analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

multi dimensional fuzzy reasoning this paper suggests a method of multi dimensional fuzzy reasoning concerned with both modus ponens and modus tollens it also discusses an example to show how the method works

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

design and analysis of a fuzzy proportional integral derivative controller abstract this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional integral pi plus a derivative d controller first the fuzzy pi d controller is derived from the conventional continuous time linear pi d controller then the fuzzification control rule base and defuzzification in the design of the fuzzy controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pi d controller which has the same linear structure in the proportional integral and derivative parts but has nonconstant gains the proportional integral and derivative gains are nonlinear functions of the input signals the new fuzzy pi d controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self tuning control capability computer simulation results have demonstrated the advantages of the fuzzy controller particularly when the process to be controlled is nonlinear after a brief stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are shown to compare with the conventional pi d controller computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance

unbounded solutions of the equation asymptotic behavior of solutions of first order differential equation with deviating arguments in the email protected t email protected email protected i t y email protected i y email protected i is discussed for t a criterion for representing solutions in exponential form is proved inequalities for solution estimation are given sufficient conditions for the existence of unbounded solutions are derived a relevant illustrative example is given as well known results are discussed and compared

a new adaptive fuzzy controller using the parallel structure of fuzzy controller and its application abstract the paper suggests a new fuzzy adaptive controller which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers it explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system as well as related mathematical theorems and their proofs are also given the performance of the proposed adaptive control algorithm is analyzed through a design example and an experiment on hybrid force position robot control system

brief paper preservation of exponential stability for linear non autonomous functional differential systems we consider preservation of exponential stability for a system of linear equations with a distributed delay under the addition of new terms and a delay perturbation as particular cases the system includes models with concentrated delays and systems of integrodifferential equations our method is based on bohl perron type theorems

asymptotic equivalence of neutral and infinite retarded differential equations staffan a demontre qu une equation differentielle fonctionnelle fde neutre avec d operateur stable peut souvent etre traitee comme une fde a retard avec retardement infini le but principal de l article est d illustrer comment les techniques de staffans peuvent etre employees pour etudier le comportement asymptotique de solutions de certaines fde neutres non lineaires et non autonomes en particulier on considere une equation neutre scalaire de la forme d dt x t cx t r f t x t x t r

a model based fuzzy controller abstract to avoid the heuristic search for linguistic control rules a fuzzy controller which is based on a fuzzy model of the plant is introduced in a first step the plant is to be identified and described by a fuzzy relation in a second step this relation is used to find trajectories from any point of the discrete state space to the origin the resulting fuzzy control system predicts the point in state space to be reached next and selects the corresponding actuating variable from the fuzzy relation

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

preservation of stability in delay equations under delay perturbations we consider a class of linear delay equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations as an example we show how our results can be used to obtain an estimate on the maximum allowable sampling interval in the stabilization of a hybrid system with feedback delays we also present applications of our perturbation theorem to obtain stability conditions for delay equations with multiple delays

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

the design methodology of radial basis function neural networks based on fuzzy k nearest neighbors approach various approaches to partitioning of high dimensional input space have been studied with the intent of developing homogeneous clusters formed over input and output spaces of variables encountered in system modeling in this study we propose a new design methodology of a fuzzy model where the input space is partitioned by making use of some classification algorithm especially fuzzy k nearest neighbors k nn classifier being guided by some auxiliary information granules formed in the output space this classifier being regarded in the context of this design as a supervision mechanism is used to capture the distribution of data over the output space this type of supervision is beneficial when developing the structure in the input space it is demonstrated that data involved in a partition constructed by the fuzzy k nn method realized in the input space show a high level of homogeneity with regard to the data present in the output space this enhances the performance of the fuzzy rule based model whose premises in the rules involve partitions formed by the fuzzy k nn the design is illustrated with the aid of numeric examples that also provide a detailed insight into the performance of the fuzzy models and quantify several crucial design issues

approximation accuracy analysis of fuzzy systems as function approximators this paper establishes the approximation error bounds for various classes of fuzzy systems i e fuzzy systems generated by different inferential and defuzzification methods based on these bounds the approximation accuracy of various classes of fuzzy systems is analyzed and compared it is seen that the class of fuzzy systems generated by the product inference and the center average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center average defuzzifier and the class of fuzzy systems defuzzified by the mom defuzzifier in addition it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the mom defuzzified method are given

asymptotic convergence criteria of solutions of delayed functional differential equations abstract the convergence of all solutions of the scalar equation x f t x t is studied under the main assumption that every constant is its solution the criterion and the sufficient conditions for convergence are proved for the considered classes of equations it is among others proved that all solutions are convergent if and only if there exists at least one increasing and convergent solution as applications criteria for some classes of linear equations as well as for nonlinear equations are obtained some comparisons with already known results are given too

trajectory stabilization of a model car via fuzzy control abstract this paper deals with trajectory stabilization of a computer simulated model car via fuzzy control stability conditions of fuzzy systems are given in accordance with the definition of stability in the sense of lyapunov first we approximate a computer simulated model car whose dynamics is nonlinear by t s takagi and sugeno fuzzy model fuzzy control rules which guarantee stability of the control system under a condition are derived from the approximated fuzzy model the simulation results show that the fuzzy control rules effectively realize trajectory stabilization of the model car along a given reference trajectory from all initial positions under a condition and the dynamics of the approximated fuzzy model agrees well with that of the model car

an efficient immune based symbiotic particle swarm optimization learning algorithm for tsk type neuro fuzzy networks design in this paper we propose a new learning algorithm that can be used to design tsk type neuro fuzzy networks though there has been a great deal of interest in the use of immune algorithms ias for computer science and engineering in terms of fundamental methodologies they are not dramatically different from other algorithms in order to enhance the ia performance we propose the immune based symbiotic particle swarm optimization ispso for use in tsk type neuro fuzzy networks for solving the prediction and skin color detection problems the proposed ispso embeds the symbiotic evolution scheme in an ia and utilizes particle swarm optimization pso to improve the mutation mechanism in order to avoid trapping in a local optimal solution and to ensure the search capability of a near global optimal solution mutation plays an important role therefore we employed the advantages of pso to improve the mutation mechanism and used a method that introduces chaotic mapping with certainty ergodicity and the stochastic property into pso to improve global convergence unlike the ia that uses each individual in a population as a full solution to a problem symbiotic evolution assumes that each individual in a population represents only a partial solution to a problem complex solutions combine several individuals in the population

pad analysis of fuzzy control stability abstract by means of an index represented rule mapping the response g of a fuzzy controller is decomposed into two parts f the classical component and g f the nonlinear component called pad we intend to analyse the pad in order to know what the relation is between fuzzy and classical pid controllers fuzzy controllers mentioned here are defuzzified by the typical center of gravity method in the 1 input case we get that f g 0 which means that the fuzzy controller is exactly the same as the classical p controller whenever the rule mapping is simple definition 1 2 and the linguistic values are a binary family definition 4 1 in the 2 input case of error and error change for simple rule mapping and for simple linguistic values family 4 7 and perfectly for the wxyz linguistic values family definition 6 1 the fuzzy controller can be viewed as a series connection of a classical pd controller and a 1 pad element the describing function of a 1 pad element is very simple and fine and ensures that such fuzzy controller will be stable if the pd controller is the similar consequences are also obtained for the case of three inputs

a centered formulation of takagi sugeno rules for improved learning efficiency abstract we derive the gradient descent optimization equations for takagi sugeno fuzzy rule bases learning with symmetric triangular membership functions minimum operator as and operator and affine output functions standard sugeno rules a new type of affine output takagi sugeno rules called centred takagi sugeno rules is proposed as proved on a simple example it enables to avoid convergence problems which appear in precisely defined cases especially when there are many rules or when the variation domain of the inputs is not centred around zero gradient descent is tested for the approximation of a specially built one input one output analytical function including a discontinuity and a high curvature point and for the approximation of two input functions test and theoretical results are consistent and show that the proposed method is more efficient when the stated conditions are verified

robust h sub spl infin performance for linear delay differential systems with time varying uncertainties the present paper concerns robust h spl infin performance for linear delay differential systems which involve an uncertain time delay and time varying norm bounded parameter uncertainties based on the lyapunov functional a simple criterion is proposed which assures the pseudo quadratic stability as a well as an h sub spl infin norm bound the criterion is given in the form of a linear matrix inequality which is affine or convex in additional scalar parameters a simple criterion is presented to evaluate the extent of the performance robustness

invariance and stability of fuzzy systems the elaboration of a stability theory of fuzzy systems is fully justified by the use in a variety of practical situations of fuzzy controllers 11 27 28 however such a theory may be founded upon ideas that arise from a historical study of dynamical systems theory during the last quarter of the nineteenth century the study of ordinary differential equations underwent some rather radical changes prior to this period the major emphasis in the subject had been on the methods of solving equations it was during this period that peano 20 gave a rigorous proof of the existence theorem for solutions of ordinary differential equations during the same period lipschitz 151 and picard 22 showed that the method of successive approximations led to a proof of the existence and the uniqueness of solutions to the initial value problem these developments represent the dhuement of the attempts to solve differential equations as the works of peano lipschitz and picard were finishing one chapter in the book of differential equations another was being initiated with the research of liapunov 141 and poincare 23 this new chapter was based on an entirely different approach where one did not attempt to compute the solutions rather one tried to exploit their topological properties poincart in his famous m moire 23 was the first to look at an ordinary differential equation from the point of view of the geometry of the trajectories thereby creating the topological theory of ordinary differential equations almost at the same time the stability theory created by liapunov 141 although heavily quantitative in its methods stressed the importance of some topological features of ordinary differential equations during the 50 years following liapunov and poincare many important advances were made it is with the works of birkhoff 4 nemytskii and stepanov 191 and smale 26 that researchers realized that the essence of this theory was based on the notion of dynamical system based on liapunov s original works classical stability theory is concerned with the equilibrium points of the system and the dynamical

a self adaptive neural fuzzy network with group based symbiotic evolution and its prediction applications in this paper we propose a self adaptive neural fuzzy network with group based symbiotic evolution sanfn gse method a self adaptive learning algorithm consists of two major components first a self clustering algorithm sca identifies a parsimonious internal structure an internal structure is said to be parsimonious in the sense that the number of clusters fuzzy rules is equal to the true number of clusters in a given training data set the proposed sca is an online method and is a distance based connectionist clustering method unlike the traditional cluster techniques that only consider the total variation to updates the only one mean and deviation the proposed sca method considers the variation of each dimension for the input data second a group based symbiotic evolution learning gse method is used to adjust the parameters for the desired outputs the gse method is different from traditional gas genetic algorithms with each chromosome in the gse method representing a fuzzy system moreover in the gse method there are several groups in the population each group represents a set of the chromosomes that belong to a cluster computing by the sca in this paper we used numerical time series examples one step ahead prediction mackey glass chaotic time series and sunspot number forecasting to evaluate the proposed sanfn gse model the performance of the sanfn gse model compares excellently with other existing models in our time series simulations

optimal design of fuzzy sliding mode control a comparative study abstract the fuzzy logic controller is widely used in many control applications the advantages of using fuzzy logic controller are that the fuzzy logic controller can extract the control strategy from experts also the linguistic control rules of fuzzy controller are fit for human s thought however a primary drawback of the fuzzy logic controller is that the linguistic control rules are hard to generate it also requires knowledge and experience of human experts another drawback is the stability and robustness of the fuzzy control system are hard to check to achieve the stability and robustness properties of a fuzzy control system the fuzzy sliding mode control technique is proposed in the spirit of fuzzy control and sliding mode control strategy to simplify the design procedure of fuzzy sliding mode control rules two design procedures that is taguchi s method and the genetic algorithms are applied the controller design of a third order nonlinear oscillation system is illustrated as a study case comparisons between these two design procedures are also given

gensofnn a generic self organizing fuzzy neural network existing neural fuzzy neuro fuzzy networks proposed in the literature can be broadly classified into two groups the first group is essentially fuzzy systems with self tuning capabilities and requires an initial rule base to be specified prior to training the second group of neural fuzzy networks on the other hand is able to automatically formulate the fuzzy rules from the numerical training data no initial rule base needs to be specified prior to training a cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters however most existing neural fuzzy systems whether they belong to the first or second group encountered one or more of the following major problems they are 1 inconsistent rule base 2 heuristically defined node operations 3 susceptibility to noisy training data and the stability plasticity dilemma and 4 needs for prior knowledge such as the number of clusters to be computed hence a novel neural fuzzy system that is immune to the above mentioned deficiencies is proposed in this paper this new neural fuzzy system is named the generic self organizing fuzzy neural network gensofnn the gensofnn network has strong noise tolerance capability by employing a new clustering technique known as discrete incremental clustering dic the fuzzy rule base of the gensofnn network is consistent and compact as gensofnn has built in mechanisms to identify and prune redundant and or obsolete rules extensive simulations were conducted using the proposed gensofnn network and its performance is encouraging when benchmarked against other neural and neural fuzzy systems

maximum rank of a legendrian web abstract we propose the legendrian web in a contact three manifold as a second order generalization of the planar web an abelian relation for a legendrian web is analogously defined as an additive equation among the first integrals of its foliations for a class of legendrian d webs defined by simple second order ode s we give an algebraic construction of d d 1 d 2 2 d 3 6 linearly independent abelian relations we then employ the method of local differential analysis and the theory of linear differential systems to show that d is the maximum rank of a legendrian d web in the complex analytic category we give a possible projective geometric interpretation of d as an analogue of castelnuovo bound for degree 2 d surfaces in the 3 quadric q 3 p 4 via the duality between p 3 and q 3 associated with the rank two complex simple lie group sp 2 c the legendrian 3 webs of maximum rank three are analytically characterized and their explicit local normal forms are found for an application we give an alternative characterization of a darboux super integrable metric as a two dimensional riemannian metric g which admits a mate metric g such that a legendrian 3 web naturally associated with the geodesic foliations of the pair g has maximum rank

fuzzy control theory the linear case abstract a linear fuzzy proportional integral pi controller with one input and one output is defined in terms of piecewise linear membership functions for fuzzification control rules and defuzzification algorithm it is shown that a linear fuzzy controller is not equivalent to a linear non fuzzy pi controller if the rules are evaluated using the zadeh probability or lukasiewicz fuzzy logic alone however the linear fuzzy controller is precisely equivalent to a linear non fuzzy pi controller if mixed fuzzy logic is used to evaluate the control rules when the fuzzy logics used are selected with due regard to prior associations implied by the control rule operands themselves this finding has relevance to the selection of fuzzy logics in fuzzy expert systems and for fuzzy logics in general

aks hierarchy and bi hamiltonian geometry of gelfand zakharevich type a bi hamiltonian system is a system of differential equations which can be written in hamiltonian form in two distinct ways the applications of gelfand zakharevich bi hamiltonian structure which is an extension of a poisson nijenhuis structure on phase space has been extensively explored by falqui magri and pedroni in the context of separation of variables it is well known that the integrable hamiltonian systems defined by the adler kostant symes aks scheme contains bi hamiltonian structure in this paper we unveil the connection between adler kostant symes formalism applied to loop algebra and the gelfand zakharevich bi hamiltonian structure by superposition the results of fordy and kulish in the aks scheme we also study the commuting flows of the aks hierachy and its connection to the zakharov shabat hierarchy

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

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

stability analysis of control system having pd type of fuzzy controller stability of a control system having pd type of fuzzy controller a two input and single output controller is analyzed in this paper using yakubovich s method in this analysis the controller is treated as a two input and two output controller and the nonlinearity of the controller is characterized as the sector condition absolute stability conditions are derived for the control system as three conditions two are conditions for either one of control modes p or d is independently operating the third is the condition for two modes are simultaneously active the former two conditions are nothing but popov s conditions for two siso systems a new graphical method is proposed to solve the latter condition this method is explained illustratively using an example and the results obtained are compared numerically with those by other graphical methods as well as simulation results

adaptive asymmetric fuzzy neural network controller design via network structuring adaptation this paper proposes a self structuring fuzzy neural network sfnn using asymmetric gaussian membership functions in the structure and parameter learning phases an adaptive self structuring asymmetric fuzzy neural network control asafnc system which consists of an sfnn controller and a robust controller is proposed the sfnn controller uses an sfnn with structure and parameter learning phases to online mimic an ideal controller simultaneously the structure learning phase consists of the growing and pruning algorithms of fuzzy rules to achieve an optimal network structure and the parameter learning phase adjusts the interconnection weights of neural network to achieve favorable approximation performance the robust controller is designed to compensate for the modeling error between the sfnn controller and the ideal controller an online training methodology is developed in the lyapunov sense and thus the stability of the closed loop control system can be guaranteed finally the proposed asafnc system is applied to a second order chaotic dynamics system the simulation results show that the proposed asafnc can achieve favorable tracking performance

singularities of bi hamiltonian systems we study the relationship between singularities of bi hamiltonian systems and algebraic properties of compatible poisson brackets as the main tool we introduce the notion of linearization of a poisson pencil from the algebraic viewpoint a linearized poisson pencil can be understood as a lie algebra with a fixed 2 cocycle in terms of such linearizations we give a criterion for non degeneracy of singular points of bi hamiltonian systems and describe their types

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

stability analysis and stabilization of fuzzy state space models abstract a new stability test method for linguistic fuzzy state space models is proposed in this paper this method allows the determination of stability of fuzzy models by applying the lyapunov function to each rule a gradient based algorithm is suggested to simplify the stability tests using this algorithm the lyapunov equation can be updated towards the direction where the stability can be determined more correctly an additional gradient based stabilizing algorithm is also derived which allows a systematic approach to find stabilizing controls by updating the lyapunov equations towards the direction where unstable eigenvalues are decreased examples demonstrate the convenience of the stability test and the two suggested gradient based algorithms

an approach to the analysis of fuzzy systems this paper deals with a formal description of ill defined processes fuzzy systems by the use of fuzzy relational equations it is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory some equivalence between these two kinds of description is presented basic problems of fuzzy systems e g identification prediction sensitivity and stability are shown and numerical algorithms are given indices of each method are introduced especially the degree of fuzziness the sensitivity index which makes it possible to express the quality of each of them

webs veronese curves and bihamiltonian systems abstract we define a special kind of multidimensional webs connected with the veronese curve for these webs the foliations in question depend not on a discrete parameter but on the point on a projective line for each bihamiltonian system of odd dimension in general position we construct such a web and show how to reconstruct the original bihamiltonian system based on these data

piecewise linear identification of non linear systems methods of identifying a series of piecewise linear models which approximate to a non linear system over some operating range are investigated spatial linear models and models with signal dependent parameters are considered

structure and control of piecewise linear systems elementary algebraic topology is used in the study of the structure and optimal control of piecewise linear and non linear systems

robust stability analysis of fuzzy control systems abstract robust stability of fuzzy control systems is studied through the popov lyapunov approach first we transform a fuzzy control system into a lur e system with uncertainties or nonlinearities second the lyapunov s direct method is used to guarantee the stability of the perturbed lur e system and then a robustness measurement which gives the bound on allowable uncertainties or nonlinearities is derived also if the bound of the uncertainties nonlinearities of the system is known we can find an estimated region of asymptotic stability in phase space a nonlinear numerical example and a magnetic bearing experiment demonstrating the feasibility of the method are illustrated

simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms this paper examines the applicability of genetic algorithms ga s in the simultaneous design of membership functions and rule sets for fuzzy logic controllers previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions however the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology when ga s have been used to develop both it has been done serially e g design the membership functions and then use them in the design of the rule set this however means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently ga s are fully capable of creating complete fuzzy controllers given the equations of motion of the system eliminating the need for human input in the design loop this new method has been applied to two problems a cart controller and a truck controller beyond the development of these controllers we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules

a new kernel based fuzzy clustering approach support vector clustering with cell growing in this paper the support vector clustering is extended to an adaptive cell growing model which maps data points to a high dimensional feature space through a desired kernel function this generalized model is called multiple spheres support vector clustering which essentially identifies dense regions in the original space by finding their corresponding spheres with minimal radius in the feature space a multisphere clustering algorithm based on adaptive cluster cell growing method is developed whereby it is possible to obtain the grade of memberships as well as cluster prototypes in partition the effectiveness of the proposed algorithm is demonstrated for the problem of arbitrary cluster shapes and for prototype identification in an actual application to a handwritten digit data set

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

constructive theory for fuzzy systems abstract in this paper a constructive theory is developed to establish the fact that we can build a fuzzy system to approximate any continuous function on a compact set within a prescribed error bound based on the theory an algorithm is described that can actually construct a near minimum fuzzy system for a given function to a desired accuracy

on a class of integrable systems of monge ampere type we investigate a class of multi dimensional two component systems of monge ampere type that can be viewed as generalisations of heavenly type equations appearing in a self dual ricci flat geometry based on the jordan kronecker theory of the skew symmetric matrix pencils a classification of normal forms of such systems is obtained all two component systems of monge ampere type turn out to be integrable and can be represented as the commutativity conditions of parameter dependent vector fields geometrically systems of monge ampere type are associated with linear sections of the grassmannians this leads to an invariant differential geometric characterisation of the monge ampere property

recursion operators and bi hamiltonian structures in multidimensions ii the algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied in particular the factorization of certain operators called recursion operators establishes the bi hamiltonian nature of all these equations recently we have presented the recursion operator and the bi hamiltonian formulation of the kadomtsev petviashvili equation a two spatial dimensional analogue of the korteweg devries equation here we present the general theory associated with recursion operators for bi hamiltonian equations in two spatial and one temporal dimensions as an application we show that general classes of equations which include the kadomtsev petviashvili and the davey stewartson equations possess infinitely many commuting symmetries and infinitely many constants of motion in involution under two distinct poisson brackets furthermore we show that the relevant recursion operators naturally follow from the underlying isospectral eigenvalue problems

efficient self evolving evolutionary learning for neurofuzzy inference systems this study proposes an efficient self evolving evolutionary learning algorithm seela for neurofuzzy inference systems nfiss the major feature of the proposed seela is that it is based on evolutionary algorithms that can determine the number of fuzzy rules and adjust the nfis parameters the seela consists of structure learning and parameter learning the structure learning attempts to determine the number of fuzzy rules a subgroup symbiotic evolution is adopted to yield several variable fuzzy systems and an elite based structure strategy is adopted to find a suitable number of fuzzy rules for solving a problem the parameter learning is to adjust parameters of the nfis it is a hybrid evolutionary algorithm of cooperative particle swarm optimization cpso and cultural algorithm called cultural cpso ccpso the ccpso which uses cooperative behavior among multiple swarms can increase the global search capacity using the belief space experimental results demonstrate that the proposed method performs well in predicting time series and solving nonlinear control problems

long term learning for type 2 neural fuzzy systems abstract the development of a new long term learning framework for interval valued neural fuzzy systems is presented for the first time in this article the need for such a framework is twofold to address continuous batch learning of data sets and to take advantage the extra degree of freedom that type 2 fuzzy logic systems offer for better model predictive ability the presented long term learning framework uses principles of granular computing grc to capture information knowledge from raw data in the form of interval valued sets in order to build a computational mechanism that has the ability to adapt to new information in an additive and long term learning fashion the latter is to accommodate new input output mappings and new classes of data without significantly disturbing existing input output mappings therefore maintaining existing performance while creating and integrating new knowledge rules this is achieved via an iterative algorithmic process which involves a two step operation iterative rule base growth capturing new knowledge and iterative rule base pruning removing redundant knowledge for type 2 rules the two step operation helps create a growing but sustainable model structure the performance of the proposed system is demonstrated using a number of well known non linear benchmark functions as well as a highly nonlinear multivariate real industrial case study simulation results show that the performance of the original model structure is maintained and it is comparable to the updated model s performance following the incremental learning routine the study is concluded by evaluating the performance of the proposed framework in frequent and consecutive model updates where the balance between model accuracy and complexity is further assessed

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm

linguistic stability analysis of fuzzy closed loop control systems abstract a linguistic analysis method for fuzzy closed loop control systems where both fuzzy controller and controlled processes are described by linguistic rules is proposed in this paper first a linguistic relation model of a fuzzy closed loop control system is deduced from the linguistic rule models of the fuzzy controller and the controlled process then the linguistic stability of the fuzzy closed loop system is discussed by a linguistic relation matrix finally an example is given to illustrate the proposed method