system matrix is not guaranteed to be stable even when the true linear system is known to be stable in this paper stability is imposed by using regularization the regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive semi definite weighting matrix the amount of regularization can be determined from a generalized eigenvalue problem the data augmentation method of chui and maciejowski 1996 is obtained by using specific choices for the weighting matrix in the regularization term

identification of non linear parametrically varying models using separable least squares in this paper a novel identification algorithm for a class of non linear possibly parameter varying models is proposed the algorithm is based on separable least squares ideas these models are given in the form of a linear fractional transformation lft where the forward part is represented by a conventional linear regression and the feedback part is given by a non linear map which can take into account scheduling variables available for measurement the non linear part of the model can be parameterized according to various paradigms like e g neural network nn or general nonlinear autoregressive exogenous narx models the estimation algorithm exploits the separability of the criterion used to estimate the parameters when using a nn it is possible the explicit computation of the frechet derivative needed to implement a separable least square algorithm

inference of disjoint linear and nonlinear sub domains of a nonlinear mapping this paper investigates new ways of inferring nonlinear dependence from measured data the existence of unique linear and nonlinear sub spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub spaces are derived the importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task specifically once the linear nonlinear sub spaces are known by definition the explanatory variables may be transformed to form two disjoint sub sets spanning respectively the linear and nonlinear sub spaces the nonlinear modelling task is confined to the latter sub set which will typically have a smaller number of elements than the original set of explanatory variables constructive algorithms are proposed for inferring the linear and nonlinear sub spaces from noisy data

data based identification and control of nonlinear systems via piecewise affine approximation the piecewise affine pwa model represents an attractive model structure for approximating nonlinear systems in this paper a procedure for obtaining the pwa autoregressive exogenous arx autoregressive systems with exogenous inputs models of nonlinear systems is proposed two key parameters defining a pwarx model namely the parameters of locally affine subsystems and the partition of the regressor space are estimated the former through a least squares based identification method using multiple models and the latter using standard procedures such as neural network classifier or support vector machine classifier having obtained the pwarx model of the nonlinear system a controller is then derived to control the system for reference tracking both simulation and experimental studies show that the proposed algorithm can indeed provide accurate pwa approximation of nonlinear systems and the designed controller provides good tracking performance

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

data driven detrending of nonstationary fractal time series with echo state networks abstract in this paper we propose a novel data driven approach for removing trends detrending from nonstationary fractal and multifractal time series we consider real valued time series relative to measurements of an underlying dynamical system that evolves through time we assume that such a dynamical process is predictable to a certain degree by means of a class of recurrent networks called echo state network esn which are capable to model a generic dynamical process in order to isolate the superimposed multi fractal component of interest we define a data driven filter by leveraging on the esn prediction capability to identify the trend component of a given input time series specifically the estimated trend is removed from the original time series and the residual signal is analyzed with the multifractal detrended fluctuation analysis procedure to verify the correctness of the detrending procedure in order to demonstrate the effectiveness of the proposed technique we consider several synthetic time series consisting of different types of trends and fractal noise components with known characteristics we also process a real world dataset the sunspot time series which is well known for its multifractal features and has recently gained attention in the complex systems field results demonstrate the validity and generality of the proposed detrending method based on esns

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

nonlinear identification with local model networks using gtls techniques and equality constraints local model networks approximate a nonlinear system through multiple local models fitted within a partition space the main advantage of this approach is that the identification of complex nonlinear processes is alleviated by the integration of structured knowledge about the process this paper extends these concepts by the integration of quantitative process knowledge into the identification procedure quantitative knowledge describes explicit dependences between inputs and outputs and is integrated in the parameter estimation process by means of equality constraints for this purpose a constrained generalized total least squares algorithm for local parameter estimation is presented furthermore the problem of proper integration of constraints in the partitioning process is treated where an expectation maximization procedure is combined with constrained parameter estimation the benefits and the applicability of the proposed concepts are demonstrated by means of two illustrative examples and a practical application using real measurement data

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

quantifying origin and character of long range correlations in narrative texts in natural language using short sentences is considered efficient for communication however a text composed exclusively of such sentences looks technical and reads boring a text composed of long ones on the other hand demands significantly more effort for comprehension studying characteristics of the sentence length variability slv in a large corpus of world famous literary texts shows that an appealing and aesthetic optimum appears somewhere in between and involves selfsimilar cascade like alternation of various lengths sentences a related quantitative observation is that the power spectra s f of thus characterized slv universally develop a convincing 1 fs scaling with the average exponent s 1 2 close to what has been identified before in musical compositions or in the brain waves an overwhelming majority of the studied texts simply obeys such fractal attributes but especially spectacular in this respect are hypertext like stream of consciousness novels in addition they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals scaling of s f in the present context implies existence of the long range correlations in texts and appearance of multifractality indicates that they carry even a nonlinear component a distinct role of the full stops in inducing the long range correlations in texts is evidenced by the fact that the above quantitative characteristics on the long range correlations manifest themselves in variation of the full stops recurrence times along texts thus in slv but to a much lesser degree in the recurrence times of the most frequent words in this latter case the nonlinear correlations thus multifractality disappear even completely for all the texts considered treated as one extra word the full stops at the same time appear to obey the zipfian rank frequency distribution however

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

quantum moment hydrodynamics and the entropy principle this paper presents how a non commutative version of the entropy extremalization principle allows to construct new quantum hydrodynamic models our starting point is the moment method which consists in integrating the quantum liouville equation with respect to momentum p against a given vector of monomials of p like in the classical case the so obtained moment system is not closed inspired from levermore s procedure in the classical case 26 we propose to close the moment system by a quantum wigner distribution function which minimizes the entropy subject to the constraint that its moments are given in contrast to the classical case the quantum entropy is defined globally and not locally as the trace of an operator therefore the relation between the moments and the lagrange multipliers of the constrained entropy minimization problem becomes nonlocal and the resulting moment system involves nonlocal operators instead of purely local ones in the classical case in the present paper we discuss some practical aspects and consequences of this nonlocal feature

quantum dynamical semigroups for diffusion models with hartree interaction we consider a class of evolution equations in lindblad form which model the dynamics of dissipative quantum mechanical systems with mean field interaction particularly this class includes the so called quantum fokker planck poisson model the existence and uniqueness of global in time mass preserving solutions is proved thus establishing the existence of a nonlinear conservative quantum dynamical semigroup the mathematical difficulties stem from combining an unbounded lindblad generator with the hartree nonlinearity

a flexible state space model for learning nonlinear dynamical systems we consider a nonlinear state space model with the state transition and observation functions expressed as basis function expansions the coefficients in the basis function expansions are learned f

kernel based partially linear models and nonlinear identification in this note we propose partially linear models with least squares support vector machines ls svms for nonlinear arx models we illustrate how full black box models can be improved when prior information about model structure is available a real life example based on the silverbox benchmark data shows significant improvements in the generalization ability of the structured model with respect to the full black box model reflected also by a reduction in the effective number of parameters

identification of nonlinear systems using polynomial nonlinear state space models in this paper we propose a method to model nonlinear systems using polynomial nonlinear state space equations obtaining good initial estimates is a major problem in nonlinear modelling it is solved here by identifying first the best linear approximation of the system under test the proposed identification procedure is successfully applied to measurements of two physical systems

approximate dynamic programming based approaches for input output data driven control of nonlinear processes we propose two approximate dynamic programming adp based strategies for control of nonlinear processes using input output data in the first strategy which we term j learning one builds an empirical nonlinear model using closed loop test data and performs dynamic programming with it to derive an improved control policy in the second strategy called q learning one tries to learn an improved control policy in a model less manner compared to the conventional model predictive control approach the new approach offers some practical advantages in using nonlinear empirical models for process control besides the potential reduction in the on line computational burden it offers a convenient way to control the degree of model extrapolation in the calculation of optimal control moves one major difficulty associated with using an empirical model within the multi step predictive control setting is that the model can be excessively extrapolated into regions of the state space where identification data were scarce or nonexistent leading to performances far worse than predicted by the model within the proposed adp based strategies this problem is handled by imposing a penalty term designed on the basis of local data distribution a cstr example is provided to illustrate the proposed approaches

on the hinge finding algorithm for hingeing hyperplanes this correspondence concerns the estimation algorithm for hinging hyperplane hh models a piecewise linear model for approximating functions of several variables suggested in breiman 1993 the estimation algorithm is analyzed and it is shown that it is a special case of a newton algorithm applied to a sum of squared error criterion this insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed in addition the way of updating the parameters in the hh model is discussed in breiman a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step this connects closely to some previously suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters

nonlinear system identification via laguerre network based fuzzy systems in this study identification of nonlinear systems via laguerre network based fuzzy model is introduced we first describe the proposed modeling approach in detail and suggest a fast learning scheme for its training the proposed approach is applied in three dynamic system modeling problems including box jenkins gas furnace data and forced van der pol oscillator when we compare the performance of the proposed approach against the classical sugeno and adaptive network based fuzzy inference system modeling our approach is found to have superior modeling performance and generalization capability