a new completely general class of variational inclusions with noncompact valued mappings abstract in this paper we introduce and study a new completely general class of variational inclusions with noncompact valued mappings and construct some new iterative algorithms we prove the existence of solutions for the completely general class of variational inclusions and the convergence of iterative sequences generated by the algorithms

noisy input output system identification using cumulants and the steiglitz mcbride algorithm we consider the problem of identifying a linear time invariant system from its noisy input output data the input and output are assumed to be non gaussian while the input and output noises are assumed to be mutually correlated colored and gaussian using third order cross and auto cumulants we extend the well known steiglitz mcbride 1965 identification method to cumulant domains and show that it is consistent under a certain third order persistency of excitation condition by comparison the steiglitz mcbride method is not consistent when either input noise is present or when the output noise is colored for an empirical assessment we provide simulations that demonstrate the proposed method s usefulness

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

third order cumulants based methods for continuous time errors in variables model identification in this paper the problem of identifying stochastic linear continuous time systems from noisy input output data is addressed the input of the system is assumed to have a skewed probability density function whereas the noises contaminating the data are assumed to be symmetrically distributed the third order cumulants of the input output data are then asymptotically insensitive to the noises that can be coloured and or mutually correlated using this noise cancellation property two computationally simple estimators are proposed the usefulness of the proposed algorithms is assessed through a numerical simulation

covariance matching for continuous time errors in variables problems a covariance matching approach for continuous time errors in variables problems is considered the noise free input signal is not explicitly modeled and is only assumed to be a stationary process it is described how three different systems of equations in the model parameters are obtained and how the parameters are estimated based on these systems of equations the approach is illustrated by some numerical studies

on the accuracy of a covariance matching method for continuous time errors in variables identification on the accuracy of a covariance matching method for continuous time errors in variables identification

regularization aspects in continuous time model identification this paper presents an analysis of some regularization aspects in continuous time model identification the study particulary focuses on linear filter methods and shows that filtering the data before estimating their derivatives corresponds to a regularized signal derivative estimation by minimizing a compound criterion whose expression is given explicitly a new structure based on a null phase filter corresponding to a true regularization filter is proposed and allows to discuss the filter phase effects on parameter estimation by comparing its performances with those of the poisson filter based methods based on this analysis a formulation of continuous time model identification as a joint system input output signal and model parameter estimation is suggested in this framework two linear filter methods are interpreted and a compound criterion is proposed in which the regularization is ensured by a model fitting measure resulting in a new regularization filter structure for signal estimation

stochastic system identification with noisy input output measurements using polyspectra two new classes of parametric frequency domain approaches are proposed for estimation of the parameters of scalar linear errors in variables models i e linear systems where measurements of both input and output of the system are noise contaminated the first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross bispectrum or the integrated cross polyspectrum the system transfer function is first estimated at a number of frequencies exceeding one half the number of unknown parameters the estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations in the second class of approaches quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used the proposed parameter estimators are shown to be consistent in gaussian measurement noise when trispectral approaches are used

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

l 2 optimal identification of mimo errors in variables models from the v gap geometrical interpretation an l 2 optimal identification method is extended to cope with mimo errors in variables eiv model estimation based on a geometrical interpretation for the v gap metric the l 2 optimal approximate models are composed of system and noise models and characterised by a normalised right graph symbol nrgs and its complementary inner factor cif respectively this metric can be evaluated as the supreme of sine values of the maximal principal angles between nrgs frequency responses of two concerned models in order to make full use of the angular cosine formula for complex vectors to reduce computational loads a cif of the nrgs of the perturbed model is introduced and thus the system parameter optimisation can be efficiently solved by sequential quadratic programming methods with the estimated system model the associated noise model can be built by right multiplication of an inner matrix finally a simulation example demonstrates the effectiveness of the proposed identification method

brief paper unifying some higher order statistic based methods for errors in variables model identification in this paper the problem of identifying linear discrete time systems from noisy input and output data is addressed several existing methods based on higher order statistics are presented it is shown that they stem from the same set of equations and can thus be united from the viewpoint of extended instrumental variable methods a numerical example is presented which confirms the theoretical results some possible extensions of the methods are then given

instrumental variable methods for closed loop system identification in this paper several instrumental variable iv and instrumental variable related methods for closed loop system identification are considered and set in an extended iv framework extended iv methods require the appropriate choice of particular design variables as the number and type of instrumental signals data prefiltering and the choice of an appropriate norm of the extended iv criterion the optimal iv estimator achieves minimum variance but requires the exact knowledge of the noise model for the closed loop situation several iv methods are put in an extended iv framework and characterized by different choices of design variables their variance properties are considered and illustrated with a simulation example

consistent identification of stochastic linear systems with noisy input output data abstract a novel criterion is introduced for parametric errors in variables identification of stochastic linear systems excited by non gaussian inputs the new criterion is at least theoretically insensitive to a class of input output disturbances because it implicitly involves higher than second order cumulant statistics in addition it is shown to be equivalent to the conventional mean squared error mse as if the latter was computed in the ideal case of noise free input output data the sampled version of the criterion converges to the novel mse and guarantees strongly consistent parameter estimators the asymptotic behavior of the resulting parameter estimators is analyzed and guidelines for minimum variance experiments are discussed briefly informative enough input signals and persistent of excitation conditions are specified computatonally attractive recursive least squares variants are also developed for on line implementation of arma modeling and their potential is illustrated by applying them to time delay estimation in low snr environment the performance of the proposed algorithms and comparisons with conventional methods are corroborated using simulated data

completely generalized strongly nonlinear quasi complementarity problems in hilbert spaces in this paper we introduce and study a class of completely generalized strongly nonlinear quasi complementarity problems and construct a new iterative algorithm which includes many existing algorithms as special cases for solving the complementarity problems we prove the existence of solutions for this class of quasi complementarity problems and the convergence of iterative sequences generated by this algorithm

generalized nonlinear mixed quasi variational inequalities abstract in this paper we introduce and study a new class of quasi variational inequalities which is called the generalized nonlinear set valued mixed quasi variational inequality using the resolvent operator technique for maximal monotone mapping we construct some new iterative algorithms for solving this class of generalized nonlinear set valued mixed quasi variational inequalities we prove the existence of solution for this kind of generalized nonlinear set valued mixed quasivariational inequalities without compactness and the convergence of iterative sequences generated by the algorithms we also discuss the convergence and stability of perturbed iterative algorithm for solving a class of generalized nonlinear mixed quasi variational inequalities

fast frequency template matching using higher order statistics this correspondence proposes a novel template matching technique using a fourth central moment the fourth central moment is an established estimator which uses higher order statistics theory important in the presence of an additive gaussian noise by use of some substitutions and complex arithmetic computation of the fourth central moment is derived from correlation functions of substituting functions the fourth central moment can be computed using the fast fourier transform fft approach simulation results show that the proposed algorithm performs better than the classical estimators in terms of robustness while the extra computational cost is negligible

worst case identification of errors in variables models in closed loop a worst case identification method in frequency domain is proposed to cope with the identification of errors in variables models eivms in closed loop with a priori bound for the disturbing noises of an eivm in closed loop a frequency domain normalized coprime factor model ncfm with perturbation is derived and thus the identification of the eivm becomes that of the ncfm by employing the v gap metric as an optimization criterion the worst case error for an identified nominal ncfm is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities lmis during the parameter optimization the derivative of the nominal ncfm is constrained to some degree to reduce the effect of overfitting phenomenon different from other eivm identification methods we use v gap metric to characterize the disturbing noises and quantify the worst case error for the nominal ncfm as a result the identification result is not a deterministic model but a model set moreover this model set can be perfectly combined with the robust controller design finally a numerical simulation is presented to verify the proposed method

closed loop identification revisited identification of systems operating in closed loop has long been of prime interest in industrial applications the problem offers many possibilities and also some fallacies and a wide variety of approaches have been suggested many quite recently the purpose of the current contribution is to place most of these approaches in a coherent framework thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates the common framework is created by the basic prediction error method and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models the so called indirect methods e g are indeed direct methods employing noise models that contain the regulator the asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations we also study a new projection approach to closed loop identification with the advantage of allowing approximation of the open loop dynamics in a given and user chosen frequency domain norm even in the case of an unknown nonlinear regulator

dynamics for the diffusive mutualist model with advection and different free boundaries abstract in this paper we study the diffusive mutualist model with advection and different free boundaries in one space dimension these two free boundaries may intersect each other as time evolves and can be used to describe the spreading of invasive and native species directly we first prove the existence and uniqueness regularity and uniform estimates of global solution then we provide the criteria governing spreading and vanishing at last we investigate long time behaviors and asymptotic spreading speeds of two species and asymptotic speeds of two free boundaries

new consistent methods for order and coefficient estimation of continuous time errors in variables fractional models the errors in variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise several estimation methods have been proposed for identifying dynamic errors in variables rational models this paper presents new consistent methods for order and coefficient estimation of continuous time systems by errors in variables fractional models first differentiation orders are assumed to be known and only differential equation coefficients are estimated two estimators based on higher order statistics third order cumulants are developed the fractional third order based least squares algorithm ftocls and the fractional third order based iterative least squares algorithm ftocils then they are extended using a nonlinear optimization algorithm to estimate both the differential equation coefficients and the commensurate order the performances of the proposed algorithms are illustrated with a numerical example

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

hybrid viscosity like approximation methods for nonexpansive mappings in hilbert spaces consider on a real hilbert space h a nonexpansive mapping t with a fixed point a contraction f with coefficient 0 0 respectively let 0 1 with m n m n and prove the strong convergence of the iterative algorithm to a fixed point x fix t c which is the unique solution of the variational inequality for short v i a i m b cf c 0 x c on the other hand assume c is the intersection of the fixed point sets of a finite number of nonexpansive mappings on h we devise another iterative algorithm which generates a sequence x n from an arbitrary initial point x 0 h the sequence x n is proven to converge strongly to an element of c which is the unique solution x of the v i a i m b cf c applications to constrained generalized pseudoinverses are included

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities