performance limitations of non minimum phase systems in the servomechanism problem abstract this paper studies the cheap regulator problem and the cheap servomechanism problem for systems which may be non minimum phase the study extends some well known properties of perfect regulation and the perfect tracking and disturbance rejection of minimum phase systems to non minimum phase systems it is shown that perfect rejection to disturbances applied to the plant input can be achieved no matter whether the system is minimum phase or non minimum phase whereas a fundamental limitation exists in the achievable transient performance of tracking and rejection to disturbances applied to the plant output for a non minimum phase system and that this limitation can be simply and completely characterized by the number and locations of those zeros of the system which lie in the right half of the complex plane furthermore this limitation provides a quantitative measure of the degree of difficulty which is inherent in the control of such non minimum phase systems

stable inversion of continuous time nonlinear systems by finite difference methods introduces finite difference methods for stable inversion of continuous time nonlinear systems a relationship between the new finite difference methods and the existing picard methods is established a damped newton finite difference method is shown to possess superior convergence properties and its effectiveness is illustrated with an inverted pendulum example

asymmetric subsethood product fuzzy neural inference system asupfunis this work presents an asymmetric subsethood product fuzzy neural inference system asupfunis that directly extends the supfunis model by permitting signal and weight fuzzy sets to be modeled by asymmetric gaussian membership functions the asymmetric subsethood product network admits both numeric as well as linguistic inputs input nodes which act as tunable feature fuzzifiers fuzzify numeric inputs with asymmetric gaussian fuzzy sets and linguistic inputs are presented as is the antecedent and consequent labels of standard fuzzy if then rules are represented as asymmetric gaussian fuzzy connection weights of the network the model uses mutual subsethood based activation spread and a product aggregation operator that works in conjunction with volume defuzzification in a gradient descent learning framework despite the increase in the number of free parameters the proposed model performs better than supfunis on various benchmarking problems both in terms of the performance accuracy and architectural economy and compares excellently with other various existing models with a performance better than most of them

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple example

approximated stable inversion for nonlinear systems with nonhyperbolic internal dynamics a technique to achieve output tracking for nonminimum phase nonlinear systems with nonhyperbolic internal dynamics is presented the present paper integrates stable inversion techniques that achieve exact tracking with approximation techniques that modify the internal dynamics to circumvent the nonhyperbolicity of the internal dynamics this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques the theory is developed for nonlinear systems and the method is applied to a two cart with inverted pendulum example

approximation analysis of feedforward regular fuzzy neural network with two hidden layers the closure fuzzy mapping is employed to analyze approximation capability of feedforward regular fuzzy neural networks fnns with two hidden layers the bridge to do that is the fuzzy valued bernstein polynomial by the fuzzy polynomial approximation theorem this paper establishes some equivalent conditions for the fuzzy functions that can be approximated by the regular fnns to any degree of accuracy thus universal approximation of regular fnns based on zadeh s extension principle and fuzzy arithmetic can be studied systematically finally a simulation example is used to demonstrate the constructive procedure of approximating fnns

fuzzy continuous input output controllers are universal approximators the aim of this paper is twofold i to analyse why the fuzzy input output controllers proposed by buckley and hayashi fuzzy sets and systems 58 1993 273 are hardly continuous and based on this analysis a special necessary and sufficient condition for the controllers being continuous is obtained ii to amend buckley hayashi s controllers so that to make them unconditionally continuous

fuzzy nonlinear regression with fuzzified radial basis function network a fuzzified radial basis function network frbfn is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model rbfn a frbfn contains fuzzy weights and can handle fuzzy in fuzzy out data this paper shows that a frbfn can also be interpreted as a kind of fuzzy expert system hence it owns the advantages of simple structure and clear physical meaning some metrics for fuzzy numbers have been extended to the metrics for n dimensional fuzzy vectors which are applicable to computations in frbfns the corresponding metric spaces for n dimensional fuzzy vectors are proved to be complete further frbfns are proved to be able to act as universal function approximators for any continuous fuzzy function defined on a compact set this paper applies the proposed frbfn to nonparametric fuzzy nonlinear regression problems for multidimensional lr type fuzzy data fuzzy nonlinear regression with frbfns can be formulated as a nonlinear mathematical programming problem two training algorithms are proposed to quickly solve the two types of problems under different criteria and constraint conditions namely the two stage and bp back propagation training algorithms simulation studies are carried out to verify the feasibility and demonstrate the advantages of the proposed approaches

tracking nonlinear non minimum phase systems using sliding control nonlinear systems affine in the input and having a well defined vector relative degree are considered the invertibility of the input output dynamics can be used to achieve tracking of smooth desired trajectories if the associated zero dynamics are stable we consider tracking in nonlinear systems with unacceptable zero dynamics i e non minimum phase systems the desired trajectories are assumed to be generated by some exosystem we use sliding control to achieve tracking independent of disturbances entering in the channels of the input the main idea is i to do an output redefinition such that the zero dynamics with respect to this new output are acceptable ii to define a modified desired trajectory for the new output to track such that in the process the original output tracks the original desired trajectory asymptotically

higher order approximate feedback linearization about a manifold for multi input systems considers the problem of approximately feedback linearizing a multi input nonlinear system around the equilibrium manifold spl epsi while making the error terms be of highest order on spl epsi necessary and sufficient conditions are given for approximately feedback linearizing the system around spl epsi with error terms of order spl rho on spl epsi a simple multi input example is given to illustrate the higher order approximate feedback linearization procedure

output regulation of nonlinear systems with nonhyperbolic zero dynamics previous solvability conditions for the output relation of nonlinear systems are applicable only to those with hyperbolic zero dynamics it is shown in this note that output regulation of nonlinear systems with nonhyperbolic zero dynamics is also possible by a reduction of the plant dynamics and an augmentation of the exosystem

prolongation structures of nonlinear equations and infinite dimensional algebras prolongation structures of the sine gordon equation the ernst equation and the chiral model are systematically discussed it is shown that the prolongation structures generate the kac moody algebra for the sine gordon equation and another type of infinite dimensional algebra for the ernst equation this algebra includes the kac moody algebra and the virasoro algebra as its subalgebra

characterization of compact subsets of fuzzy sets a characterization of compact subsets is presented for the metric space of normal fuzzy convex fuzzy sets on the base space rn the metric for which is the supremum over the hausdorff distances between corresponding level sets it is shown that a closed subset is compact if and only if it is uniformly support bounded and the corresponding set of support functions is equileftcontinuous in the membership grade variable

fuzzy input output controllers are universal approximators abstract in this paper we show that a fuzzy input output controller can approximate to any degree of accuracy a continuous fuzzy system this generalizes the known result that fuzzy controllers crisp input output can approximate continuous functions

iterative inversion of fuzzified neural networks the inversion of a neural network is a process of computing inputs that produce a given target when fed into the neural network the inversion algorithm of crisp neural networks is based on the gradient descent search in which a candidate inverse is iteratively refined to decrease the error between its output and the target in this paper we derive an inversion algorithm of fuzzified neural networks from that of crisp neural networks first we present a framework of learning algorithms of fuzzified neural networks and introduce the idea of adjusting schemes for fuzzy variables next we derive the inversion algorithm of fuzzified neural networks by applying the adjusting scheme for fuzzy variables to total inputs in the input layer finally we make three experiments on the parity three problem examine the effect of the size of training sets on the inversion and investigate how the fuzziness of inputs and targets of training sets affects the inversion

a hybrid genetic fuzzy neural network algorithm designed for classification problems involving several groups we propose a multigroup classification algorithm based on a hybrid genetic fuzzy neural net gfnn framework recent results on evolutionary computation and fuzzy neural network methodology are combined to effectively adapt the membership functions of the fuzzifier and the defuzzifier to the data set separate membership functions are defined for each dimension in the fuzzifier and for each fuzzy output group in the defuzzifier the signal inherent in the fuzzifier is aggregated by a suitable t norm and transmitted to the defuzzifier the defuzzifier aggregates the response i e the predicted group membership by a suitable conorm if misclassifications occur during training the membership functions of both the fuzzifier and the defuzzifier are adapted by a systematic robust procedure the algorithm is successfully tested with real economic data in total the gfnn performs as good as the best of the competing methods in our test the results suggest economically meaningful interpretations

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

evaluative linguistic expressions vs fuzzy categories in this paper we discuss the distinction between categories characterized by verbal labels taken from a fuzzy rating scale and special class of linguistic expressions called evaluative the latter form a general class of expressions that includes gradable and evaluative adjectives and their hedges first we will provide a brief linguistic analysis of them then we outline basic principles for construction of the mathematical model of semantics of evaluative expressions in section 3 we will analyze the concepts of rating scale with verbal labels fuzzy rating scale their semantics and demonstrate that the latter cannot be identified with the semantics of evaluative expressions finally we suggest a method for construction of fuzzy rating scales on the basis of evaluative linguistic expressions the main goal of this paper is to demonstrate the power of fuzzy set theory and to show that it is capable of providing tools for advanced modeling of linguistic semantics

the prolongation structure of the inhomogeneous equation of the reaction diffusion type the inhomogeneous extension of equations of the reaction diffusion type is investigated by means of the covariant prolongation structures theory we construct the sl 2 r r t prolongation structure for an inhomogeneous equation of the reaction diffusion type and give the corresponding akns type

pseudopotentials lax equations and backlund transformations for nonlinear evolution equations it is shown how to generate both lax equations and backlund transformations for nonlinear evolution equations using the concept of pseudopotentials associated with the properties of the riccati equation several examples are given modified korteweg de vries harry dym kaup kupershmidt and sawada kotera equations

a neural network approach to the fuzzy transform the paper deals with the f transform technique which was introduced as a method for an approximate representation of continuous functions the same task is solved by many methods from different areas neural networks also belong to techniques which have been proved to be powerful for approximation objectives they provide us with many advantages especially incremental way of learning parameters the paper inherits neural approaches to the f transform method and presents experiments justifying the proposed approach incremental way of determination of certain parameters of the f transform method which were up to now given by batch formula enriches possible areas of application of the method by fast on line processes moreover the neural approach is demonstrated to be an appropriate one for finding such fuzzy partition of a domain which respects better a given set of measured samples which are to be approximated by a continuous function with no predetermined shape

analysis of approximation of continuous fuzzy functions by multivariate fuzzy polynomials for the given fuzzy valued function j rn f0 r the fuzzy valued bernstein polynomial is introduced to show the fact that continuous fuzzy valued functions can be approximately represented as the fuzzy valued polynomials on any compact set u rn some equivalent condition for the continuous fuzzy function f f0 r n f0 r that can be approximated to any degree of accuracy by fuzzy polynomials on arbitrary compact set u f0 r n are presented

approximation capabilities of multilayer fuzzy neural networks on the set of fuzzy valued functions this paper first introduces a piecewise linear interpolation method for fuzzy valued functions based on this we present a concrete approximation procedure to show the capability of four layer regular fuzzy neural networks to perform approximation on the set of all d p continuous fuzzy valued functions this approach can also be used to approximate d continuous fuzzy valued functions an example is given to illustrate the approximation procedure

stable inversion for nonlinear nonminimum phase time varying systems we extend stable inversion to nonlinear time varying systems and study computational issues the technique is applicable to minimum phase as well as nonminimum phase systems the inversion technique is new even in the linear time varying case and relies on partitioning the dichotomic split of the linearized system dynamics into time varying stable and unstable submanifolds this dichotomic split is used to build time varying filters which are in turn the basis of a contraction used to find a bounded inverse input state trajectory finding the inverse input state trajectory allows the development of exact output tracking controllers the method is local to the time varying trajectory and requires that the internal dynamics vary slowly however the method represents a significant advance relative to presently available tracking controllers present techniques are restricted to time invariant nonlinear systems and in the general case track only asymptotically

inversion of nonlinear time varying systems a procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or more generally to mechanical structures is given the procedure is presented in a general setting for nonlinear time varying systems an iterative algorithm that computes a smooth controlled invariant time varying manifold the mathematical properties of which are illustrated and exploited is also proposed an application to a flexible two link manipulator illustrates the algorithm and its computational advantages

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

universal approximations of continuous fuzzy valued functions by multi layer fuzzy neural networks abstract the fact that four layer feedforward regular fuzzy neural networks with sigmoid function in the first hidden layer are capable of approximately representing continuous fuzzy valued functions on any compact set of r is shown at first bernstein polynomials associated with fuzzy valued functions are employed to approximate continuous fuzzy valued function defined on a compact set secondly by the conclusions related to standard feedforward networks universal approximations of continuous fuzzy valued functions by regular fuzzy neural networks are obtained

exact output tracking theory for systems with parameter jumps in this paper we consider the exact output tracking problem for systems with parameter jumps necessary and sufficient conditions are derived for the elimination of switching introduced output transient previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps switches such techniques are however only applicable to minimum phase systems in contrast our approach is applicable to nonminimum phase systems and obtains bounded but possibly non causal solutions if the reference trajectories are generated by an exo system then we develop an exact tracking controller in a feedback form as in standard regulator theory we obtain a linear map from the states of the exo system to the desired system state which is defined via a matrix differential equation the constant solution of this differential equation provides asymptotic tracking and coincides with the feedback law used in standard regulator theory the obtained results are applied to a simple flexible manipulator with jumps in the pay load mass

backlund transformations for the ernst equation presented is a systematic approach to the transformation theories for the ernst equation from the viewpoint of the backlund transformation it is explicitly shown that the method of clairin gives a simple derivation of various transformations such as transformations found by ehlers neugebauer and harrison

an intelligent stock trading decision support system through integration of genetic algorithm based fuzzy neural network and artificial neural network the stock market which has been investigated by various researchers is a rather complicated environment most research only concerned the technical indexes quantitative factors instead of qualitative factors e g political effect however the latter plays a critical role in the stock market environment thus this study develops a genetic algorithm based fuzzy neural network gfnn to formulate the knowledge base of fuzzy inference rules which can measure the qualitative effect on the stock market next the effect is further integrated with the technical indexes through the artificial neural network ann an example based on the taiwan stock market is utilized to assess the proposed intelligent system evaluation results indicate that the neural network considering both the quantitative and qualitative factors excels the neural network considering only the quantitative factors both in the clarity of buying selling points and buying selling performance

on the existence and uniqueness of solutions to the output regulation equations for periodic exosystems a b s t r a c t in this paper we prove that for a general class of control affine systems the output regulation equations are uniquely solvable whenever the exosystem is periodic and the linearized zero dynamics of the plant does not contain periodic solutions of the same period as those of the exosystem our main result can therefore be applied to cases when the linearized zero dynamics are non hyperbolic as an application we consider the important case of when the exosystem is composed of k uncoupled harmonic oscillators 2012 elsevier b v all rights reserved

topological properties of fuzzy numbers fuzzy numbers are defined and a metric is assigned to this class of fuzzy sets topological properties of the resulting metric space are studied the notion of q crisp fuzzy numbers is introduced and in particular it is shown that this class of fuzzy numbers is homeomorphic to the hilbert cube

prolongation structures of the supersymmetric sine gordon equation and infinite dimensional superalgebras prolongation structures of the supersymmetric sine gordon equation are discussed it is shown that an infinite dimensional superalgebra is associated with these structures and that a linear representation of the algebra gives the super lax pairs of the equation

sugeno type controllers are universal controllers abstract we show that given any continuous real valued function on a compact set there is a sugeno type controller that will approximate this function to any degree of accuracy an application of this result to fuzzy control is presented which shows that this type of sugeno controller is a universal controller

a learning algorithm of fuzzy neural networks with triangular fuzzy weights abstract in this paper first we propose an architecture of fuzzy neural networks with triangular fuzzy weights the proposed fuzzy neural network can handle fuzzy input vectors as well as real input vectors in both cases outputs from the fuzzy neural network are fuzzy vectors the input output relation of each unit of the fuzzy neural network is defined by the extension principle of zadeh next we define a cost function for the level sets i e cuts of fuzzy outputs and fuzzy targets then we derive a learning algorithm from the cost function for adjusting three parameters of each triangular fuzzy weight finally we illustrate our approach by computer simulations on numerical examples

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

universal fuzzy controllers based on generalized t s fuzzy models this paper investigates the universal fuzzy control problem based on generalized t s fuzzy models the universal approximation capability of the generalized t s fuzzy models is shown and an approach to robust controller design for general nonlinear systems based on this kind of generalized t s fuzzy models is developed the results of universal fuzzy controllers for two classes of nonlinear systems are then given and constructive procedures to obtain the universal fuzzy controllers are also provided an example is finally presented to show the effectiveness of our approach

formalized theory of general fuzzy reasoning first a rigorous mathematical theory for calculating the conclusion of general fuzzy reasoning is proposed second a formalized non fuzzy version of the theory of general fuzzy reasoning is founded in classical logics

universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule this paper presents a special hierarchical fuzzy system where the outputs of the previous layer are not used in the if parts but used only in the then parts of the fuzzy rules of the current layer the proposed scheme can be shown to be a universal approximator to any continuous function on a compact set if complete fuzzy sets are used in the if parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier from the simulation of ball and beam control system it is demonstrated that the proposed scheme approximates with good accuracy the model nonlinear controller with fewer fuzzy rules than the centralized fuzzy system and its control performance is comparable to that of the nonlinear controller

fuzzy hyperbolic neural network with time varying delays in this paper the formula of fuzzy basis functions with time varying delays dfbf is firstly given based on the dfbf a novel fuzzy hyperbolic neural network with time varying delays dfhnn and its approximation properties are presented respectively by constructing an appropriate lyapunov krasovskii functional the stability of dfhnn is discussed and some new criteria concerning the global exponential stability of dfhnn are proposed finally three numerical examples are given to demonstrate the effectiveness of the obtained results

the fuzzy neural network approximation lemma abstract it is well known that artificial neural networks are universal approximators but what about fuzzy neural networks only buckley and hayashi 1 presented a theoretical result for these networks they showed that there are fuzzy functions which cannot be approximated by a certain fuzzy neural network in this paper we answer the question for a special type of fuzzy neural networks especially with regard to the fuzzy arithmetic that is used it is simplified in order to minimize the computational expense as well as to simplify the theoretical examinations we prove that the class of fuzzy functions which is identical to the class of all continuous real functions extended by means of the extension principle can be approximated by certain fuzzy neural networks

a behavioral approach to inversion based control abstract a new simplified behavior theory is proposed to address inversion based control for linear nonminimum phase siso systems the chosen space of signals is the set of piecewise c functions and input output pairs as weak solutions satisfy a differential integral equation with additional smoothness requirements a related key result is the output input or inverse representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded noncausal desired outputs are allowed it is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one when this straightforward condition is satisfied a closed form expression provides the inverse input then an analysis on preaction and postaction control follows two examples are included showing the relevance of output signal design in control applications

fuzzy neural networks a survey abstract in this paper a fuzzy neural network will be a layered feedforward neural net that has fuzzy signals and or fuzzy weights we survey recent results on learning algorithms and applications for fuzzy neural networks

numerical relationships between neural networks continuous functions and fuzzy systems abstract in this survey paper we first discuss computational equivalence between continuous functions regular neural nets fuzzy controllers and discrete fuzzy expert systems we also discuss how to build hybrid neural nets numerically identical to a fuzzy controller or a discrete fuzzy expert system we then discuss computational equivalence between continuous fuzzy functions regular fuzzy neural nets and fuzzy systems we also discuss how to construct hybrid fuzzy neural nets to approximate continuous fuzzy functions

max min fuzzy hopfield neural networks and an efficient learning algorithm abstract we set up a dynamical fuzzy neural network system i e the so called max min fuzzy hopfield network in the paper and prove the lyapunov stability of the equilibrium points attractor of the system also we discuss the uniform stability of the system and show some sufficient conditions with which the given fuzzy pattern is the attractor of the system moreover we obtain a nontrivially attractive basin of the attractor therefore our models have good fault tolerance with an analytic method we design an efficient learning algorithm for connected weights of the networks finally simulation examples demonstrate our conclusions

fuzzy i o controller abstract we describe a fuzzy controller which accepts and produces fuzzy data linguistic variables as well as crisp data real numbers for the control of man machine systems

analyses of regular fuzzy neural networks for approximation capabilities abstract by introducing a trapezoidal fuzzy function and using the properties of the function we set up a continuously increasing fuzzy function that cannot be arbitrarily closely approximated on a compact set of f 0 r by the regular fuzzy neural network rfnn thus the conclusions in buckley and hayashi fuzzy sets and systems 61 1994 43 51 are improved and the problem if the rfnn is the universal approximator to the class of continuously increasing fuzzy functions is solved finally we obtain the universal approximation to the extended fuzzy functions by rfnn

infinite dimensional estabrook wahlquist prolongations for the sine gordon equation we are looking for the universal covering algebra for all symmetries of a given partial differential equation pde using the sine gordon equation as a typical example for a nonevolution equation for nonevolution equations estabrook wahlquist prolongation structures for nonlocal symmetries depend on the choice of a specific subideal of the contact module to define the pde for each inequivalent such choice we determine the most general solution of the prolongation equations as subalgebras of the infinite dimensional algebra of all vector fields over the space of nonlocal variables associated with the pde in the style of vinogradov covering spaces we show explicitly how previously known prolongation structures known to lie within the kac moody algebra a 1 1 are special cases of these general solutions although we are unable to identify the most general solutions with previously studied algebras we show the existence of gauge transformations between prolongation structures viewed as determinin

a new approach to the zero dynamics assignment problem for nonlinear discrete time systems using functional equations the present research work aims at the development of a systematic method to arbitrarily assign the zero dynamics of a nonlinear discrete time real analytic system by constructing the requisite synthetic output maps the problem under consideration is motivated by the need to adequately address the control problem of nonminimum phase nonlinear discrete time systems since the latter represent a rather broad class of systems due to the well known effect of sampling on the stability of zero dynamics in the proposed approach the above control objective can be attained through i a systematic computation of synthetic output maps that induce minimum phase behavior while being statically equivalent to the original output maps both vanish on the equilibrium manifold and ii the subsequent integration into the methodological framework of currently available nonminimum phase compensation schemes for nonlinear discrete time systems that rely on output redefinition the mathematical formulation of the zero dynamics assignment problem is realized via a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a solution method that is easily programmable with the aid of a symbolic software package the synthetic output maps that induce the prescribed zero dynamics for the original nonlinear discrete time system can be explicitly computed on the basis of the solution to the aforementioned system of functional equations

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

universal fuzzy controllers a collection b of fuzzy controllers is a universal fuzzy controller if and only if given any controllable process p it can also be controlled by some fuzzy controller in b this paper identifies a new type of universal fuzzy controller

approximations of continuous functionals by neural networks with application to dynamic systems the paper gives several strong results on neural network representation in an explicit form under very mild conditions a functional defined on a compact set in c a b or l sup p a b spaces of infinite dimensions can be approximated arbitrarily well by a neural network with one hidden layer the results are a significant development beyond earlier work where theorems of approximating continuous functions defined on a finite dimensional real space by neural networks with one hidden layer were given all the results are shown to be applicable to the approximation of the output of dynamic systems at any particular time

theory of the fuzzy controller abstract we first introduce notation in an attempt to standardize the description of a basic fuzzy controller if r 1 r 2 r n are the real number inputs to the fuzzy controller and is its defuzzified output then f r 1 r n for some function f by the theory of the fuzzy controller we mean in this paper the study of the structure of f for elementary fuzzy controllers using this standardized notation we first survey the known results on the theory of the fuzzy controller and then discuss important future research topics in this area

prolongation approach to backlund transformation of zhiber mikhailov shabat equation the prolongation structure of zhiber mikhailov shabat zms equation is studied by using wahlquist estabrook s method the lax pair for zms and riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure based on nonlinear realization of the prolongation structure an auto backlund transformation of zms equation is obtained

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

controllable processes and the fuzzy controller abstract we show that any controllable process can be controlled by the scaled and averaged output of multiple elementary fuzzy controllers operating simultaneously

universal approximators for fuzzy functions abstract we show how to construct a large class of universal approximators for fuzzy functions which continuously map fuzzy numbers into fuzzy numbers and are the extension principle extensions of continuous real valued functions one important application is that layered feedforward neural nets with real weights and bias terms and fuzzy signals whose output is computed using the extension principle are universal approximators for these functions

similarity measures for general type 2 fuzzy sets based on the α plane representation abstract similarity measures are very important concepts in fuzzy sets fss theory there are many different definitions of similarity measures for both type 1 t1 fss and interval type 2 it2 fss in this paper one similarity measure for it2 fss which is extended from the jaccard similarity measure for t1 fss is reviewed then based on the plane representation for a general type 2 gt2 fs this similarity measure is generalized to such t2 fss some examples that demonstrate how to compute the similarity measures for different t2 fss are given

efficient learning algorithms for three layer regular feedforward fuzzy neural networks a key step of using gradient descend methods to develop learning algorithms of a regular feedforward fuzzy neural network fnn is to differentiate max min functions which contain max spl or and min spl and operations the paper aims at several objectives first investigate further the differentiation of spl or spl and functions second employ general fuzzy numbers which include triangular and trapezoidal fuzzy numbers as special cases to define a three layer regular fnn the general fuzzy numbers related can be approximately determined by their corresponding finite level sets so we can approximately represent the input output i o relationship of the regular fnn as functions of the endpoints of all finite level sets third a fuzzy back propagation algorithm is presented and to speed up the convergence of the learning algorithm a fuzzy conjugate gradient algorithm for fuzzy weights and biases is developed furthermore the convergence of the algorithm is analyzed systematically finally some real simulations demonstrate the efficiency of our learning algorithms the regular fnn is applied to the approximate realization of fuzzy inference rules and fuzzy functions defined on given compact sets

expansion of det a b c and robustness analysis of discrete time state space systems in this paper the expansion of det a b c is given the robustness problem for discrete time state space systems with uncertain parameters is investigated by applying the schur stability theory of interval polynomials a stability robustness criterion for the uncertain systems is derived illustrative examples are presented

applying fuzzy adaptive network to fuzzy regression analysis abstract a fuzzy inference system based on the sugeno inference model is first formulated for fuzzy regression analysis this system is then represented by a fuzzy adaptive network this approach combines the power of representation of fuzzy inference system with the ability of learning of the neural network numerical examples are trained and solved to illustrate the approach the results are compared with other approaches

a class of hierarchical fuzzy systems with constraints on the fuzzy rules this paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in if parts but only in then parts of the fuzzy rules of the current layer the proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the if parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier from the example of ball and beam control system simulation it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system and its control performance is comparable to that of a nonlinear controller

the relation between inference and interpolation in the framework of fuzzy systems abstract this papers aims at clarifying the meaning of different interpretations of the max min or more generally the max t norm rule in fuzzy systems it turns out that basically two distinct approaches play an important role in fuzzy logic and its applications fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information

a fuzzy neural network algorithm for multigroup classification we propose a multigroup classification algorithm based on a hybrid fuzzy neural net framework a key feature of the approach is the adaptation of membership functions to new data in this way learning is reflected in the shape of the membership functions by defining separate membership functions for each fuzzy output class we allow dynamic adjustment of the functions during training the algorithm is successfully tested with real economic data the results suggest economically meaningful interpretations

an approximation method for the nonlinear servomechanism problem an analysis of the nonlinear servomechanism problem by the authors 1992 is shown to lead naturally to a straightforward and practical method for solving the problem in an approximate sense the results are based on a kth order approximate solution for the plant zero error manifold and corresponding control law constructions are shown to yield kth order asymptotic tracking and disturbance rejection properties for the closed loop system the approach is illustrated by application to the ball and beam system

approximation of fuzzy functions by regular fuzzy neural networks in this paper we investigate the ability of regular fuzzy neural networks to provide approximations to fuzzy functions since the operation of regular fuzzy neural networks is based on zadeh s extension principle we first present a level characterization of the zadeh s extensions of level continuous fuzzy valued functions and consider the continuity of these extensions on the basis of this we give characterizations of fuzzy functions which can be approximated by a class of four layer regular fuzzy neural networks according to supremum metric and level convergence

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators