model structure simplification of nonlinear systems via immersion this paper concerns the simplification of model structures of nonlinear systems while preserving their input output maps the basic technique is an immersion of a system which is a mapping of the initial state from the original system to another system of an identical input output map the necessary and sufficient conditions are presented for the immersibility of a given system into a state space representation of such particular structures as rational functions or polynomials with respect to the state the conditions are so mild that many types of nonlinear systems can be represented by rational or polynomial model structures moreover it is also shown that a polynomial state space representation can always be constructed to be at most quadratic with respect to the state

approximate dynamic programming based approaches for input output data driven control of nonlinear processes we propose two approximate dynamic programming adp based strategies for control of nonlinear processes using input output data in the first strategy which we term j learning one builds an empirical nonlinear model using closed loop test data and performs dynamic programming with it to derive an improved control policy in the second strategy called q learning one tries to learn an improved control policy in a model less manner compared to the conventional model predictive control approach the new approach offers some practical advantages in using nonlinear empirical models for process control besides the potential reduction in the on line computational burden it offers a convenient way to control the degree of model extrapolation in the calculation of optimal control moves one major difficulty associated with using an empirical model within the multi step predictive control setting is that the model can be excessively extrapolated into regions of the state space where identification data were scarce or nonexistent leading to performances far worse than predicted by the model within the proposed adp based strategies this problem is handled by imposing a penalty term designed on the basis of local data distribution a cstr example is provided to illustrate the proposed approaches

a bootstrap method for structure detection of narmax models many systems may be described by narmax models using only a few terms however depending on the order of the system the number of candidate terms can become very large selection of a subset of these candidate terms is necessary for an efficient system description this is an unresolved issue in system identification for over parameterized models therefore in this paper we develop a bootstrap structure detection bsd algorithm as a means of determining the structure of highly over parameterized models the performance of this bsd technique was evaluated by using it to estimate the structure of a 1 simple narmax model 2 moderately over parameterized narmax model and 3 highly over parameterized narmax model the results demonstrate that the bsd algorithm is a robust method for detecting the structure of narmax models this method provides accurate estimates of parameter statistics without relying on assumptions made by traditional procedures and yields a parsimonious description of the system

rewriting systems in sufficiently large artin tits groups abstract a conjecture of dehornoy claims that given a presentation of an artin tits group every word that represents the identity can be transformed into the trivial word using the braid relations together with certain rules between pairs of words that are not both positive that can be derived directly from the braid relations as well as free reduction but without introducing trivial factors s s 1 or s 1 s this conjecture is known to be true for artin tits groups of spherical type or of fc type we prove the conjecture for artin tits groups of sufficiently large type

symmetries as integrability criteria for differential difference equations in this paper we review the results obtained by the generalized symmetry method in the case of differential difference equations during the last 20 years together with general theory of the method classification results are discussed for classes of equations which include the volterra toda and relativistic toda lattice equations

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

invariant conservation law preserving discretizations of linear and nonlinear wave equations symmetry and conservation law preserving finite difference discretizations are obtained for linear and nonlinear one dimensional wave equations on five and nine point stencils using the theory of lie point symmetries of difference equations and the discrete direct multiplier method of conservation law construction in particular for the linear wave equation an explicit five point scheme is presented that preserves the discrete analogs of its basic geometric point symmetries and six of the corresponding conservation laws for a class of nonlinear wave equations arising in hyperelasticity a nine point implicit scheme is constructed preserving four point symmetries and three local conservation laws other discretizations of the nonlinear wave equations preserving different subsets of conservation laws are discussed

lie symmetries of multidimensional difference equations a method is presented for calculating the lie point symmetries of a scalar difference equation on a two dimensional lattice the symmetry transformations act on the equations and on the lattice they take solutions into solutions and can be used to perform symmetry reduction the method generalizes the one presented in a recent publication for the case of ordinary difference equations in turn it can easily be generalized to difference systems involving an arbitrary number of dependent and independent variables

bounded rank subgroups of coxeter groups artin groups and one relator groups with torsion we obtain a number of results regarding the freeness of subgroups of coxeter groups artin groups and one relator groups with torsion in the case of coxeter groups we also obtain results on quasiconvexity and subgroup separability

rapid decay and baum connes for large type artin groups we prove that many artin groups of large type satisfy the rapid decay property including all those of extra large type for many of these including all 3 generator groups of extra large type a result of lafforgue applies to show that the groups satisfy the baum connes conjecture without coefficients our proof of rapid decay combines elementary analysis with combinatorial techniques and relies on properties of geodesic words in artin groups of large type that were observed in earlier work by two of the authors of this current article

small cancellation groups and translation numbers in this paper we prove that c 4 t 4 p c 3 t 6 p and c 6 p small cancellation groups are translation discrete in the strongest possible sense and that in these groups for any g and any n there is an algorithm deciding whether or not the equation xn g has a solution there is also an algorithm for calculating for each g the maximum n such that g is an n th power of some element we also note that these groups cannot contain isomorphic copies of the group of p adic fractions and so in particular of the group of rational numbers besides we show that for c 4 t 4 and c 3 t 6 groups all translation numbers are rational and have bounded denominators

an adaptive multi scale basis method for modelling discrete time nonlinear dynamical systems based on locally applicable autoregressive moving average with exogenous armax models this paper proposes two new adaptive modelling schemes for discrete time non linear dynamic systems based on the concept of a multiscale which originates in approximation theory a general result on the convergence of modelling based on the multiscale basis functions with a least square estimated is derived with the advantage of the multiresolution nature of the multiscale basis the new modelling scheme can be used to capture both the global and local characteristics of a non linear system over distinct scales the algorithms also provide a trade off between the model structure model size and the modelling error one of which emphasizes the modelling error with variable model structure whilst the other stresses a desired model size with better modelling error data based modelling examples are used to demonstrate the effectiveness of the multiscale modelling schemes with different multiscale basis

fuzzy sets of rules for system identification the synthesis of fuzzy systems involves the identification of a structure and its specialization by means of parameter optimization in doing this symbolic approaches which encode the structure information in the form of high level rules allow further manipulation of the system to minimize its complexity and possibly its implementation cost while all parametric methodologies often achieve better approximation performance in this paper we rely on the concept of a fuzzy set of rules to tackle the rule induction problem at an intermediate level an online adaptive algorithm is developed which almost surely learns the extent to which inclusion of a rule in the rule set significantly contributes to the reproduction of the target behavior then the resulting fuzzy set of rules can be defuzzified to give a conventional rule set with similar behavior comparisons with high level and low level methodologies show that this approach retains the most positive features of both

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

the adjoint equation method for constructing first integrals of difference equations a new method for finding first integrals of discrete equations is presented it can be used for discrete equations which do not possess a variational lagrangian or hamiltonian formulation the method is based on a newly established identity which links symmetries of the underlying discrete equations solutions of the discrete adjoint equations and first integrals the method is applied to an invariant mapping and to discretizations of second order and third order ordinary differential equations in examples the set of independent first integrals makes it possible to find the general solution of the discrete equations

analysis and design of fuzzy control systems using dynamic fuzzy global models a method for analysis and design of a fuzzy controller is developed for a class of fuzzy discrete time systems the method is based on a dynamical fuzzy state space model it is shown that the closed loop fuzzy system can be represented by a dynamical interval system and thus the methods of stability analysis in uncertain linear system theory can be used to analyse the global stability of the closed loop fuzzy system some examples are given to illustrate the application of the method

multiobjective parameter estimation for non linear systems affine information and least squares formulation this paper defines a class of system information affine information that includes both the dynamic residuals and some types of auxiliary information that can be used in system parameter estimation as special cases the types of information that can be cast under the affine information format give rise to quadratic functions that measure the extent to which a model fits such information and that can be aggregated in a single weighted quadratic cost functional this allows the definition of a multiobjective methodology for parameter estimation in non linear system identification which allows taking into account any type of affine information the results are presented in terms of a set of efficient solutions of the multiobjective estimation problem such a solution set is more meaningful than a single model since any affine information leads to a convex quadratic functional the whole set of efficient solutions is exactly accessible via the minimization of the quadratic functional with different weighti

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

difference schemes with point symmetries and their numerical tests symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented they have the same three or four dimensional symmetry groups as the original differential equations the new difference schemes are tested as numerical methods the obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost for an example involving a solution with a singularity in the integration region the symmetry preserving scheme contrary to standard ones provides solutions valid beyond the singular point

truncated chebyshev series approximation of fuzzy systems for control and nonlinear system identification the lack of mathematical models that pertains fuzzy control systems imposes a serious drawback regarding some important tasks such as stability analysis and system identification for that purpose the availability of analytical expressions for the fuzzy systems is very important this paper provides a systematic practical way of approximating fuzzy systems by chebyshev polynomials which depend on a finite number of parameters the proposed methodology is illustrated with two examples a a control problem concerning a tubular reactor which depending on the operating conditions may exhibit multiple steady states and b the problem of identifying a continuous stirred tank reactor which at certain values of structural parameters exhibits stable or unstable steady states or limit cycles

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

a recursive local linear estimator for identification of nonlinear arx systems asymptotical convergence and applications in this paper we propose a recursive local linear estimator rlle for nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx first the rlle is introduced next the strong consistency as well as the asymptotical mean square error properties of the rlle are established and then an application of the rlle to an additive nonlinear system is discussed the rlle provides recursive estimates not only for the function values but also their gradients at fixed points a simulation example is provided to confirm the theoretical analysis

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

conditions for the existence of higher symmetries of evolutionary equations on the lattice in this paper we construct a set of five conditions necessary for the existence of generalized symmetries for a class of differential difference equations depending only on nearest neighboring interaction these conditions are applied to prove the existence of new integrable equations belonging to this class

artin groups and infinite coxeter groups if the associated coxeter group 7 is finite for the braid group b the associated coxeter group is the symmetric group s brieskorn and saito 4 and independently deligne 6 have investigated artin groups of finite type in 1969 garside 7 solved the conjugacy problem for braid groups brieskorn this work was supported by nsf grants mcs 7902512 and mcs 7703452 the authors would like to thank the referee for an extremely careful reading of the paper and many helpful sugges tions

discrete approximations on functional classes for the integrable nonlinear schrodinger dynamical system a symplectic finite dimensional reduction approach abstract we investigate discretizations of the integrable discrete nonlinear schrodinger dynamical system and related symplectic structures we develop an effective scheme of invariant reducing the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter we construct a finite set of recurrent algebraic regular relations allowing to generate solutions of the discrete nonlinear schrodinger dynamical system and we discuss the related functional spaces of solutions finally we discuss the fourier transform approach to studying the solution set of the discrete nonlinear schrodinger dynamical system and its functional analytical aspects

invariant difference schemes and their application to sl 2 hbox mathbb r invariant ordinary differential equations we present an exposition of a method of discretizing ordinary differential equations while preserving their lie point symmetries this method is very general and can be applied to any ordinary differential equations ode with a nontrivial symmetry group the method is applied to obtain numerical solutions of second and third order odes invariant under two different realizations of the symmetry preserving method is shown to provide a better qualitative description of solutions than standard methods in particular it provides solutions that are valid close to singularities and beyond them

asymptotic properties of least squares estimates of hammerstein wiener models this paper investigates the asymptotic properties of least squares estimates of hammerstein wiener model structures and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process the inputs and the static non linearities in relation to the asymptotic distributional results a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided a key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting in this respect the hammerstein wiener model structure serves as a demonstration example a simulation study complements the theoretical findings

semiglobal stabilization of nonlinear systems using fuzzy control and singular perturbation methods singular perturbation methods based on a lyapunov approach are implemented for the derivation of sufficient conditions for the semiglobal stabilization with output tracking of nonlinear systems having internal dynamics the key idea of this approach lies in the decomposition of the full system into a subsystem exhibiting fast dynamics and to a subsystem with slow dynamics resulting in a substantial simplification of the stability analysis this two time scale behavior is achieved by implementing a properly designed fuzzy logic controller the key element of the proposed model based composite controller for the construction of the model based controller a new identification technique based on both classical and fuzzy tools is proposed results are presented for the semiglobal stabilization of a continuous stirred tank reactor which is a process with high nonlinear behavior

accuracy analysis for wavelet approximations constructive wavelet networks are investigated as a universal tool for function approximation the parameters of such networks are obtained via some direct monte carlo procedures approximation bounds are given typically it is shown that such networks with one layer of wavelons achieve an l sub 2 error of order o n sup spl rhod where n is the number of nodes d is the problem dimension and spl rho is the number of summable derivatives of the approximated function an algorithm is also proposed to estimate this approximation based on noisy input output data observed from the function under consideration unlike neural network training this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated backpropagation and it completely avoids the problem of poor convergence or undesirable local minima

an interactive term approach to non parametric fir nonlinear system identification in this technical note a framework for designing specially structured input sequences for non parametric nonlinear system identification is presented so that interaction terms which describe interactions among variables can be identified separately in a sense the approach decomposes a general difficult nonlinear identification problem into a number of problems that are of lower orders corresponding identification algorithms are proposed

building a model based fuzzy controller a new form of fuzzy model based controller is introduced the new controller is based on a conventional predictive controller design but utilises a fuzzy relational model the controller is described and compared with existing fuzzy controllers practical advice is given on generating suitable relational models for control purposes and an appropriate identification algorithm is recommended the controller is tested on a liquid level process and its performance compared to another fuzzy model based controller which has been previously reported

identification of structured nonlinear systems this paper is concerned with the identification of static nonlinear components in a complex interconnected system these nonlinear components are treated nonparametrically in the sense that no natural parameterization is assumed to be available

the korteweg de vries equation and its symmetry preserving discretization the korteweg de vries equation is one of the most important nonlinear evolution equations in the mathematical sciences in this article invariant discretization schemes are constructed for this equation both in the lagrangian and in the eulerian form we also propose invariant schemes that preserve the momentum numerical tests are carried out for all invariant discretization schemes and related to standard numerical schemes we find that the invariant discretization schemes give generally the same level of accuracy as the standard schemes with the added benefit of preserving galilean transformations which is demonstrated numerically as well

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

term and variable selection for non linear system identification the purpose of variable selection is to pre select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection it is required that the selected significant variables alone should sufficiently represent the system generally not all the model terms which are produced by combining different variables make an equal contribution to the system output and terms which make little contribution can be omitted a parsimonious representation which contains only the significant terms can often be obtained without the loss of representational accuracy by eliminating the redundant terms based on these observations a new variable and term selection algorithm is proposed in this paper the term detection algorithm can be applied to the general class of non linear modelling problems which can be expressed as a linear in the parameters form the variable selection procedure is based on locally linea

average case complexity and decision problems in group theory abstract we investigate the average case complexity of decision problems for finitely generated groups in particular the word and membership problems using our recent results on generic case complexity we show that if a finitely generated group g has word problem solvable in subexponential time and has a subgroup of finite index which possesses a non elementary word hyperbolic quotient group then the average case complexity of the word problem of g is linear time uniformly with respect to the collection of all length invariant measures on g this results applies to many of the groups usually studied in geometric group theory for example all braid groups b n all groups of hyperbolic knots many coxeter groups and all artin groups of extra large type

hyperplane complements of large type let f2 be an open convex subset of a finite dimensional real vectorspace v and m a collection of linear hyperplanes we shall suppose that m is locally finite on f2 this means that each point of f2 has a neighborhood meeting only finitely many hyperplanes in m as in 2 chap 5 f2 is partitioned by m in facets recalling that a plinth is a codimension 2 facet we shall say that m is of large type on f2 if for each plinth p its multiplicity m m p c m 3 the main result of the paper is the following

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

parabolic subgroups of artin groups abstract let a be an artin system for x we denote by a x the subgroup of a generated by x such a group is called a parabolic subgroup of a we reprove van der lek s theorem a parabolic subgroup of an artin group is an artin group we give an algorithm which decides whether two parabolic subgroups of an artin group are conjugate let a be a finite type artin group and let a x be a parabolic subgroup with connected associated coxeter graph the quasi centralizer of a x in a is the set of in a such that x 1 x we prove that the commensurator of a x in a is equal to the normalizer of a x in a and that this group is generated by a x and the quasi centralizer of a x in a moreover if a x is not of type d l l 4 and l even then this group is generated by a x and the centralizer of a x in a

continuous symmetries of difference equations lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations in this article we review the results of a much more recent program the use of lie groups to study difference equations we show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners one is to use generalized symmetries acting on solutions of difference equations but leaving the lattice invariant the other is to restrict them to point symmetries but to allow them to also transform the lattice

indirect adaptive fuzzy sliding mode control part i fuzzy switching in this paper by using the concept of sliding mode control design and lyapunov synthesis approach we propose an indirect adaptive fuzzy sliding mode control iafsmc scheme for a class of nonlinear systems in contrast to the existing sliding mode fuzzy control system designs where the sliding mode control law is directly substituted by a fuzzy controller in our approach both the equivalent control term and switching type control term in the sliding mode control law are approximated by fuzzy systems respectively an on line adaptive tuning algorithm for the consequent parameters in the fuzzy rules is also designed the sliding mode based design procedure ensures the stability and robustness of the proposed iafsmc we prove that the proposed adaptive scheme can achieve asymptotically stable tracking of a reference input with a guarantee of the bounded system signals the chattering phenomena in the sliding mode control is attenuated and the steady error is also alleviated simulation studies have shown that the presented adaptive design of fuzzy sliding mode controller performs very well in the presence of an unknown disturbance

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

hinging hyperplanes for regression classification and function approximation a hinge function y h x consists of two hyperplanes continuously joined together at a hinge in regression prediction classification pattern recognition and noiseless function approximation use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters a simple and effective method for finding good hinges is presented

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

an iv qr algorithm for neuro fuzzy multivariable online identification in this paper a new algorithm for neuro fuzzy identification of multivariable discrete time nonlinear dynamic systems more specifically applied to consequent parameters estimation of the neuro fuzzy inference system is proposed based on a decomposed form as a set of coupled multiple input and single output miso takagi sugeno ts neuro fuzzy networks an on line scheme is formulated for modeling a nonlinear autoregressive with exogenous input narx recurrent neuro fuzzy structure from input output samples of a multivariable nonlinear dynamic system in a noisy environment the adaptive weighted instrumental variable wiv algorithm by qr factorization based on the numerically robust orthogonal householder transformation is developed to modify the consequent parameters of the ts multivariable neuro fuzzy network

conjugacy in artin groups of extra large type abstract we describe a constructive cubic time solution to the conjugacy problem in artin groups of extra large type which was proved soluble in those groups in 2 we use results from 7 6 that characterise geodesic words in those groups as well as the description of conjugacy between elements involving three or more generators that is given in 2

identification of stable models in subspace identification by using regularization in subspace identification methods the system matrices are usually estimated by least squares based on estimated kalman filter state sequences and the observed inputs and outputs for a finite number of data points the estimated system matrix is not guaranteed to be stable even when the true linear system is known to be stable in this paper stability is imposed by using regularization the regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive semi definite weighting matrix the amount of regularization can be determined from a generalized eigenvalue problem the data augmentation method of chui and maciejowski 1996 is obtained by using specific choices for the weighting matrix in the regularization term

inference of disjoint linear and nonlinear sub domains of a nonlinear mapping this paper investigates new ways of inferring nonlinear dependence from measured data the existence of unique linear and nonlinear sub spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub spaces are derived the importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task specifically once the linear nonlinear sub spaces are known by definition the explanatory variables may be transformed to form two disjoint sub sets spanning respectively the linear and nonlinear sub spaces the nonlinear modelling task is confined to the latter sub set which will typically have a smaller number of elements than the original set of explanatory variables constructive algorithms are proposed for inferring the linear and nonlinear sub spaces from noisy data

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

realization of pid controls by fuzzy control methods abstract this paper shows that pid controllers can be realized by fuzzy control methods of product sum gravity method and simplified fuzzy reasoning method pid controllers however cannot be constructed by min max gravity method known as mamdani s fuzzy reasoning method furthermore extrapolative reasoning can be executed by the product sum gravity method and simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules

fuzzy systems and approximation abstract the basic motivation of using fuzzy rule based systems especially for control purposes is to deduce simple and fast approximations of the unknown or too complicated models fuzzy rule based systems have become very popuar because of their transparency and easiness of tuning and modification recently some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of functions that could be implemented in this way some parallel results on the other hand attempted to prove that the main advantage of using fuzzy systems was the suitability for approximation with arbitrary accuracy in their universality the explicit formulas and some very recent theoretical results made it clear however that fuzzy systems were not really good approximators as realistic fuzzy controllers could generate only very rough approximations of given transference functions in connection with approximation the question can be asked whether there is an optimal fineness roughness of a fuzzy rule base that controls a certain action with roughness gives minimal time complexity as an example a target tracking problem was chosen cat and mouse or hawk and sparrow problem where the antagonistic criteria of minimizing inference time by the given rule base and minimizing action time search for the target with given uncertainty provided by the rule model were examined under certain assumptions the solution of this optimization problem leads to nontrivial rule base sizes these results have also practical applicability since if a fine enough model of the system is known it is always possible to generate a rougher version of the same by applying the model transformation technique offered by rule interpolation with levels

on line fuzzy identification using genetic algorithms the design and implementation of an on line fuzzy identification method using genetic algorithms gas is reported in this paper in the proposed algorithm the rule table of a fuzzy system is first divided into several independent and much smaller fuzzy systems which in turn are encoded into separate bit strings for genetic operations a novel ga updating architecture is then proposed to search the optimal rule base of these fuzzy systems at each sample interval the performance of this identification algorithm is evaluated by simulation of a non linear system moreover an experiment on simple behavior learning of a mobile robot is also reported the results indicate an improvement in design cycle and convergence to the optimal rule base within a relatively short period of time

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

explicit formulas for fuzzy controller abstract in this paper we present some explicit formulas of fuzzy control in the simple case of one condition these formulas are then used on the one hand to study the effects of some design factors inference operators number of partitions etc and on the other hand to carry out simulations

lie point symmetries of differential difference equations we present an algorithm for determining the lie point symmetries of differential equations on fixed non transforming lattices i e equations involving both continuous and discrete independent variables the symmetries of a specific integrable discretization of the krichever novikov equation the toda lattice and toda field theory are presented as examples of the general method

metric systolicity and two dimensional artin groups we introduce the notion of metrically systolic simplicial complexes we study geometric and large scale properties of such complexes and of groups acting on them geometrically we show that all two dimensional artin groups act geometrically on metrically systolic complexes as direct corollaries we obtain new results on two dimensional artin groups and all their finitely presented subgroups we prove that the conjugacy problem is solvable and that the dehn function is quadratic we also show several large scale features of finitely presented subgroups of two dimensional artin groups lying background for further studies concerning their quasi isometric rigidity

kernel based partially linear models and nonlinear identification in this note we propose partially linear models with least squares support vector machines ls svms for nonlinear arx models we illustrate how full black box models can be improved when prior information about model structure is available a real life example based on the silverbox benchmark data shows significant improvements in the generalization ability of the structured model with respect to the full black box model reflected also by a reduction in the effective number of parameters

fuzzy on line identification of siso nonlinear systems abstract a new fuzzy on line identification algorithm for a single input single output continuous time nonlinear dynamic system is presented this method combines the conventional on line identification with fuzzy logic system the nonlinear system is approximated by a set of fuzzy rules that describe the local linear dynamic in each subspace formed by fuzzifying the input and output space the continuous time fuzzy input output model is identified on line by using the input and output measurements a fuzzy identification algorithm has been developed and a convergence analysis is carried out simulation studies have demonstrated that this fuzzy on line identifier can match the time varying nonlinear system within 5 accuracy

the discretized boussinesq equation and its conditional symmetry reduction in this article we show that we can carry out the symmetry preserving discretization of the boussinesq equation with respect to three of its more significant conditional symmetries we perform the symmetry reduction of the obtained nonlinear discrete schemes with respect to the conditional symmetries and obtain the reduced discrete equations which unlike in the continuous case are not always reducible to second order difference equations a numerical comparison with the exact continuous solution given by weierstrass elliptic functions is carried out

identification of nonlinear systems using polynomial nonlinear state space models in this paper we propose a method to model nonlinear systems using polynomial nonlinear state space equations obtaining good initial estimates is a major problem in nonlinear modelling it is solved here by identifying first the best linear approximation of the system under test the proposed identification procedure is successfully applied to measurements of two physical systems

on the hinge finding algorithm for hingeing hyperplanes this correspondence concerns the estimation algorithm for hinging hyperplane hh models a piecewise linear model for approximating functions of several variables suggested in breiman 1993 the estimation algorithm is analyzed and it is shown that it is a special case of a newton algorithm applied to a sum of squared error criterion this insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed in addition the way of updating the parameters in the hh model is discussed in breiman a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step this connects closely to some previously suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters

generic case complexity decision problems in group theory and random walks abstract we give a precise definition of generic case complexity and show that for a very large class of finitely generated groups the classical decision problems of group theory the word conjugacy and membership problems all have linear time generic case complexity we prove such theorems by using the theory of random walks on regular graphs

symmetries and conditional symmetries of differential difference equations two different methods of finding lie point symmetries of differential difference equations are presented and applied to the two dimensional toda lattice continuous symmetries are combined with discrete ones to obtain various reductions to lower dimensional equations in particular to differential equations of the delay type the concept of conditional symmetries is extended from purely differential to differential difference equations and shown to incorporate backlund transformations

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

lie point symmetries of the discrete liouville equation the liouville equation is well known to be linearizable by a point transformation it has an infinite dimensional lie point symmetry algebra isomorphic to a direct sum of two virasoro algebras we show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries we do however construct a difference system approximating the liouville equation that is invariant under the maximal finite subgroup the invariant scheme is an explicit one and provides a much better approximation of exact solutions than a comparable standard noninvariant scheme and also than a scheme invariant under an infinite dimensional group of generalized symmetries