on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

a blind approach to hammerstein model identification this paper discusses the hammerstein model identification using a blind approach by fast sampling at the output it is shown that identification of the linear part can be achieved based only on the output measurements that makes the hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variables

some further generalizations of the hyers ulam rassias stability of functional equations abstract in this paper we study the hyers ulam rassias stability theory by considering the cases where the approximate remainder is defined by f x y f x f y x y x y g 1 f x y g x h y x y x y g 2 2f x y 1 2 f x f y x y x y g 3 where g is a certain kind of algebraic system e is a real or complex hausdorff topological vector space and f g h are mappings from g into e we prove theorems for the hyers ulam rassias stability of the above three kinds of functional equations and obtain the corresponding error formulas

on an n dimensional mixed type additive and quadratic functional equation in this paper we investigate the generalized hyers ulam stability of the functional email protected k 2 k n 01fx email protected i 2n 1 k ix i 2 n 1f x 1 2 n email protected i 2nf x i f x i 0for integer values of n such that n 2 where f is a function from a normed space x to a banach space y the solutions of the equation are called additive quadratic mappings

continuous time hammerstein system identification a continuous time hammerstein system i e a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one is identified the system is driven and disturbed by white random signals the a priori information about both subsystems is nonparametric which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown an algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown the impulse response of the dynamic part is recovered with a correlation method the algorithms are computationally independent results of a simulation example are given

system based component test plans and operating characteristics binomial data component test plans are often designed by allocating system reliability among the system s components then choosing individual component plans suitable for demonstrating achievcment of each component s reliability goal this approach does not consider how much information relative to the system reliability goal is provided by the ensemble of component tests we consider the notion of system reliability operating characteristic oc curves based on the component tests and illustrate their use in designing or evaluating an overall test program by specifying oc values akin to producer s and consumer s risks optimum system ortented component test plans can be derived these ideas are illustrated for a series system and for a simple series parallel system with binomial data

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

on stability of a functional equation with n variables abstract generalized hyers ulam stability problems of the quadratic functional equation f i 1 n x i n 2 i 1 n f x i 1 i j n f x i x j shall be treated under the approximately even or odd condition and some behaviors of quadratic mappings and additive mappings shall be investigated

on an equation characterizing multi additive quadratic mappings and its hyers ulam stability in this paper we unify the system of functional equations defining a multi additive quadratic mapping to obtain a single equation we also prove using the fixed point method the generalized hyers ulam stability of this equation thus generalizing some known results

the problem of s m ulam for approximately multiplicative mappings in the present paper we study the problem of s m ulam for approximately multiplicative mappings and we consider new open problems

optimum component test plans for systems with dependent components an unrealistic and very restrictive assumption of component testing models in the literature is the stochastic independence of the components the independence assumption is hardly true for a complex system where all components operate under the same environmental conditions which may change randomly in time we consider such a model where stochastic dependence is due to the common environment that all components of the system are subjected to in particular we concentrate on component testing and show that most of the results in the literature can be extended to our general model involving dependent components

a generalization of the hyers ulam rassias stability of the pexiderized quadratic equations abstract in this paper we prove the hyers ulam rassias stability by considering the cases that the approximate remainder is defined by f x y f x y 1 2g x 2g y x y f x y g x y 1 2h x 2k y x y where g is a group x is a real or complex hausdorff topological vector space and f g h k are functions from g into x

on a cauchy jensen functional equation and its stability abstract in this paper we obtain the general solution and stability of the cauchy jensen functional equation 2 f x y z w 2 f x z f x w f y z f y w

brief estimation of an n l n hammerstein wiener model estimation of a single input single output block oriented model is studied the model consists of a linear block embedded between two static nonlinear gains hence it is called n l n hammerstein wiener model first the model structure is motivated and the disturbance model is discussed the paper then concentrates on parameter estimation a relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in parameters this leads to a simple algorithm which minimizes the original loss function the convergence and consistency of the algorithm are studied in order to reduce the variance error the obtained linear model is further reduced using frequency weighted model reduction simulation study will be used to illustrate the method

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

on the stability of a functional equation deriving from an inequality of popoviciu for convex functions abstract in this paper we solve the jensen type functional equation n n 2 k 2 f x 1 x n n n 2 k 1 i 1 n f x i k 1 i 1 k n f x i 1 x i k k deriving from an inequality of popoviciu for convex functions likewise we investigate the stability of this functional equation in the spirit of hyers ulam rassias and g vru

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

adaptive control of weiner type nonlinear systems abstract this study is concerned with the problem of adaptive control of a wiener type nonlinear process it is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order with stable inverse followed by a known time delay the memoryless nonlinearity is one to one on a compact set and belongs to one of two classes 1 piecewise linear with known breakpoints or 2 smooth function in which case an approximation is made it is represented by linear splines the output signal from the linear part is not available for measurement the global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints otherwise there will be a residual tracking error which depends on the nonlinearity approximation error but the boundedness of all signals can be assured the proposed scheme is used for adaptive control of the ph process in a continuous flow reactor

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

generalized hyers ulam rassias stability of n sesquilinear quadratic mappings on banach modules over c algebras assume that x is a left banach module over a unital c algebra a it is shown that almost every n sesquilinear quadratic mapping h xxxxx n a is an n sesquilinear quadratic mapping when h rx y z 1 z n h x ry z 1 z n h x y rz 1 z 2 z n h x y z 1 z 2 rz n rh x y z 1 z 2 z n r 0 r 1 holds for all x y z 1 z email protected x moreover we prove the generalized hyers ulam rassias stability of an n sesquilinear quadratic mapping on a left banach module over a unital c algebra

a generalization of the hyers ulam rassias stability of jensen s equation in this paper we prove a generalization of the stability of the jensen s equation in the spirit of hyers ulam rassias and g vruta

on the cauchy rassias stability of a generalized additive functional equation let x and y be banach spaces and f x y an odd mapping we solve the following generalized additive functional equation rf j 1dxjr j 0 1 j 1d j lrf j 1d 1 j xjr cld 1 cl 1d 1 1 j 1df xj for all x1 xd x moreover we deal with the above functional equation in banach modules over a c algebra and obtain generalizations of the cauchy rassias stability the concept of cauchy rassias stability for the linear mapping was originated from th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

on the hyers ulam stability of linear mappings abstract let e1 be a real normed vector space and e2 a real banach space s m ulam posed the problem when does a linear mapping near an approximately linear mapping e1 e2 exist we give a new generalized solution to this problem an example illustrates when the answer to this question is negative the behaviour of bounded approximately additive mappings which do not satisfy hyers uiam stability is also investigated

on the stability of the linear mapping in banach modules abstract we prove the generalized hyers ulam rassias stability of the linear mapping in banach modules over a unital banach algebra

auxiliary model based least squares identification methods for hammerstein output error systems abstract the difficulty in identification of a hammerstein a linear dynamical block following a memoryless nonlinear block nonlinear output error model is that the information vector in the identification model contains unknown variables the noise free true outputs of the system in this paper an auxiliary model based least squares identification algorithm is developed the basic idea is to replace the unknown variables by the output of an auxiliary model convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition the simulation results show the effectiveness of the proposed algorithms

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

on a problem of g isac and th m rassias concerning the stability of mappings abstract we give an answer to a problem of g isac and th m rassias concerning hyers ulam rassias stability of the linear mappings a new characterization of additive mappings is also given

on the stability of the orthogonal pexiderized cauchy equation abstract we investigate the stability of pexiderized mappings in banach modules over a unital banach algebra as a consequence we establish the hyers ulam stability of the orthogonal cauchy functional equation of pexider type f 1 x y f 2 x f 3 y x y in which is the orthogonality in the sense of ratz

stability of a jensen type equation in the space of generalized functions abstract we reformulate and solve the stability problem of a jensen type functional equation 3 f x y z 3 f x f y f z 2 f x y 2 2 f y z 2 2 f z x 2 0 in the spaces of some generalized functions such as tempered distributions and fourier hyperfunctions

the hyers ulam rassias stability of the pexiderized equations abstract in this paper we prove the hyers ulam rassias stability of the equations f x y g x h y 0 f x y g x y 2 h x 2 k y 0 f xy g x y h xy x k y 0

stability of a functional equation deriving from quadratic and additive functions in quasi banach spaces abstract in this paper we establish the general solution of the functional equation f 2 x y f 2 x y f x y f x y 2 f 2 x 2 f x and investigate the hyers ulam rassias stability of this equation in quasi banach spaces

on hyers ulam rassias stability of the pexider equation abstract in this paper using the idea of p g vruta 1994 j math anal appl 184 431 436 we prove a generalization of the stability of approximately additive mappings in the spirits of hyers ulam and rassias

the cost of complexity in system identification frequency function estimation of finite impulse response systems in this paper we consider full order modeling i e when the true system belongs to the model set we investigate the minimum amount of input energy required to estimate a given linear system with a full order model within a prescribed degree of accuracy as a function of the model complexity this quantity we define to be the cost of complexity the degree of accuracy is measured by the inverse of the maximum variance of the discrete time frequency function estimator over a given frequency range b b it is commonly believed that the cost increases as the model complexity increases however the amount of information that is to be extracted from the system also influences the cost the objective of this paper is to quantify these dependencies for systems described by finite impulse response models it is shown that asymptotically in the model order n and sample size the cost is well approximated by o2n b where o2 is the noise variance this expression can be used as a simple rule of thumb for assessing trade offs that have to be made in a system identification project where full order models are used for example for given experiment duration excitation level and desired accuracy one can assess how the achievable frequency range depends on the required model order this type of consideration is useful when formally planning experiments in addition we establish several properties of the cost of complexity we find for example that if b is very close but not necessarily equal to the optimal input satisfies the model quality constraint for all frequencies

asymptotic behavior of generalized derivations on c algebras with applications we consider generalized derivations on c algebra and we will first study the conditions for a linear generalized derivation on c algebra then we prove some theorems involving approximate linear generalized derivations on c algebra so approximate linear generalized derivations on c algebra are characterized

a functional equation having monomials as solutions for each n 1 2 3 we obtain the general solution and the stability of the functional equation f 2x y f 2x y 2 n 2 f x y f x y 6f x and we obtain the general solution and the stability of the functional equation f 2x y f 2x y 6f y 4 f x y f x y 6f x using the fixed point method we prove the generalized hyers ulam stability of these functional equations

the design of optimum component test plans in the demonstration of system reliability abstract system testing is often not feasible and it is a common practice in these situations to attempt to draw inferences about the reliability of the system from the results of component tests an acceptance procedure based on the sum of failures during component tests has been previously suggested in the literature for a series system a parallel system and a serial connection of redundant subsystems methods for computing the individual component test times which minimize total test cost and guarantee the probability requirements for this acceptance procedure and for such system structures have also been given none of them considers a priori information on component reliabilities in this paper we consider the question of whether these optimum solutions are modified if a priori deterministic information on individual component failure rates is available results have shown that it is profitable to use the given information we also provide a procedure to compute optimum component test times for general systems this procedure is based on the well known cutting plane idea and column generation technique and eventually solves a semi infinite linear program we also discuss the conditions for the existence of optimum component test times

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

optimum attributes component test plans for k out of n f weibull systems using prior information abstract assuming that the proportion defective in a production process p is variable and the component lifetimes are weibull distributed integer nonlinear programming problems are formulated and solved in order to determine the optimum component inspection scheme by attributes for k out of n f system reliability demonstration using available prior knowledge a limited beta prior model is adopted to reflect the random fluctuations on p the required quantity of components to test and the permissible number of component failures up to a specified censoring time are found by solving a minimisation problem with nonlinear constraints which are related to the tolerable average producer and consumer risks first order taylor polynomials of the operating characteristic function are used to derive a quite accurate approximate solution lower and upper bounds are also deduced optimal solutions are usually robust to small variations in the weibull parameters and prior information existing technical knowledge and experience are shown to be of great practical value in designing optimal sampling plans for lot acceptance purposes the proposed approach generalises the classical viewpoint to those cases in which appreciable prior information on the fraction of defective systems exists and also allows the analyst to determine the acceptability of a k out of n f system before assembly and to limit the range of p moreover the practitioners may attain substantial savings in sample size and improved assessments of the true producer and consumer risks a 4 out of 5 f system of independent water pumps for cooling a reactor is considered to illustrate the suggested component test plans

parametric identification of parallel wiener hammerstein systems block oriented nonlinear models are popular in nonlinear modeling because of their advantages to be quite simple to understand and easy to use to increase the flexibility of single branch block oriented models such as hammerstein wiener and wiener hammerstein models parallel block oriented models can be considered this paper presents a method to identify parallel wiener hammerstein systems starting from input output data only in the first step the best linear approximation is estimated for different input excitation levels in the second step the dynamics are decomposed over a number of parallel orthogonal branches next the dynamics of each branch are partitioned into a linear time invariant subsystem at the input and a linear time invariant subsystem at the output this is repeated for each branch of the model the static nonlinear part of the model is also estimated during this step the consistency of the proposed initialization procedure is proven the method is validated on real world measurements using a custom built parallel wiener hammerstein test system

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

recursive identification of mimo wiener systems stochastic approximation sa algorithms are proposed to identify a multi input and multi output mimo wiener system in which the system input is taken to be a sequence of independent and identically distributed i i d gaussian random vectors uk n 0 i the algorithm for identifying the nonlinear part is designed with multi variable kernel functions under suitable conditions we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one

recursive identification for multi input multi output hammerstein wiener system abstractin this paper an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi input multi output hammerstein wiener system with process noise in the proposed identification method the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible then the auxiliary variable is constructed the parameters of the regression equations are identified and the system parameter matrices can be obtained by matrix composition of the parameter product matrix a theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance the effectiveness of the proposed method is validated through the experiments

identification of hammerstein wiener models this paper develops and illustrates a new maximum likelihood based method for the identification of hammerstein wiener model structures a central aspect is that a very general situation is considered wherein multivariable data non invertible hammerstein and wiener nonlinearities and colored stochastic disturbances both before and after the wiener nonlinearity are all catered for the method developed here addresses the blind wiener estimation problem as a special case

stability of the multi jensen equation abstract in this paper we study the stability in the sense of th m rassias of multi jensen equation

hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation this is applied to investigate homomorphisms between quasi banach algebras the concept of hyers ulam rassias stability originated from th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

on the stability of the functional equation f x y xy f x f y xf y yf x abstract in this paper we study the hyers ulam stability and the superstability of the functional equation f x y xy f x f y xf y yf x

a generalization of the hyers ulam rassias stability of the pexider equation in this paper we prove a generalization of the stability of the pexider equation f x y g x h y in the spirit of hyers ulam rassias and g vruta

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed