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

covering relations for multidimensional dynamical systems abstract we present a topological technique for analyzing dynamical systems with complex behavior based on the general notion of covering relations our method can be used to study multidimensional dynamical systems with an arbitrary number of topologically expanding directions

a new topological technique for characterizing homoclinic tangles we have developed a topological approach called homotopic lobe dynamics for describing the qualitative structure of homoclinic tangles this approach begins from an efficient and accurate description of the initial development of a tangle up to some finite number of iterates j where the value of j indicates the amount of information that one puts into the theory our approach can then compute the topologically forced structure of the tangle at all iterates after j this allows one for example to predict a minimal set of homoclinic intersections this technique places few assumptions on the homoclinic tangles considered in fact one main advantage is its ability to describe the wide variety of behaviour seen in physically significant tangles

convergence analysis of an online approach to parameter estimation problems based on binary observations in this paper we present an online identification method to the problem of parameter estimation from binary observations a recursive identification algorithm with low storage requirements and computational complexity is derived we prove the convergence of this method provided that the input signal satisfies a strong mixing property some simulation results are then given in order to illustrate the properties of this method under various scenarios this method is appealing in the context of micro electronic devices since it only requires a 1 bit analog to digital converter with low power consumption and minimal silicon area

a groupoid approach to pseudodifferential calculi we give an algebraic geometric characterization of the classical pseudodifferential operators on a smooth manifold in terms of the tangent groupoid and its natural r action specifically we show that a properly supported semiregular distribution on m m is the schwartz kernel of a classical pseudo differential operator if and only if it extends to a smooth family of distributions on the range fibres of the tangent groupoid which is homogeneous for the r action modulo smooth functions moreover we show that the basic properties of pseudo differential operators can be proven directly from this characterization finally we show that with the appropriate generalization of the tangent bundle the same definition applies without change to define pseudodifferential calculi on arbitrary filtered manifolds and in particular the heisenberg calculus

minlip for the identification of monotone wiener systems this paper studies the minlip estimator for the identification of wiener systems consisting of a sequence of a linear fir dynamical model and a monotonically increasing or decreasing static function given t observations this algorithm boils down to solving a convex quadratic program with o t variables and inequality constraints implementing an inference technique which is based entirely on model complexity control a technique which is dubbed as einstein s razor this technique is proven to yield here almost consistent estimates in case the given data is suitably rich local persistently exciting of sufficient order and if the samples obey a true monotone wiener system satisfying some regularity conditions it is then indicated how to extend the method in order to cope with noisy data and empirical evidence is given in order to support the claim of efficiency

strong consistence of recursive identification for wiener systems the paper concerns identification of the wiener system consisting of a linear subsystem followed by a static nonlinearity f with no invertibility and structure assumption recursive estimates are given for coefficients of the linear subsystem and for the value f v at any fixed v the main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values this probably is the first strong consistency result for this kind of wiener systems a numerical example is given which justifies the theoretical analysis

identification of wiener systems with binary valued output observations this work is concerned with identification of wiener systems whose outputs are measured by binary valued sensors the system consists of a linear fir finite impulse response subsystem of known order followed by a nonlinear function with a known parametrization structure the parameters of both linear and nonlinear parts are unknown input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible it is shown that under scaled periodic inputs identification of wiener systems can be decomposed into a finite number of core identification problems the concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the wiener system can be identified with binary valued observations under scaled full rank conditions and joint identifiability a strongly convergent algorithm is constructed the algorithm is shown to be asymptotically efficient for the core identification problem hence achieving asymptotic optimality in its convergence rate for computational simplicity recursive algorithms are also developed

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

iterative algorithm for parameter identification of hammerstein systems with two segment nonlinearities this paper deals with parameter identification of hammerstein systems having two segment polynomial nonlinearities the application of a simple decomposition technique and using switching sequences provide a special form of a hammerstein model that is linear in parameters this model is used in an iterative algorithm enabling simultaneous estimation of all of the model parameters to demonstrate the feasibility of the identification method more illustrative examples are included

adaptive filtering using quantized output measurements a normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response fir model is discussed the algorithm identifies the system exactly given only coarsely quantized output measurements a description of the quantizer is included in the overall input output model and the scheme exploits an approximation of the derivative of the quantizer using an associated differential equation global convergence is established to a zero output error except for possible colored measurement disturbances parameter setting or to the boundary of the model set

intrinsic pseudo differential calculi on any compact lie group abstract in this paper we define in an intrinsic way operators on a compact lie group by means of symbols using the representations of the group the main purpose is to show that these operators form a symbolic pseudo differential calculus which coincides or generalises the local hormander pseudo differential calculus on the group viewed as a compact manifold

convolution on homogeneous groups abstract let g be a homogeneous group with homogeneous dimension q and let s o denote the space of schwartz functions on g with all moments vanishing let be the usual euclidean fourier transform for j r we let d j s o be the space of j smooth away from 0 satisfying j c j where both and are taken in the homogeneous sense we characterize d j and show that d j 1 d j 2 d j 1 j 2 as elements of s o if j 1 j 2 j 1 j 2 q one can replace s o s o by s s in this result a key ingredient of our proof is a lemma from the fundamental wavelet paper from 1985 by frazier and jawerth 4 we believe that in turn our result will be useful in the theory of wavelets on homogeneous groups

subspace identification for non linear systems with measured input non linearities this paper uses subspace methods to identify a class of multi input multi output discrete time non linear time varying systems specifically we identify systems that are non linear in measured data and linear in unmeasured states numerical examples are presented to demonstrate the efficacy of the method

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

parameter identification of wiener systems with discontinuous nonlinearities abstract the paper deals with modeling and parameter identification of wiener type nonlinear dynamic systems having discontinuous asymmetric piecewise linear characteristics with preloads and dead zones multiple application of a decomposition technique provides a special form of static nonlinearity description its incorporation into the wiener model leads to an input output equation where all the model parameters are separated and can be estimated iteratively using input output data and internal variable estimates more illustrative examples are included to demonstrate the feasibility of the proposed approach

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

the atiyah singer index formula for subelliptic operators on contact manifolds part i the atiyah singer index theorem gives a topological formula for the index of an elliptic differential operator the topological index depends on a cohomology class that is constructed from the principal symbol of the operator on contact manifolds the important fredholm operators are not elliptic but hypoelliptic their symbolic calculus is noncommutative and is closely related to analysis on the heisenberg group for a hypoelliptic differential operator in the heisenberg calculus on a contact manifold we construct a symbol class in the k theory of a noncommutative c algebra that is associated to the algebra of symbols there is a canonical map from this analytic k theory group to the ordinary cohomology of the manifold which gives a de rham class to which the atiyah singer formula can be applied we prove that the index formula holds for these hypoelliptic operators our methods derive from connes tangent groupoid proof of the index theorem

an improved algorithm for computing topological entropy a new algorithm is presented for computing the topological entropy of a unimodal map of the interval the accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed

optimal recursive state estimation with quantized measurements a set of exact nonlinear filters is derived and analyzed the filters perform recursive state estimation when only coarsely quantized output signals are available a system with the dynamics given by n integrators together with a uniform prior on the state vector form the model assumptions in the case with one integrator properties of the quantizer allows the construction of an exact recursive algorithm for the updating of the probability density function p d f using only the corners of a convex polygon defining the region where the p d f is nonzero it is also shown how to generalize the algorithm to handle multiple measurements quantized with vector quantizers

identifiability and convergence analysis of the minlip estimator this paper studies the problem of identifying a monotone wiener system from observed noiseless input output signals specifically we study identifiability of such systems as well as the convergence properties of the recently introduced minimal lipschitz minlip estimator this estimator finds a system with minimal complexity by exploiting ordering of the output samples this makes the approach conceptual quite different from traditional identification schemes based on least squares prediction errors maximum likelihood or numerical projections sufficient conditions from which the result follows are given in terms of rotational complete inputs rci a generalization of the notion of persistency of excitation pe as used for the study of linear identification methods finally it is derived that a gaussian i i d sequence satisfies this rci property while any binary sequence does not

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

circle criteria in recursive identification positive real conditions and differential sector conditions have recently been shown to imply global convergence w p 1 for recursive identification schemes based on a class of single input single output linear wiener models the models consist of linear dynamics followed by a static output nonlinearity the model structure is hence closely related to that of the lure problem in the stability theory of feedback systems this paper proves that the conditions for convergence can be transformed to graphical circle criteria depending on the sector conditions and on the nyquist plot of a transfer function related to the prior knowledge of the poles of the identified system

estimation of quantized linear errors in variables models we present an estimation algorithm for dynamic shock error models dsem given 1 bit quantized noisy measurements of the input and output the algorithm is called the binary series estimation algorithm bsea bsea is computationally inexpensive since it involves counting the number of occurrences of particular patterns of zeros and ones in the input and output sequences it yields consistent parameter estimates that are asymptotically normal

noncommutative residue for heisenberg manifolds applications in cr and contact geometry abstract this paper has four main parts in the first part we construct a noncommutative residue for the hypoelliptic calculus on heisenberg manifolds that is for the class of h do operators introduced by beals greiner and taylor this noncommutative residue appears as the residual trace on integer order h dos induced by the analytic extension of the usual trace to non integer order h dos moreover it agrees with the integral of the density defined by the logarithmic singularity of the schwartz kernel of the corresponding h do in addition we show that this noncommutative residue provides us with the unique trace up to constant multiple on the algebra of integer order h dos in the second part we give some analytic applications of this construction concerning zeta functions of hypoelliptic operators logarithmic metric estimates for green kernels of hypoelliptic operators and the extension of the dixmier trace to the whole algebra of integer order h dos in the third part we present examples of computations of noncommutative residues of some powers of the horizontal sublaplacian and the contact laplacian on contact manifolds in the fourth part we present two applications in cr geometry first we give some examples of geometric computations of noncommutative residues of some powers of the horizontal sublaplacian and of the kohn laplacian second we make use of the framework of noncommutative geometry and of our noncommutative residue to define lower dimensional volumes in pseudohermitian geometry e g we can give sense to the area of any 3 dimensional cr manifold endowed with a pseudohermitian structure on the way we obtain a spectral interpretation of the einstein hilbert action in pseudohermitian geometry

computing the topological entropy of maps we give an algorithm for determining the topological entropy of a unimodal map of the interval given its kneading sequence we also show that this algorithm converges exponentially in the number of letters of the kneading sequence

recursive identification of fir systems with binary valued outputs and communication channels this paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary valued quantization and the communication unreliability the discrete memoryless channel with packet losses and the additive white gaussian noise channel with time delay are considered a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters under some mild conditions the algorithms can be proved to be convergent in the almost sure and mean square senses also the convergence rates are given numerical examples are included to illustrate the performance of the algorithms

complex valued b spline neural networks for modeling and inverting hammerstein systems many communication signal processing applications involve modeling and inverting complex valued cv hammerstein systems we develop a new cv b spline neural network approach for efficient identification of the cv hammerstein system and effective inversion of the estimated cv hammerstein model in particular the cv nonlinear static function in the hammerstein system is represented using the tensor product from two univariate b spline neural networks an efficient alternating least squares estimation method is adopted for identifying the cv linear dynamic model s coefficients and the cv b spline neural network s weights which yields the closed form solutions for both the linear dynamic model s coefficients and the b spline neural network s weights and this estimation process is guaranteed to converge very fast to a unique minimum solution furthermore an accurate inversion of the cv hammerstein system can readily be obtained using the estimated model in particular the inversion of the cv nonlinear static function in the hammerstein system can be calculated effectively using a gaussian newton algorithm which naturally incorporates the efficient de boor algorithm with both the b spline curve and first order derivative recursions the effectiveness of our approach is demonstrated using the application to equalization of hammerstein channels

generalizations of the classical weyl and colin de verdiere s formulas and the orbit method the classical weyl formula expresses the leading term of the asymptotics of the counting function n h of the spectrum of a self adjoint operator h in an invariant form one can hear the volume of the subset of the cotangent bundle where the symbol of the operator h is less than in particular it is applicable to schrodinger operators with electric potentials growing at infinity the weyl formula is formulated in an invariant form however it gives for magnetic schrodinger operators with magnetic tensors growing at infinity for these operators colin de verdiere s formula is known but the form of the latter is not invariant in this article we suggest an invariant generalization of both weyl s and colin de verdiere s formulas for wide classes of schrodinger operators with polynomial electric and magnetic fields the construction is based on the orbit method due to kirillov and it allows one to hear the geometry of coadjoint orbits

compensated compactness for differential forms in carnot groups and applications abstract in this paper we prove a compensated compactness theorem for differential forms of the intrinsic complex of a carnot group the proof relies on an l s hodge decomposition for these forms because of the lack of homogeneity of the intrinsic exterior differential hodge decomposition is proved using the parametrix of a suitable 0 order laplacian on forms

computation of symbolic dynamics for one dimensional maps in this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise monotone continuous maps of the interval the algorithms are based on computing forwards and backwards approximations of the boundary discontinuity and critical points we explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint the method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced van der pol equation

estimates for the bergman and szego kernels in mathbf c 2 the purpose of this paper some of whose conclusions were announced in nrsw is to study the bergman and szegd projection operators on pseudoconvex domains q of finite type in c2 the results we obtain are of three kinds i the size estimates of the bergman and szeg6 kernels and their derivatives ii the cancellation properties of those kernels expressed in terms of the actions of these operators on suitable bump functions these properties have an interest in their own right but are also crucial in iii below iii the sharp mapping properties of these operators on functions spaces such as lp the nonisotropic sobolev spaces and the nonisotropic lipschitz spaces which are naturally attached to the geometry of the boundary this also leads ultimately to sharp results in the regularity properties of solutions of the equation du f in q and 9bu f on the boundary let us describe these matters in more detail our starting points are certain basic geometric constructs associated to q a metric p defined in terms of the vector fields x1 and x2 which are the real and imaginary parts of the tangential levi vector field on d 2 and a function a p 8 a polynomial in 8 for p e d 2 which represents the higher levi invariant attached to d 9 the significance of these to the geometry of d q can be understood from the following facts the ball b p 8 c d q centered at p of radius 8 in the metric p when viewed in the appropriate coordinates has width 8 in the complex tangential directions but its width is a p 8 in the complementary direction thus the volume of the ball is 82a p 8 among other crucial properties

a symbolic calculus and l2 boundedness on nilpotent lie groups abstract we work on a general nilpotent lie group g g 1 g 2 g r where r 1 and g k j k r is the descending central series of g a composition theorem and an l 2 boundedness theorem for convolution operators f f a are proved the composition theorem holds for symbols a a satisfying the estimates d a c m g where m is a weight and g g 1 1 g r r where g k 1 j k 1 r j 2 1 2 1 2 the class of weights admissible for the calculus is considerably larger than those of the existing calculi for the l 2 boundedness it is sufficient that d a c g this goes in the direction of howe s conjecture and improves the results of howe and manchon it is very likely that our methods could also be used to extend the calculus of melin to general homogeneous groups

series expansion approach to the analysis and identification of discrete hammerstein systems in this paper a finite series expansion method is presented for the analysis and parameter identification of a discrete non linear system that is described by a hammerstein model consisting of a memoryless gain of polynomial form followed by a linear discrete system by expanding the system variables in discrete legendre orthogonal polynomials dlops and using the shift and product operational properties of dlops the hammerstein model is converted into a set of linear equations in the dlop coefficients of unknown output variables and in the system parameters this converted set of linear algebraic equations is convenient for finding the dlop coefficients of unknown variables also it allows one to determine the unknown system parameters using the least squares method when the system input and output data are available

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

discrete time adaptive control of linear dynamic systems with a two segment piecewise linear asymmetric nonlinearity in this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a two segment piecewise linear asymmetric nonlinearity followed by a linear system a switching gain sequence is introduced to make the parameter identification time invariant the algorithm will ensure that the closed loop system is globally convergent and stable for both the deterministic and stochastic cases

kneading theory a functorial approach we study the homology theory of modal maps of the interval we give another proof of the milnor and thurston results about zeta functions and we give a functorial approach to kneading theory our results give explicit methods for computing the sequences of lap numbers f k and the sequences of numbers of periodic points in an arbitrary interval x y

formule de weyl pour les groupes de lie nilpotents pour tout groupe de lie g reel nilpotent simplement connexe on definit les classes de symboles sur le dual de son algebre de lie pour toute representation unitaire irreductible de g et pour tout symbole p on definit l operateur de symbole de weyl p agissant sur l espace de la representation on etablit alors une formule donnant le comportement asymptotique des valeurs propres de l operateur en fonction des valeurs prises par son symbole de weyl sur l orbite co adjointe associee a la representation par la methode de kirillov dans le cas ou le symbole est elliptique dans la direction du cone asymptote a l orbite

recursive identification for wiener model with discontinuous piece wise linear function this paper deals with identification of wiener systems with nonlinearity being a discontinuous piece wise linear function recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid gaussian inputs the estimates are proved to converge to the corresponding true values with probability one a numerical example is given to justify the obtained theoretical results

identification of fir systems based on quantized output measurements a quadratic programming based method this technical note proposes a quadratic programming qp based method for identification of finite impulse response fir dynamic systems from quantized or binary data the main idea of the proposed method is to reformulate this identification problem usually viewed as a nonlinear estimation problem with discontinuous nonlinearities in the form of a standard qp problem which is a convex optimization problem and can be solved efficiently the so called complete input conditions to ensure the unique solution of the qp problem are developed and the consistency of the estimated parameters is established under the complete input conditions numerical examples demonstrate the effectiveness of the proposed method

quantized identification with dependent noise and fisher information ratio of communication channels system identification is studied in which the system output is quantized transmitted through a digital communication channel and observed afterwards this paper explores strong convergence efficiency and complexity of identification algorithms under colored noise and dependent communication channels it first presents algorithms for certain core identification problems using quantized observations on the basis of empirical measures and nonlinear mappings strong consistency with probability one convergence is established under mixing noises furthermore with pre quantization signal processing it is shown that certain modified algorithms can achieve asymptotic efficiency under correlated noises to improve convergence speeds quantization threshold adaptation algorithms are introduced these results are then used to study the impact of communication channels on system identification under dependent channels the concept of fisher information ratio is introduced to characterize such impact it is shown that the fisher information ratio can be calculated from certain channel characteristic matrices the relationship between the fisher information ratio and shannon s channel capacity is discussed from the angle of time and space information the methods of identification input designs that link general system parameters to core identification problems are reviewed

on estimation of errors caused by non linear undermodelling in system identification the problem of quantifying errors due to non linear undermodelling is addressed in particular the wiener system which consists of a linear dynamic block followed by a static non linearity and the hammerstein system in which the order of these two blocks is reversed are studied in either case it is assumed that the objective is to identify the linear part of the system using a purely linear model these scenarios can be interpreted as linear identification applied to systems where non linearity errors may occur and hence need to be quantified the stochastic embedding approach is therefore applied to capture the on average properties of the undermodelling due to inadequate representation of the non linear effects as compared to previous methods the priors on the covariance matrix of the embedding parameters are reduced as a result an expression for the amplitude error bound of the estimated transfer function that does not require knowledge of the true system parameters is obtained the quality of t

fixed order fir approximation of linear systems from quantized input and output data the problem of identifying a fixed order fir approximation of linear systems with unknown structure assuming that both input and output measurements are subjected to quantization is dealt with in this paper a fixed order fir model providing the best approximation of the input output relationship is sought by minimizing the worst case distance between the output of the true system and the modeled output for all possible values of the input and output data consistent with their quantized measurements the considered problem is firstly formulated in terms of robust optimization then two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented the effectiveness of the proposed approach is illustrated by means of a simulation example

identification of sparse fir systems using a general quantisation scheme this paper presents an identification scheme for sparse fir systems with quantised data we consider a general quantisation scheme which includes the commonly deployed static quantiser as a special case to tackle the sparsity issue we utilise a bayesian approach where an l1 a priori distribution for the parameters is used as a mechanism to promote sparsity the general framework used to solve the problem is maximum likelihood ml the ml problem is solved by using a generalised expectation maximisation algorithm

computing the topological entropy of maps of the interval with three monotone pieces an algorithm is presented for computing the topological entropy of a piecewise monotone map of the interval having three monotone pieces the accuracy of the algorithm is discussed and some graphs of the topological entropy obtained using the algorithm are displayed some of the ideas behind the algorithm have application to piecewise monotone functions with more than three monotone pieces

output error convergence of adaptive filters with compensation for output nonlinearities output error convergence of a wiener model based nonlinear stochastic gradient algorithm is analyzed the normalized scheme estimates the parameters of a linear finite impulse response model in cascade with a known output nonlinearity the algorithm can be interpreted as a normalized least mean square algorithm with compensation for an output nonlinearity linearizing inversion of the nonlinearity is not utilized global output error convergence is then proved provided that the nonlinearity is monotone not strictly monotone and provided that a previously observed mechanism resulting in deadlock does not occur the algorithm and the analysis include important practical cases like sensor saturation and dead zones that must be excluded when global parametric convergence is studied

brief paper computational complexity analysis of set membership identification of hammerstein and wiener systems this paper analyzes the computational complexity of set membership identification of hammerstein and wiener systems its main results show that even in cases where a portion of the plant is known the problems are generically np hard both in the number of experimental data points and in the number of inputs wiener or outputs hammerstein of the nonlinearity these results provide new insight into the reasons underlying the high computational complexity of several recently proposed algorithms and point out the need for developing computationally tractable relaxations

on the regularity of inverses of singular integral operators sur r d on considere un operateur de convolution sf f k ou k est une distribution homogene de degre d on suppose que s s etend a un operateur borne et inversible sur l 2 r d l inverse de s est donne par convolution avec une distribution l aussi homogene de degre d on montre qu une regularite possedee par k est partagee par l

an analytic geometry approach to wiener system frequency identification this paper addresses the problem of wiener system identification the underlying linear subsystem is stable but not necessarily parametric the nonlinear element in turn is allowed to be nonparametric noninvertible and nonsmooth as wiener models are uniquely defined up to an uncertain multiplicative factor it makes sense to start the frequency identification process estimating the system phase which is common to all models to this end a consistent estimator is designed using analytic geometry tools accordingly the system frequency behavior is characterized by a family of lissajous curves interestingly all these curves are candidates to modelling the system nonlinearity but the most convenient one is the less spread of them finally the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates

identification input design for consistent parameter estimation of linear systems with binary valued output observations input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values this paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary valued output observations necessary and sufficient conditions on periodic signals are derived for sufficient richness these conditions are further studied under different system configurations including open loop and feedback systems and different scenarios of noises including actuator noise input measurement noise and output measurement noise in addition to system parameter estimation essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown the findings of this paper provide a foundation to study identification of systems that either use binary valued or quantized sensors or involve communication channels which mandate quantization of signals

identification of wiener hammerstein and narx systems as markov chains with improved estimates for their nonlinearities abstract the wiener hammerstein and nonlinear arx systems are identified not only for their linear subsystems if they exist but also for the nonlinearities with their first derivatives it is assumed that the input signals and noises are mutually independent and both are sequences of independent and identically distributed iid random variables the estimates based on the stochastic approximation algorithms with expanding truncations saawet are proved to be strongly consistent with the help of the markov properties possessed by these systems the estimates of the first derivatives improve the accuracy of interpolating the nonlinearity curves as validated by simulation examples

towards identification of wiener systems with the least amount of a priori information on the nonlinearity in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the fir linear part is identifiable in the non gaussian input case three types of a priori information are considered including quadrant information point information and locally monotonous information in all three cases identifiability has been established and corresponding identification algorithms are developed with their convergence proofs

recursive identification of hammerstein systems with discontinuous nonlinearities containing dead zones this note deals with the recursive parameter identification of hammerstein systems with discontinuous nonlinearities i e two segment piecewise linear with dead zones and preloads a special form of the hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables the proposed method is illustrated by examples

towards identification of wiener systems with the least amount of a priori information iir cases in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non gaussian input case under the white noise input three types of a priori information are considered quadrant information point information and monotonic information in all three cases identifiability has been established and the corresponding nonparametric identification algorithms are developed along with their convergence proofs

adaptive regulator for hammerstein and wiener systems with noisy observations for hammerstein and wiener systems observed with additive noises the adaptive regulation control is produced by a truncated stochastic approximation sa algorithm with truncation regions expanding with a prescribed rate it is proved that the stochastic adaptive control given in this note is optimal in the sense that it minimizes the long run average of regulation errors a s

calcul symbolique sur les groupes de lie nilpotents et applications abstract for any real nilpotent connected and simply connected lie group g and for any unitary irreducible representation of g we define the generally unbounded operator with left symbol p acting on the hilbert space of the representation the symbol p being some c function defined on the dual g of the lie algebra g of g and prove that the operator thus defined can be viewed as a classical pseudo differential operator whose left symbol r is explicitly related to p we also compute the link between left and weyl symbolic calculus on g as an application we prove that if the symbol p defined on g vanishes on a neighbourhood of the coadjoint orbit associated to by means of kirillov s method then the operator with weyl or left symbol p is a smoothing operator hence we extend the weyl formula proved in previous work to elliptic symbols

brief paper discrete time adaptive control of linear systems with preload nonlinearity in this note a method is presented for doing discrete time adaptive control of a nonlinear system which is given by a cascade connection of a preload nonlinearity followed by a linear system it is shown that the algorithm will ensure that the closed loop system is globally convergent with a specific residue and stable for both the deterministic and stochastic cases

what you need to know to knead 1 introduction 2 the main kneading identity 3 milnor and thurston s definitions 4 an identity for the kneading determinant 5 the inverse of the kneading matrix 6 meromorphic functions in the unit disk 7 piecewise linear models 8 counting fixed points 9 total variation 10 an invariant measure with maximal entropy 11 appendix kneading theory for mappings with discontinuities

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

identification of wiener type nonlinear systems in a noisy environment wiener systems are widely encountered in engineering and science applications this paper proposes a straightforward approach to the identification of wiener systems in a noisy environment the obtained models are represented in terms of the frequency response for the linear subsystem and the inverse of the static nonlinearity a variety of input excitation signals including random binary and periodic can be used with the proposed method simulation studies using a ph neutralization continuous stirred tank reactor show that excellent results are obtained with relatively short data lengths

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

a weighted least squares approach to parameter estimation problems based on binary measurements we present a new approach to parameter estimation problems based on binary measurements motivated by the need to add integrated low cost self test features to microfabricated devices this approach is based on the use of original weighted least squares criteria as opposed to other existing methods it requires no dithering signal and it does not rely on an approximation of the quantizer in this technical note we focus on a simple choice for the weights and establish some asymptotical properties of the corresponding criterion to achieve this the assumption that the quantizer s input is gaussian and centered is made in this context we prove that the proposed criterion is locally convex and that it is possible to use a simple gradient descent to find a consistent estimate of the unknown system parameters regardless of the presence of measurement noise at the quantizer s input

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

parameter identification of discontinuous hammerstein systems the paper deals with the parameter identification of hammerstein systems having discontinuous asymmetric nonlinearities two segment piecewise linear with preload and dead zone application of a simple decomposition technique provides a special form of hammerstein model with a minimum number of parameters the identification is carried out with only one record of measured input output data despite the dead zone to demonstrate the feasibility of the identification method some illustrative examples are included

identification of wiener systems with quantized inputs and binary valued output observations this paper investigates identification of wiener systems with quantized inputs and binary valued output observations by parameterizing the static nonlinear function and incorporating both linear and nonlinear parts we begin by investigating system identifiability under the input and output constraints then a three step algorithm is proposed to estimate the unknown parameters by using the empirical measure input persistent patterns and information on noise statistics convergence properties of the algorithm including strong convergence and mean square convergence rate are established furthermore by selecting a suitable transformation matrix the asymptotic efficiency of the algorithm is proved in terms of the cramrrao lower bound finally numerical simulations are presented to illustrate the main results of this paper

recursive identification of systems with binary valued outputs and with arma noises abstract this paper considers the identification problem of the arma system followed by a binary sensor in which the internal variables are corrupted by additive arma noises recursive estimates for the parameters of the linear system and for the threshold of the binary sensor are given by the stochastic approximation algorithms with expanding truncations saawet under reasonable conditions all the estimates are proved to be convergent to the true values with probability one the almost surely convergence rates are also investigated a simulation example is included to justify the theoretical results

parameter identification of wiener systems with multisegment piecewise linear nonlinearities the paper deals with the identification of wiener systems having multisegment piecewise linear nonlinearities a special form of nonlinearity representation is used in the wiener system description the resulting output equation contains the least possible number of parameters required for the blocks of given system the proposed iterative method enables simultaneous estimation of both the linear block parameters and all the parameters characterizing the nonlinearity i e the slopes of linear segments and the constants determining the partition of domain limits for the constants are the only a priori knowledge required

how nonlinear parametric wiener system identification is under gaussian inputs a number of methods exist for identifying nonlinear wiener systems however there is no attempt to address the fundamental question of how nonlinear these identification problems really are in this technical note we try to address this question by investigating the average squared error cost function used in identification by a proper normalization and a clever characterization of the cost function in terms of the angle between the true but unknown parameter vector and its estimate it is shown in the technical note that under iid gaussian inputs for parametric wiener systems with polynomial nonlinear parts and fir linear parts the cost function is globally monotonic and has one and only one local and global minimum the implication is that identification of such systems is nonlinear but very close to linear further any local search based identification algorithms would converge globally for such systems

stochastic gradient identification of polynomial wiener systems analysis and application this paper presents analytical numerical and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial type nonlinear system with memory for noisy output observations the analysis includes the computation of the stationary points the mean square error surface and the stability regions of the algorithm for gaussian data convergence of the mean is studied using l sub 2 and euclidian norms monte carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise an application is presented for the identification of a nonlinear time delayed feedback system

combined frequency prediction error identification approach for wiener systems with backlash and backlash inverse operators wiener systems identification is studied in the presence of possibly infinite order linear dynamics and memory nonlinear operators of backlash and backlash inverse types the latter is laterally bordered with polynomial lines of arbitrary shape it turns out that the borders are allowed to be noninvertible and crossing making possible to account within a unified theoretical framework for memory and memoryless nonlinearities moreover the prior knowledge of the nonlinearity type being backlash or backlash inverse or memoryless is not required using sine excitations and getting benefit from model plurality the initial complex identification problem is made equivalent to two tractable though still nonlinear prediction error problems these are coped with using linear and nonlinear least squares estimators which all are shown to be consistent

noncommutative topology and the world s simplest index theorem in this article we outline an approach to index theory on the basis of methods of noncommutative topology we start with an explicit index theorem for second order differential operators on 3 manifolds that are fredholm but not elliptic this low brow index formula is expressed in terms of winding numbers we then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds finally we discuss the noncommutative topology that is employed in the proof of this theorem the article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry