universal approximations of discrete time control systems over finite time we present an algorithm for obtaining approximate internal descriptions for a discrete time control system given a finite number of external experiments input output data the system is required only to be causal with a continuous input output map the experiments should be done in a prescribed way with bounded inputs acting over a finite period of time the approximation will be valid over the ranges of inputs and time covered by the experiments the algorithm can be considered as an exact partial realization procedure for state affine systems an e stable computer program will be sketched

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

nonlinear model based control using second order volterra models abstract a nonlinear controller synthesis scheme is presented that retains the original spirit and characteristics of conventional linear model predictive control mpc while extending its capabilities to nonlinear systems the scheme employs a volterra model a simple and convenient nonlinear extension of the linear convolution model employed by conventional mpc and gives rise to a controller composed of a conventional linear controller augmented by an auxiliary loop of nonlinear corrections simulation case studies involving two different examples representative of the typical spectrum of nonlinear behavior in real chemical processes an industrial polymerization reactor and an isothermal reactor exhibiting inverse response are used to demonstrate the practical utility of the control scheme and to evaluate its performance

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

tensor based aam with continuous variation estimation application to variation robust face recognition the active appearance model aam is a well known model that can represent a non rigid object effectively however the fitting result is often unsatisfactory when an input image deviates from the training images due to its fixed shape and appearance model to obtain more robust aam fitting we propose a tensor based aam that can handle a variety of subjects poses expressions and illuminations in the tensor algebra framework which consists of an image tensor and a model tensor the image tensor estimates image variations such as pose expression and illumination of the input image using two different variation estimation techniques discrete and continuous variation estimation the model tensor generates variation specific aam basis vectors from the estimated image variations which leads to more accurate fitting results to validate the usefulness of the tensor based aam we performed variation robust face recognition using the tensor based aam fitting results to do we propose indirect aam feature transformation experimental results show that tensor based aam with continuous variation estimation outperforms that with discrete variation estimation and conventional aam in terms of the average fitting error and the face recognition rate

fast active appearance model search using canonical correlation analysis a fast aam search algorithm based on canonical correlation analysis cca aam is introduced it efficiently models the dependency between texture residuals and model parameters during search experiments show that cca aams while requiring similar implementation effort consistently outperform standard search with regard to convergence speed by a factor of four

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

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

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

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

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

modeling of nonlinear discrete time systems from input output data abstract an algorithm is presented that produces a polynomial state affine model for a discrete time nonlinear system the method uses only input output information and is based on a difference equation approximation to the input output map from the difference equation a behaviour matrix is constructed to be used in the state affine realization algorithm the difference equation approach requires the estimation of fewer parameters than the usual volterra series a state space model is then obtained directly from the difference equation as a byproduct a method for calculating the volterra series directly from the difference equation is obtained practical applications to nonlinear systems are included

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

volterra series arising from the discrete schrodinger wave equation in l2 a b space the wave solution of the stationary schrodinger wave equation has been studied extensively however after removing restriction on potential function the problem of obtaining the wave solution becomes considerably difficult methods available in the literature for the closed form wave solution are applicable to specific potential for this reason it is important to strive for the wave solution with a general class of potential functions this paper introduces the volterra series framework to address this limitation the volterra system is a natural extension of linear systems such systems take into account quadratic cubic and more generally polynomial kind of non linearities in the systems the volterra system is a non linear system with the structure of the volterra series here we decompose first a wave function in an appropriate function space and subsequently the wave equation is discretized as a result of this we obtain a bilinear system treating potential as input and wave function as output such an analysis is based on inherent bilinear character of the schrodinger equation in which potential is bilinearly coupled to the wave function this paper discusses state space methodology to recover the volterra series from the bilinear systems the volterra series is attractive from the system theoretic point of view since it describes the output of a class of non linear systems explicitly in terms of the input rather than involving coupling terms and allows substantial simplifications for the numerical simulation a simulation result is introduced to demonstrate the efficacy of the proposed analysis

a finiteness criterion for nonlinear input output differential systems we solve the following problem which has been dealt with in several publications when does a system have the same input output behaviour as a system depending linearly on the state variables precise definitions of this question are supplied in the text a particular case of the problem is the equivalence of a system with a bilinear one at the end we illustrate our methods and the scope of our results by a brief study of several examples

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

on two definitions of observation spaces this paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of differentiable controls

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

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

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

representing a nonlinear state space system as a set of higher order differential equations in the inputs and outputs an algorithm is presented for transforming a nonlinear state space system into a threefold set of equations the first subset describing the dynamics of the unobservable part of the system the second subset representing the remaining state variables as functions of inputs and outputs and their derivatives and the last subset defining the external behaviour of the system

normal forms for matrices over uniserial rings of length two this paper develops methods to describe the conjugacy classes of gl n r on rn n for a serial ring r of length two the main result is a reduction to a computation in the matrix algebra over the residue class field of r which in some cases can be done theoretically without any actual computation

on the trade off between feasibility and performance in bilinear and state affine model based predictive control closed loop stabilizing model based predictive control mpc algorithms for discrete time bilinear and state affine models are presented stability of the closed loop is obtained through the use of an appropriate end point weighting and end point inequality constraint in this way the infinite horizon performance index is bounded from above by the objective function that is minimized in the mpc algorithm this paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off line the region that is defined by the end point inequality constraint in order to improve the performance of the mpc algorithm the conservatism of the upper bound on the infinite horizon performance index is reduced in the on line computations

classical state space realizability of input output bilinear models this paper studies the realizability property of bilinear input output i o models in the classical state space form constraints on the parameters of the bilinear i o model are suggested that lead to realizable models the complete list of 2nd and 3rd order realizable input output bilinear models together with the corresponding state equations is given in the general case some subclasses of realizable bilinear models together with their state space realizations are presented including the diagonal bilinear model and the special subclass of the superdiagonal bilinear model

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

similarity classes of3 3 matrices over a discrete valuation ring abstract let q be a complete discrete valuation ring let be a prime element in q write p q for n 1 2 letqn be the factor ring q pn let g g13 qn denote by mn the g module of 3 3 matrices over qn modulo scalar matrices canonical forms are found for every element in mn and it is shown that there exist five sets of similarity classes some results about the general case of n x n matrices over q also are proved

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

stability of nonlinear polynomial arma models and their inverse stability and invertibility of discrete time polynomial arma models are studied in an extended neighbourhood to extend the local results obtained earlier the analysis combines linear robust control and classical nonlinear system theories polynomial arma models are used as examples illustrating the theory

similarity classes for nilpotent operators over dedekind domains abstract let r be a commutative dedekind domain and let v denote a finitely generated torsion free module over r let gl v denote the r module endomorphisms of v n v gl v the set of nilpotent endomorphisms and gl v the automorphisms of v we construct a canonical filtration and invariant ideals associated to elements of n v to study several gl v invariant properties of n v under the similarity action g l glg 1 l n v g gl v we use these invariants to give a finite determinacy criterion for the similarity of nilpotent endomorphisms n v

polynomial perceptrons and their applications to fading channel equalization and co channel interference suppression this paper investigates the behaviors of polynomial perceptrons and introduces a fractionally spaced recursive polynomial perceptron with low complexity and fast convergence rate the nonlinear mapping ability of the polynomial perceptron is analyzed it is shown that a polynomial perceptron with degree l spl ges 4 satisfies the stone weierstrass theorem and can approximate any continuous function to within a specified accuracy moreover the nonlinear mapping ability of a polynomial perceptron with degree l is similar to that of the three layer perceptron with one hidden layer for time same number of neurons in the input layer the nonlinear mapping ability of the fractionally spaced recursive polynomial perceptron is also presented applications of polynomial perceptrons for fading channel equalization and co channel interference suppression in a 16 level quadrature amplitude modulation receiver system are considered computer simulations are used to evaluate and compare the performance of polynomial perceptron pp and fractionally spaced bilinear perceptron fsblp with that of the synchronous decision feedback multilayer perceptron sdfmlp fractionally spaced decision feedback multilayer perceptron fsdfmlp and the conventional decision feedback equalizer dfe the results show that the performance of the fractionally spaced bilinear perceptron is clearly superior to that of the other structures

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

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

generating series for bilinear hybrid systems in this paper we introduce the novel concept of a hybrid generating series and show that continuous state and output trajectories of bilinear hybrid systems can be described in terms of these series the results represent an extension of the fliess series expansion for bilinear systems to hybrid systems

instantons and geometric invariant theory we show that the yang mills instantons can be described in terms of certain holomorphic bundles on the projective plane the proof uses explicit matrix descriptions arising from monads and an analysis of the corresponding groups of symmetries

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

active appearance models revisited active appearance models aams and the closely related concepts of morphable models and active blobs are generative models of a certain visual phenomenon although linear in both shape and appearance overall aams are nonlinear parametric models in terms of the pixel intensities fitting an aam to an image consists of minimising the error between the input image and the closest model instances i e solving a nonlinear optimisation problem we propose an efficient fitting algorithm for aams based on the inverse compositional image alignment algorithm we show that the effects of appearance variation during fitting can be precomputed projected out using this algorithm and how it can be extended to include a global shape normalising warp typically a 2d similarity transformation we evaluate our algorithm to determine which of its novel aspects improve aam fitting performance

a remark on bilinear systems and moduli spaces of instantons abstract explicit equations are given for the moduli space of framed instantons as a quasi affine variety based on the representation theory of noncommutative power series or equivalently the minimal realization theory of bilinear systems

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

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

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

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

some realizations of algorithms for nonlinear input output systems this paper develops an algorithm which given an input output differential equation produces under appropriate circumstances a parametrization of the observation space of the underlying state space system the paper extends previous results by the authors to a more general setting so that state space systems in which the controls enter nonlinearly can be accommodated and most importantly the paper deals with implicitly defined systems at both the input output and state space level fliess and hasler have demonstrated the importance of implicit input output models which yield only local state space descriptions various realizations are obtained depending on the properties of the derived candidate observation space examples of the algorithm are described with the aid of an implementation using the computer algebra system axiom

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

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

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

multilinear graph embedding representation and regularization for images given a set of images finding a compact and discriminative representation is still a big challenge especially when multiple latent factors are hidden in the way of data generation to represent multifactor images although multilinear models are widely used to parameterize the data most methods are based on high order singular value decomposition hosvd which preserves global statistics but interprets local variations inadequately to this end we propose a novel method called multilinear graph embedding mge as well as its kernelization mkge to leverage the manifold learning techniques into multilinear models our method theoretically links the linear nonlinear and multilinear dimensionality reduction we also show that the supervised mge encodes informative image priors for image regularization provided that an image is represented as a high order tensor from our experiments on face and gait recognition the superior performance demonstrates that mge better represents multifactor images than classic methods including hosvd and its variants in addition the significant improvement in image or tensor completion validates the potential of mge for image regularization

a unified gradient based approach for combining asm into aam active appearance model aam framework is a very useful method that can fit the shape and appearance model to the input image for various image analysis and synthesis problems however since the goal of the aam fitting algorithm is to minimize the residual error between the model appearance and the input image it often fails to accurately converge to the landmark points of the input image to alleviate this weakness we have combined active shape models asm into aams in which asms try to find correct landmark points using the local profile model since the original objective function of the asm search is not appropriate for combining these methods we derive a gradient based iterative method by modifying the objective function of the asm search then we propose a new fitting method that combines the objective functions of both asm and aam into a single objective function in a gradient based optimization framework experimental results show that the proposed fitting method reduces the average fitting error when compared with existing fitting methods such as asm aam and texture constrained asm tc asm and improves the performance of facial expression recognition significantly

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

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

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

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

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

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

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