fuzzy model validation using the local statistical approach the local statistical approach for fault detection and isolation is applied to fuzzy models validation the method detects the inconsistencies between a fuzzy rule base and the modelled system it can also identify which are the faulty parameters of the fuzzy model the fisher information matrix explains the detectability of changes in the parameters of the fuzzy model simulation tests illustrate the method s credibility

flatness based adaptive fuzzy control of electrostatically actuated mems using output feedback abstract the article presents an adaptive fuzzy control approach to the problem of control of electrostatically actuated mems which is based on differential flatness theory and which uses exclusively output feedback it is shown that the model of the electrostatically actuated mems is a differentially flat one and this permits to transform it to the so called linear canonical form for the new description of the system s dynamics the transformed control inputs contain unknown terms which depend on the system s parameters to identify these terms an adaptive fuzzy approximator is used in the control loop thus an adaptive fuzzy control scheme is implemented in which the unknown or unmodeled system dynamics is approximated by neurofuzzy networks and next this information is used by a feedback controller that makes the electrostatically activated mems converge to the desirable motion setpoints this adaptive control scheme is exclusively implemented with the use of output feedback while the state vector elements which are not directly measured are estimated with the use of a state observer that operates in the control loop the learning rate of the adaptive fuzzy system is suitably computed from lyapunov analysis so as to assure that both the learning procedure for the unknown system s parameters the dynamics of the observer and the dynamics of the control loop will remain stable the lyapunov stability analysis depends on two riccati equations one associated with the feedback controller and one associated with the state observer finally it is proven that for the control scheme that comprises the feedback controller the state observer and the neurofuzzy approximator an h infinity tracking performance can be achieved the functioning of the control loop has been evaluated through simulation experiments

an elementary proof for a compact imbedding result in generalized electromagnetic theory propriete de plongement compact et certaines de ses consequences on etudie la validite du plongement suivant r 9 g e q 1 d q g l 2 q loc g

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

boundary layers on sobolev besov spaces and poisson s equation for the laplacian in lipschitz domains we study inhomogeneous boundary value problems for the laplacian in arbitrary lipschitz domains with data in sobolev besov spaces as such this is a natural continuation of work in jerison and kenig j funct anal 1995 16 219 where the inhomogeneous dirichlet problem is treated via harmonic measure techniques the novelty of our approach resides in the systematic use of boundary integral methods in this regard the key results are establishing the invertibility of the classical layer potential operators on scales of sobolev besov spaces on lipschitz boundaries for optimal ranges of indices applications tolp based helmholtz type decompositions of vector fields in lipschitz domains are also presented

asymptotic statistical theory of overtraining and cross validation a statistical theory for overtraining is proposed the analysis treats general realizable stochastic neural networks trained with kullback leibler divergence in the asymptotic case of a large number of training examples it is shown that the asymptotic gain in the generalization error is small if we perform early stopping even if we have access to the optimal stopping time based on the cross validation stopping we consider the ratio the examples should be divided into training and cross validation sets in order to obtain the optimum performance although cross validated early stopping is useless in the asymptotic region it surely decreases the generalization error in the nonasymptotic region our large scale simulations done on a cm5 are in good agreement with our analytical findings

on the analyticity of the semigroup generated by the stokes operator with neumann type boundary conditions on lipschitz subdomains of riemannian manifolds we study the analyticity of the semigroup generated by the stokes operator equipped with neumann type boundary conditions on l p spaces in lipschitz domains our strategy is to regularize this operator by considering the hodge laplacian which has the additional property that it commutes with the leray projection

accuracy analysis of the frisch scheme for identifying errors in variables systems several estimation methods have been proposed for identifying errors in variables systems where both input and output measurements are corrupted by noise one of the promising approaches is the so called frisch scheme this paper provides an accuracy analysis of the frisch scheme applied to system identification the estimates of the system parameters and the noise variances are shown to be asymptotically gaussian distributed an explicit expression for the covariance matrix of the asymptotic distribution is given as well numerical simulations support the theoretical results a comparison with the cramer rao lower bound is also given in the examples and it is shown that the frisch scheme gives a performance close to the cramer rao bound for large signal to noise ratios snrs

potential theory on lipschitz domains in riemannian manifolds sobolev besov space results and the poisson problem abstract we continue a program to develop layer potential techniques for pde on lipschitz domains in riemannian manifolds building on l p and hardy space estimates established in previous papers here we establish sobolev and besov space estimates on solutions to the dirichlet and neumann problems for the laplace operator plus a potential on a lipschitz domain in a riemannian manifold with a metric tensor smooth of class c 1 for some 0 we treat the inhomogeneous problem and extend it to the setting of manifolds results obtained for the constant coefficient laplace operator on a lipschitz domain in euclidean space with the dirichlet boundary condition by d jerison and c kenig

integral estimates for null lagrangians sobolev spaces of differential forms are studied lp projections onto exact forms are introduced as a tool to obtain integral estimates for null lagrangians new results on compensated compactness are given and mean coercive variational integrals are found existence of minima of certain mean coercive functionals is established

an h s p text curl varomega estimate for the maxwell system we derive an h 0 s p text curl varomega estimate for the solutions of the maxwell type equations modeled with anisotropic and w s infty varomega regular coefficients here we obtain the regularity of the solutions for the integrability and smoothness indices p s in a plane domain characterized by the apriori lower upper bounds of a and the apriori upper bound of its holder semi norm of order s the proof relies on a perturbation argument generalizing groger s l p type estimate known for the elliptic problems to the maxwell system

checking the coherence and redundancy of fuzzy knowledge bases checking the coherence of a set of rules is an important step in knowledge base validation coherence is also needed in the field of fuzzy systems indeed rules are often used regardless of their semantics and it sometimes leads to sets of rules that make no sense avoiding redundancy is also of interest in real time systems for which the inference engine is time consuming a knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base we more particularly consider knowledge bases composed of parallel fuzzy rules then coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted i e any value for these variables is possible or at least not more restrictive than integrity constraints fuzzy rule representations can be implication based or conjunction based we show that only implication based models may lead to coherence problems however unlike conjunction based models they allow to design coherence checking processes some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules the problem of redundancy which is also of interest for fuzzy knowledge bases validation is addressed for these two kinds of rules

towards neuro linguistic modeling constraints for optimization of membership functions abstract in neuro fuzzy or fuzzy neural systems using unconstrained optimization schemes like backpropagation it is not possible to guarantee that the resulting membership functions represent human interpretable linguistic terms however one of the most interesting features of fuzzy systems is the insight provided on the linguistic relationship between their variables this work is devoted to the study of constraints which when used within an optimization scheme obviate the subjective task of interpreting membership functions to achieve this a comprehensive set of semantic properties that membership functions should have is postulated and discussed then a set of constraints is introduced and shown to be able to fulfil the properties implementation issues and one example illustrating the importance of the proposed constraints are included

the brezis nirenberg problem for the curl curl operator abstract we look for solutions e r 3 of the problem e e e p 2 e in e 0 on on a bounded lipschitz domain r 3 where denotes the curl operator in r 3 the equation describes the propagation of the time harmonic electric field e x e i t in a nonlinear isotropic material with e 2 0 where and e stand for the permeability and the linear part of the permittivity of the material the nonlinear term e p 2 e with p 2 is responsible for the nonlinear polarisation of and the boundary conditions are those for surrounded by a perfect conductor the problem has a variational structure and we deal with the critical value p for instance in convex domains or in domains with c 1 1 boundary p 6 2 is the sobolev critical exponent and we get the quintic nonlinearity in the equation we show that there exist a cylindrically symmetric ground state solution and a finite number of cylindrically symmetric bound states depending on 0 we develop a new critical point theory which allows to solve the problem and which enables us to treat more general anisotropic media as well as other variational problems

besov and triebel lizorkin regularity for the hodge decomposition and applications to magnetic potentials abstract the hodge decomposition is a fundamental result in the theory of differential forms it has been extensively studied from different perspectives and it is the source of several applications in physics and mathematics for example it is important in the analysis of navier stokes and maxwell s equations it can be used to prove results on inverse scattering problems in quantum mechanics and it is useful for the study of magnetic potentials associated to a magnetic field the regularity properties of the hodge decomposition have been studied in several works in the last decades most prominently it has been proved that sobolev regularity holds true in this paper we prove regularity for the hodge decomposition in a much larger scale of function spaces besov and triebel lizorkin spaces on compact riemannian manifolds with boundary we prove regularity in such spaces for the hodge morrey decomposition and the hodge morrey friedrichs decomposition we furthermore state and prove a refinement for the hodge morrey friedrichs decomposition with regularity that allows expressing every differential form as the sum of the differential of a form plus the co differential of another form plus a harmonic field belonging to a finite dimensional space this holds true even if the original form is barely differentiable with sth order of differentiability for every real number s 0 we finally provide an application to the study of magnetic potentials associated to magnetic fields more precisely we prove the existence of a magnetic potential associated to a magnetic field the former being one time more differentiable than the latter in terms of besov and triebel lizorkin regularity this is an important motivation for us since we have the intention to apply our results to further investigations in relativistic inverse time dependent scattering problems in quantum mechanics where besov and triebel lizorkin regularity for magnetic potentials is relevant

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

training fuzzy systems with the extended kalman filter the generation of membership functions for fuzzy systems is a challenging problem we show that for mamdani type fuzzy systems with correlation product inference centroid defuzzification and triangular membership functions optimizing the membership functions can be viewed as an identification problem for a nonlinear dynamic system this identification problem can be solved with an extended kalman filter we describe the algorithm and compare it with gradient descent and with adaptive neuro fuzzy inference system anfis based optimization of fuzzy membership functions the methods discussed in this paper are illustrated on a fuzzy filter for motor winding current estimation and are compared with butterworth filtering we demonstrate that the kalman filter can be an effective tool for improving the performance of a fuzzy system

extended accuracy analysis of a covariance matching approach for identifying errors in variables systems a system identification method for errors in variables problems based on covariance matching was recently proposed in the first step a small amount of covariances of noisy input output data are computed and then a parametric model is fitted to these covariances in this paper the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances as an important byproduct an efficient algorithm is presented for computing the covariance matrix of the computed input output covariances

why triangular membership functions abstract in this note we look at a certain theoretically sound motivation behind the common use of triangular and trapezoidal membership functions the studies are completed within a conceptual framework of fuzzy modelling whose structure comprises of input and output interfaces linked with a single transformation module aimed at processing linguistic information it is shown that under some additional mild assumptions these triangular fuzzy sets comply with a request for a uniformly excited codebook in the case of the input interfaces and a satisfaction of a zero error reconstruction criterion being formulated for the output interface

the regularity of the stokes operator and the fujita kato approach to the navier stokes initial value problem in lipschitz domains abstract we study the regularity of the navier stokes equations in arbitrary lipschitz domains

stability results on interpolation scales of quasi banach spaces and applications we investigate the stability of fredholm properties on interpolation scales of quasi banach spaces this analysis is motivated by problems arising in pde s and several applications are presented

sharp hodge decompositions maxwell s equations and vector poisson problems on nonsmooth three dimensional riemannian manifolds we solve three basic potential theoretic problems hodge decompositions for vector fields poisson problems for the hodge laplacian and inhomogeneous maxwell equations in arbitrary lipschitz subdomains of a smooth compact three dimensional riemannian manifold in each case we derive sharp estimates on sobolev besov scales and establish integral representation formulas for the solution the proofs rely on tools from harmonic analysis and algebraic topology such as calderon zygmund theory and de rham theory

incremental least squares methods and the extended kalman filter in this paper we propose and analyze nonlinear least squares methods which process the data incrementally one data block at a time such methods are well suited for large data sets and real time operation and have received much attention in the context of neural network training problems we focus on the extended kalman filter which may be viewed as an incremental version of the gauss newton method we provide a nonstochastic analysis of its convergence properties and we discuss variants aimed at accelerating its convergence

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

besov spaces on domains in rd we study besov spaces 5 lp i2 0 p q a oo on do mains i2 in rd we show that there is an extension operator w which is a bounded mapping from b lp u onto b lp rd this is then used to derive various properties of the besov spaces such as interpolation theorems for a pair of b lp il atomic decompositions for the elements of 5 lp f2 and a description of the besov spaces by means of spline approximation

on bogovskiĭ and regularized poincare integral operators for de rham complexes on lipschitz domains we study integral operators related to a regularized version of the classical poincare path integral and the adjoint class generalizing bogovski s integral operator acting on differential forms in mathbb r n we prove that these operators are pseudodifferential operators of order 1 the poincare type operators map polynomials to polynomials and can have applications in finite element analysis for a domain starlike with respect to a ball the special support properties of the operators imply regularity for the de rham complex without boundary conditions using poincare type operators and with full dirichlet boundary conditions using bogovski type operators for bounded lipschitz domains the same regularity results hold and in addition we show that the cohomology spaces can always be represented by fancyscript c infty functions

information criteria for residual generation and fault detection and isolation using an information point of view we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation fdi in linear time invariant lti state space systems in both types of approaches to off line fdi residual generation can be viewed as the design of a linear transformation of a gaussian vector the finite window input adjusted observations several statistical isolation methods are revisited using both a linear transform formulation and the information content of the corresponding residuals we formally state several multiple fault cases with or without causality assumptions and discuss an optimality criterion for the most general one new information criteria are proposed for investigating the residual optimization problem

boundary layer methods for lipschitz domains in riemannian manifolds abstract we extend to the variable coefficient case boundary layer techniques that have been successful in the treatment of the laplace equation and certain other constant coefficient elliptic partial differential equations on lipschitz domains in euclidean space we treat the laplace operator on lipschitz domains in a manifold with c 1 metric tensor and study the dirichlet neumann and oblique derivative boundary problems

hardy spaces and the neumann problem in l p for laplace s equation in lipschitz domains on donne des resultats optimaux pour la resolubilite du probleme de neumann dans des domaines de lipschitz a donnees dans l p on obtient des resultats du point extreme correspondant pour des espaces de hardy

structure adaptive approach for dimension reduction we propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates the procedure is computationally straightforward and does not require any prior information about the structure of the underlying model we show that in the case when the effective dimension m of the index space does not exceed 3 this space can be estimated with the rate n 1 2 under rather mild assumptions on the model