nonlinear damping estimation from rotor stability data using time and frequency domain techniques for estimating equivalent damping characteristics from transient response data involving nonlinear damping modifications to two stability testing methods the moving block technique and the sparse time domain method are presented and verified by the use of numerical simulations effects of large undamped response and noise on the performance of these techniques are evaluated for quadratic and coulomb dampings it is concluded that equivalent damping characteristics may be identified from sampled multimode and noisy nonlinear transient response data using modified versions of the moving block analysis and the sparse time domain method

identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

recursive identification using feedforward neural networks the paper is concerned with the identification of an unknown nonlinear dynamical system when only the inputs and outputs are accessible for measurement under certain assumptions it is shown that generically the system can be realized by a recursive input output model furthermore relying on the approximation properties of neural networks and the existence of effective training algorithms it is demonstrated how an effective identification model can be constructed simulation results are presented to complement the theoretical discussions

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

two stage orthogonal least squares methods for neural network construction a number of neural networks can be formulated as the linear in the parameters models training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms forward selection methods are popular fast subset selection approaches however they may only produce suboptimal models and can be trapped into a local minimum more recently a two stage fast recursive algorithm tsfra combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model this paper proposes unified two stage orthogonal least squares methods instead of the fast recursive based methods in contrast to the tsfra this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods furthermore a new term exchanging scheme for backward model refinement is introduced to reduce computational demand finally given the error reduction ratio criterion effective and efficient forward and backward subset selection procedures are proposed extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods

state dependent parameter models of non linear sampled data systems a velocity based linearization approach discrete time models with state dependent parameters are derived for non linear sampled data systems velocity based linearization of the continuous time system followed by integration over the sampling interval is used to represent the sampled data system by a discrete time state space model with state dependent parameters by reconstructing the state a quasi arx model is obtained the parameters of which are functions of past inputs and outputs as the velocity based linearization procedure does not involve suppression of higher order terms the state dependent state space model and the quasi arx description give exact representations of the non linear system

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

analogy between a 10d model for nonlinear wave wave interaction in a plasma and the 3d lorenz dynamics this paper investigates nonlinear wave wave interactions in a system that describes a modified decay instability and consists of three langmuir and one ion sound waves as a means to establish that the underlying dynamics exists in a 3d space and that it is of the lorenz type both continuous and discrete time multivariable global models were obtained from data these data were obtained from a 10d dynamical system that describes the modified decay instability obtained from zakharov s equations which characterise langmuir turbulence this 10d model is equivariant under a continuous rotation symmetry and a discrete order 2 rotation symmetry when the continuous rotation symmetry is modded out that is when the dynamics are represented with the continuous rotation symmetry removed under a local diffeomorphism it is shown that a 3d system may describe the underlying dynamics for certain parameter values the models obtained using global modelling techniques from three time series from the 10d dynamics with the continuous rotation symmetry modded out generate attractors which are topologically equivalent these models can be simulated easily and due to their simplicity are amenable for analysis of the original dynamics after symmetries have been modded out moreover it is shown that all of these attractors are topologically equivalent to an attractor generated by the well known lorenz system 2003 elsevier science b v all rights reserved

generalized expression for the numbers of perfect matching of cylindrical m n graphs the analytical expression for the numbers of perfect matching for the cylindrical m n lattice graphs was derived by diagonalizing the skew symmetric matrix after kasteleyn but with a little modification the results are compared with the recursion relations obtained earlier by the present authors

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

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

parameterized convergence bounds for volterra series expansion of narx models evaluation of the convergence bound in the frequency domain for volterra series expansion of nonlinear systems described by narx models is studied this provides new convergence criteria under which the nonlinear system of interest has a convergent volterra series expansion and the new criteria are expressed explicitly in terms of the input magnitude model parameters and frequency variable the new convergence criteria are firstly developed for harmonic inputs and then extended to multi tone and general input cases based on the theoretical analysis a general procedure for calculating the convergence bound is provided the results provide a fundamental basis for nonlinear signal processing using the volterra series theory

bilinear realizability is equivalent to existence of a singular affine differential i o equation abstract for continuous time analytic input output maps existence of a singular differential equation relating derivatives of controls and outputs is shown to be equivalent to bilinear realizability a similar result holds for the problem of immersion into bilinear systems the proof is very analogous to that of the corresponding and previously known result for discrete time

identification of nonlinear systems using narmax model abstract most systems encountered in the real world are nonlinear in nature and since linear models cannot capture the rich dynamic behavior of limit cycles bifurcations etc associated with nonlinear systems it is imperative to have identification techniques which are specific for nonlinear systems the problem considered in this work is the modeling of nonlinear discrete systems based on the set of input output data this is often the only approach to modeling as in most cases only external i e input output data are available this paper also discusses the practical aspects of identification of nonlinear systems the narmax nonlinear autoregressive moving average with exogenous input model provides a unified representation for a wide class of nonlinear systems and has obvious advantages over functional series representations such as volterra and wiener series this model is proven to provide a better parameter estimation and prediction accuracy than the linear model

frequency response functions for nonlinear rational models a recursive algorithm which maps a general class of nonlinear rational model defined as the ratio of two polynomial functions into the frequency domain is derived using the harmonic expansion method the new algorithm provides for the first time a direct analytic map from the time domain rational model parameters to the higher order frequency response functions complex nonlinear time domain behaviours can be analysed and interpreted in the frequency domain and simulated examples are included to illustrate the concepts involved

online identification of the bilinear model expansion on laguerre orthonormal bases this paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input to the output and to the crossed product on three independent laguerre orthonormal bases compared to classical bilinear model the resulting model entitled bilinear laguerre model ensures a significant parameter number reduction as well as simple recursive representation however this reduction is still subject to an optimal choice of the laguerre poles defining the three laguerre bases therefore we propose an analytical solution to optimise the laguerre poles which depend on fourier coefficients defining the bilinear laguerre model and that are identified using the regularised square error the identification procedures of the laguerre poles and fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the bilinear laguerre model the bilinear laguerre model as well as the proposed algorithm are illustrated and tested

difference equations versus differential equations a possible equivalence for the rossler system abstract when a set of nonlinear differential equations is investigated most of time there is no analytical solution and only numerical integration techniques can provide accurate numerical solutions in a general way the process of numerical integration is the replacement of a set of differential equations with a continuous dependence on the time by a model for which the time variable is discrete in numerical investigations a fourth order runge kutta integration scheme is usually sufficient nevertheless sometimes a set of difference equations may be required and in this case standard schemes like the forward euler backward euler or central difference schemes are used the major problem encountered with these schemes is that they offer numerical solutions equivalent to those of the set of differential equations only for sufficiently small integration time steps in some cases it may be of interest to obtain difference equations with the same type of solutions as for the differential equations but with significantly large time steps nonstandard schemes as introduced by mickens nonstandard finite difference models of differential equations world scientific 1994 allow to obtain more robust difference equations in this paper using such nonstandard scheme we propose some difference equations as discrete analogues of the rossler system for which it is shown that the dynamics is less dependent on the time step size than when a nonstandard scheme is used in particular it has been observed that the solutions to the discrete models are topologically equivalent to the solutions to the rossler system as long as the time step is less than the threshold value associated with the nyquist criterion

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

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

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

recursive hybrid algorithm for non linear system identification using radial basis function networks recursive identification of non linear systems is investigated using radial basis function networks a novel approach is adopted which employs a hybrid clustering and least squares algorithm the recursive clustering algorithm adjusts the centres of the radial basis function network while the recursive least squares algorithm estimates the connection weights of the network because these two recursive learning rules are both linear rapid convergence is guaranteed and this hybrid algorithm significantly enhances the real time or adaptive capability of radial basis function models the application to simulated real data are included to demonstrate the effectiveness of this hybrid approach

the occupation statistics for indistinguishable dumbbells on a rectangular lattice space i the method of hock and mcquistan used recently to solve the occupation statistics for indistinguishable dumbbells or dimers on a 2 2 n lattice is extended further to obtain for the l m n lattice general expressions for the normalization expectation and dispersion of the statistics and their limit as n becomes very large in particular an explicit expression of the partition function in the thermodynamic limit x is obtained for any value of the absolute activity x of dimers the developed mathematical formalism is then applied to planar lattices 1 m n with m 1 2 3 and 4 the known results for m 1 and 2 are recovered and some new ones are obtained the recurrence relation for the number a q n of arrangements of q dumbbells on a 1 m n lattice which has 3 and 5 terms when m 1 and 2 respectively is found to have 15 and 65 terms for m 3 and 4 analysis and extrapolation of the results enable one to predict the expectation 1mn on a planar 1 m n lattice to be 63 4 in the limit as both m a

identification of non linear effects in rotor systems using recursive qr factorization method there are several non linear and time variant effects in a rotor bearing dynamic system the non linear characteristics of the rolling element bearing internal damping unsymmetrical stiffness of the shaft cracks on the shaft and the radial clearance are the typical root causes of these effects 1 as rotating speeds increase and rotor weights decrease these non linear and time variant effects could significantly affect the dynamic characteristics of the rotor system 2 8 if these non linear and time variant effects are ignored the vibration response could lead to incorrect interpretation of the rotor system this will significantly affect the performance of the rotor vibration control schemes the accuracy of the diagnosis results and the performance of any schemes where an accurate rotor model is needed therefore the accurate identification of both the model structure and parameters of a rotor bearing system including the non linear effects is an important engineering problem a large body of literature concentrates on this area tiwari and vyas 9 developed a technique for estimating the non linear stiffness of rolling element bearings imam et al 10 completed an on line rotor crack detection and monitoring system krodkiewski and ding 11 found a method for on site estimation of the alignment of multi bearing rotor systems tasker and chopra 12 used the rotor stability data to estimate the non linear damping of the system compared to the parameter estimation the non linear model structure identification is quite difficult an optimal search scheme is usually needed to find an adequate model among all the possible ones desrochers and mohseni 13 used a model set that has a multi layered combinatorial tree structure they showed that searching the tree for the optimal n term model could be done in n stages kanjilal et al 14 developed a method for fast selection of significant variables in linear in the parameter models by using modified orthogonal triangular factorization also called qr factorization the distinctive characteristic of their method is that estimations of article in press

matching and symmetry of graphs abstract matching is a mathematical concept that deals with the way of spanning a given graph network with a set of pairs of adjacent points it is pointed out that in many different areas of science and culture e g physics chemistry games etc computing the perfect and imperfect matching numbers is commonly performed but under different names such as partition function for dimer statistics kekule structures of molecules paving domino problem this paper demonstrate the mathematically beautiful but somewhat mystic relation between the symmetry of a graph and the factorable nature of its perfect matching number there is introduced another interesting relation between the certain series of graphs and a family of orthogonal polynomials through the matching polynomial and topological index that are defined for counting the matching numbers

dynamical realizations of finite volterra series in this paper realizations of finite volterra series are viewed as nonlinear analytic input output systems with state space described by an analytic manifold for a minimal realization guaranteed by h j sussmann the state space which is unique up to diffeomorphism is shown to have the homogeneous space structure of a nilmanifold the quotient of two nilpotent lie groups the structure of nilmanifolds as described by a malcev is used to show that for these systems the state space has a vector space structure as a consequence of this result it is shown that a minimal realization of a finite volterra series can be described as a cascade of linear subsystems with polynomial link maps in which the dimension o f each linear subsystem is independent of the realization considered

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

an effective algorithm for obtaining polynomials for dimer statistics application of operator technique on the topological index to two and three dimensional rectangular and torus lattices recursion formulas on the numbers of ways for placing an arbitrary number of indistinguishable dumbbells on the various rectangular lattice spaces 3 n 4 n and torus spaces 2 n 3 n 2 2 n were obtained by the use of the operator technique to the counting polynomial on the topological characteristics e g nonadjacent number kekule number and topological index perfect matching numbers or kekule numbers were also obtained for larger lattices such as the 4 n torus and the 2 3 n lattice by deriving these new results the utility of the proposed method for dimer statistics is demonstrated and some of their mathematical features are discussed

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

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

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

control of nonlinear dynamical systems using neural networks ii observability identification and control for pt i see ibid vol 4 1993 this paper considers the problems of regulation and tracking of a dynamical system when the state variables of the dynamical system are not accessible the existence of the nonlinear maps describing the identifier and controller are first established and the implications for neural network realizations are described simulation results are included to complement the theoretical discussions

identification of a continuous structure with a geometrical non linearity part i conditioned reverse path method particular effort has been spent in the field of identification of multi degree of freedom non linear systems the newly developed methods permit the structural analyst to consider increasingly complex systems the aim of this paper and a companion paper is to study by means of two methods a continuous non linear system consisting of an experimental cantilever beam with a geometrical non linearity in this paper part i the ability of the conditioned reverse path method which is a frequency domain technique to identify the behaviour of this structure is assessed the companion paper part ii is devoted to the application of proper orthogonal decomposition which is an updating technique to the test example

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

generalized expression of the perfect matching number for 2 3 n lattices a closed form of the perfect matching number for the cubic lattice of 2 3 n was obtained in terms of the linear combination of determinants which was derived from its recursive expression this is the first analytic solution for dimer statistics on three dimensional cubic cell lattices it is potentially applicable to the analytic solution of the ising model for the general l m n lattice

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

recovering map static nonlinearities from chaotic data using dynamical models abstract this paper is concerned with the estimation from chaotic data of maps with static nonlinearities a number of issues concerning model construction such as structure selection over parametrization and model validation are discussed in the light of the shape of the static non linearities reproduced by the estimated maps a new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach the paper discusses model limitations and some useful principles to select the structure of nonlinear maps some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit

conformal mapping of nonsmooth domains via the kerzman stein integral equation abstract the connection between the riemann map and the szego kernel is classical but the fact that there is an efficient numerical procedure based on the kerzman stein integral equation for computing the szego kernel of a smoothly bounded domain in the plane is more recent in this paper it is shown how to extend the results of kerzman and stein to certain nonsmooth domains this provides a new method for numerically computing the szego kernel and hence the riemann map of these domains

dynamical effects of overparametrization in nonlinear models abstract this paper is concemed with dynamical reconstruction for nonlinear systems the effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated it is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns the complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters in this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes moreover some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels in order to precisely quantify the complexity of the reconstructions global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks

mapping non linear integro differential equations into the frequency domain a recursive algorithm is derived to compute the generalized frequency response functions for a large class of non linear integro differential equations applications to duffing s equation and a modified van der pol model are discussed

adaptive nn control for a class of discrete time non linear systems in this paper adaptive neural network nn control is investigated for a class of single input single output siso discrete time unknown non linear systems with general relative degree in the presence of bounded disturbances firstly the systems are transformed into a causal state space description adaptive state feedback nn control is presented based on lyapunov s stability theory then by converting the systems into a causal input output representation adaptive output feedback nn control is given finally adaptive nn observer design and observer based adaptive control are presented under the assumption of persistent excitation pe all the control schemes avoid the so called controller singularity problem in adaptive control by suitably choosing the design parameters the closed loop systems are proven to be semi globally uniformly ultimately bounded sguub simulation studies show the effectiveness of the newly proposed schemes

recursive algorithm for computing the frequency response of a class of non linear difference equation models abstract a recursive algorithm is developed which is both computationally compact and enables the nth order frequency response functions of a large class of non linear difference equation models to be found without restriction on the order n

a prediction error method for recursive indentification of nonlinear systems abstract nonlinear systems can be identified with nonlinear filters by combined estimation of parameters and state often these methods are very complex or have convergence problems as for example the extended kalman filter in this paper a new algorithm for recursive nonlinear system identification is presented convergence problems are eliminated by an improved calculation of the gradient as the total derivative of the prediction error by separately estimating parameters and states computation time is reduced the efficacy of the new identification algorithm is illustrated by studying its performance in a gravimetric filling system

analysis of the effects of time delay in nonlinear systems using generalised frequency response functions abstract a recursive algorithm for computing the generalised frequency response functions gfrfs of nonlinear time delay systems described by nonlinear differential difference equation models is derived using the operator e n and used to analyse the effects of time delay in nonlinear systems the algorithm shows an explicit relationship between the model parameters and the gfrfs such a relationship provides important insight into the behaviour of nonlinear systems the effect of delay on several properties of nonlinear systems such as harmonic generation gain compression expansion and desensitisation is studied by considering the example of a duffing oscillator with retarded damping results of the studies convincingly demonstrate that the system delay has a significant effect on several important properties of nonlinear systems

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

on critical stability of discrete time adaptive nonlinear control in this paper we examine the global stability and instability problems for a class of discrete time adaptive nonlinear stochastic control the systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics which are characterized by a nonlinear function say f x it is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares ls based adaptive control systems to be specific let the growth rate of f x be f x o spl par x spl par sup 6 with b spl ges 0 then it is found that b 4 is a critical value for global stability i e the closed loop adaptive system is globally stable if b 4 and is unstable in general if b spl ges 4 as a consequence we find an interesting phenomenon that the linear case does not have for some ls based certainty equivalence adaptive controls even if the ls parameter estimates are strongly consistent the closed loop systems may still be unstable this paper also indicates that adaptive nonlinear stochastic control that is designed based on e g taylor expansion or weierstrass approximation for nonlinear models may not be feasible in general

holomorphic reproducing kernels for piecewise smooth planar domains abstract for smoothly bounded multiply connected domains in the complex plane s bell showed how the kerzman stein method can be used to compute the szeg kernel and ahlfors map in this paper we present a modification of that method for domains that are piecewise smooth the procedure is based on a method of preliminary transformation and involves adding an explicit holomorphic function to the cauchy kernel in the last section we show the effectiveness of using this method for the special case of a square

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

input output modeling of nonlinear systems with time varying linear models time varying arma autoregressive moving average and armax autoregressive moving average with exogenous inputs models are proposed for input output modeling of nonlinear deterministic and stochastic systems the coefficients of these models are estimated by a random walk kalman filter rwkf this method requires no prior assumption on the nature of the model coefficients and is suitable for real time implementation since no off line training is needed a simulation example illustrates the method goodness of performance is judged by the quality of the residuals histograms autocorrelation functions and the kolmogorov smirnoff test

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

existence and uniqueness of realizations of nonlinear systems necessary and sufficient conditions for the existence of either analytic or smooth symmetric realizations of nonlinear input output maps are given it is also shown that two minimal realizations are diffeomorphic

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

identification of block oriented nonlinear systems starting from linear approximations a survey abstract block oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use many different identification approaches were developed over the years to estimate the parameters of a wide range of block oriented nonlinear models one class of these approaches uses linear approximations to initialize the identification algorithm the best linear approximation framework and the approximation framework or equivalent frameworks allow the user to extract important information about the system guide the user in selecting good candidate model structures and orders and prove to be a good starting point for nonlinear system identification algorithms this paper gives an overview of the different block oriented nonlinear models that can be identified using linear approximations and of the identification algorithms that have been developed in the past a non exhaustive overview of the most important other block oriented nonlinear system identification approaches is also provided throughout this paper

numerical conformal mapping via the bergman kernel a new method to compute the riemann mapping function via the bergman kernel is presented the method expresses the bergman kernel as the solution of a second kind integral equation involving the neumann kernel for symmetric regions the integral equation can be transformed into a new one that uses only a small part of the original boundary numerical implementations on some test regions are also presented

the occupation statistics for indistinguishable dumbbells on a 2 2 n lattice space a 20 term recursion relation is derived that describes exactly the occupation statistics for indistinguishable dumbbells which occupy two nearest neighbor sites distributed on a 2 2 n lattice space on the basis of this recursion the normalization expectation dispersion and continuous representation of the statistics are also developed when the lattice space is completely filled the recursion relationship reduces to four terms permitting a calculation of the orientational degeneracy of a completely filled 2 2 n lattice space

a unified wavelet based modelling framework for non linear system identification the wanarx model structure a new unified modelling framework based on the superposition of additive submodels functional components and wavelet decompositions is proposed for non linear system identification a non linear model which is often represented using a multivariate non linear function is initially decomposed into a number of functional components via the well known analysis of variance anova expression which can be viewed as a special form of the narx non linear autoregressive with exogenous inputs model for representing dynamic input output systems by expanding each functional component using wavelet decompositions including the regular lattice frame decomposition wavelet series and multiresolution wavelet decompositions the multivariate non linear model can then be converted into a linear in the parameters problem which can be solved using least squares type methods an efficient model structure determination approach based upon a forward orthogonal least squares ols algorithm which involves a stepwise o

an upper hessenberg sparse matrix algorithm for modal identification on minicomputers the time domain modal identification problem is here reduced to an eigenvalue problem of a sparse upper hessenberg matrix such a matrix has only a number of elements equal to its order one column subdiagonal elements of unity and all the other remaining elements are zeros the one vector elements of this matrix are obtained by using cholesky decomposition to solve a positive definite system of equations which is constructed by using a structure s free decay or impulse time histories any number of measurements may be used from one or more tests with a single or multiple shaker the direct use of an upper hessenberg matrix eliminates the need of transforming a full matrix to such a form and consequently greatly reduces the computational requirements when the qr algorithm is used for the eigensolution in addition to reducing computer time and storage the proposed technique has more flexibility than other comparable time domain approaches it also produces higher identification accuracy especially in the identified damping factors sample results are presented with comparisons to those of other time domain algorithms

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

non parametric identification of non linear oscillating systems the problem of system identification from a time series of measurements is solved by using non parametric additive models having only few structural information about the system a non parametric approach may be more appropriate than a parametric one for which detailed prior knowledge is needed based on non parametric regression the functions in the additive models are estimated by a penalized least squares approach using backfitting the optimal smoothing parameters are determined via generalized cross validation making this approach completely adaptive to the data the procedure is applied to identify the non linear restoring force of vibrationally excited helical wire rope isolators

variable selection algorithm for the construction of mimo operating point dependent neurofuzzy networks an input variable selection procedure is introduced for the identification and construction of multi input multi output mimo neurofuzzy operating point dependent models the algorithm is an extension of a forward modified gram schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting the proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice based modeling algorithms such as radial basis function neurofuzzy networks enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm