sharp systolic inequalities for reeb flows on the three sphere the systolic ratio of a contact form alpha on the three sphere is the quantity begin aligned rho mathrm sys alpha frac t min alpha 2 mathrm vol s 3 alpha wedge d alpha end aligned where t min alpha is the minimal period of closed reeb orbits on s 3 alpha a zoll contact form is a contact form such that all the orbits of the corresponding reeb flow are closed and have the same period our first main result is that rho mathrm sys le 1 in a neighbourhood of the space of zoll contact forms on s 3 with equality holding precisely at zoll contact forms this implies a particular case of a conjecture of viterbo a local middle dimensional non squeezing theorem and a sharp systolic inequality for finsler metrics on the two sphere which are close to zoll ones our second main result is that rho mathrm sys is unbounded from above on the space of tight contact forms on s 3

diffractive geometric optics for bloch wave packets we study for times of order 1 varepsilon solutions of wave equations which are fancyscript o varepsilon 2 modulations of an varepsilon periodic wave equation the solutions are of slowly varying amplitude type built on bloch plane waves with wavelength of order varepsilon we construct accurate approximate solutions of the three scale wkb type the leading profile is both transported at the group velocity and dispersed by a schrodinger equation given by the quadratic approximation of the bloch dispersion relation at the plane wave a ray average hypothesis of the small divisor type guarantees stability we introduce techniques related to those developed in nonlinear geometric optics which lead to new results even on time scales t fancyscript o 1 a pair of asymptotic solutions yield accurate approximate solutions of oscillatory initial value problems the leading term yields h1 asymptotics when the envelopes are only h1

fuzzy stability criterion of a class of nonlinear systems abstract a fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of lyapunov first a sufficient condition that guarantees stability of a fuzzy system is given in terms of lyapunov s direct method two concepts for stability of fuzzy systems are defined locally stable and globally table second a construction procedure for lyapunov functions is presented finally the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems

analysis of the fuzzy controllability property and stabilization for a class of t s fuzzy models in this paper the controllability property for a class of takagi sugeno t s fuzzy models is analyzed while a fully nonlinear stabilizer is designed in a practical way it is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach the existence of such controllers depends on the fuzzy controllability conditions which are derived in a straightforward way the main advantage of the proposed approach is that the convergence of the closed loop system can be imposed arbitrarily some examples are given in order to illustrate the validity of the method finally the proposed controller is applied on an underactuated system known as pendubot and the results are compared with an stabilizer designed on the basis of lmis

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

sub wavelength plasmonic crystals dispersion relations and effective properties we obtain a convergent power series expansion for the first branch of the dispersion relation for sub wavelength plasmonic crystals consisting of plasmonic rods with frequency dependent dielectric permittivity embedded in a host medium with unit permittivity the expansion parameter is h kd 2pd l where k is the norm of a fixed wavevector d is the period of the crystal and l is the wavelength and the plasma frequency scales inversely to d making the dielectric permittivity in the rods large and negative the expressions for the series coefficients also called dynamic correctors and the radius of convergence in h are explicitly related to the solutions of higher order cell problems and the geometry of the rods within the radius of convergence we are able to compute the dispersion relation and the fields and define dynamic effective properties in a mathematically rigorous manner explicit error estimates show that a good approximation to the true dispersion relation is obtained using only a few terms of the expansion the convergence proof requires the use of properties of the catalan numbers to show that the series coefficients are exponentially bounded in the h 1 sobolev norm

constructing narmax models using armax models this paper outlines how it is possible to decompose a complex non linear modelling problem into a set of simpler linear modelling problems local armax models valid within certain operating regimes are interpolated to construct a global narmax non linear narmax model knowledge of the system behaviour in terms of operating regimes is the primary basis for building such models hence it should not be considered as a pure black box approach but as an approach that utilizes a limited amount of a priori system knowledge it is shown that a large class of non linear systems can be modelled in this way and indicated how to decompose the systems range of operation into operating regimes standard system identification algorithms can be used to identify the narmax model and several aspects of the system identification problem are discussed and illustrated by a simulation example

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures we study dispersive effects of wave propagation in periodic media which can be modelled by adding a fourth order term in the homogenized equation the corresponding fourth order dispersive tensor is called burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion more precisely we consider the case of a two phase composite medium with an eightfold symmetry assumption of the periodicity cell in two space dimensions we obtain upper and lower bound for the dispersive properties along with optimal microgeometries

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

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

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

fuzzy rule based combination of linear and switching state feedback controllers this paper presents a fuzzy rule base combined controller which is a fuzzy rule based combination of linear and switching state feedback controllers for nonlinear systems subject to parameter uncertainties the switching state feedback controller is employed to drive the system states toward the origin when the system state approaches the origin the linear state feedback controller will gradually replace the switching state feedback controller the smooth transition between the linear and switching state feedback controllers is governed by the fuzzy rules by using the fuzzy rule based combination technique the proposed fuzzy rule base combined controller integrates the advantages of both the linear and switching state feedback controllers but eliminates their disadvantages as a result the proposed fuzzy controller provides good performance during the transient period and the chattering effect is removed when the system state approaches the origin stability conditions will be derived to guarantee the system stability furthermore a saturation function is employed to replace the switching component to alleviate the chattering during the transient period by using the proposed fuzzy rule based combination technique the steady state error introduced by the saturation function can be eliminated application examples will be given to show the merits of the proposed approach

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

h output feedback control of fuzzy system models under sampled measurements this paper studies the problem of control for a class of fuzzy system models by using a linear output controller the system under consideration is described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are assumed unmeasurable we develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models a design algorithm for constructing the linear output controller is given a numerical simulation example is given to show the potential of the proposed techniques

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 dynamics on three dimensional strictly convex energy surfaces we show that a hamiltonian flow on a three dimensional strictly convex energy surface s c r4 possesses a global surface of section of disc type it follows in particular that the number of its periodic orbits is either 2 or oc by a recent result of j franks on area preserving homeomorphisms of an open annulus in the plane the construction of this surface of section is based on partial differential equations of cauchy riemann type for maps from punctured riemann surfaces into r x s3 equipped with special almost complex structures

finite energy foliations of tight three spheres and hamiltonian dynamics surfaces of sections are a classical tool in the study of 3 dimensional dynamical systems their use goes back to the work of poincare and birkhoff in the present paper we give a natural generalization of this concept by constructing a system of transversal sections in the complement of finitely many distinguished periodic solutions such a system is established for nondegenerate reeb flows on the tight 3 sphere by means of pseudoholomorphic curves the applications cover the nondegenerate geodesic flows on t1s2 rp3 via its double covering s3 and also nondegenerate hamiltonian systems in ir4 restricted to sphere like energy surfaces of contact type

about the use of fuzzy clustering techniques for fuzzy model identification abstract in this work we present an alternative approach to generate fuzzy rules with a functional consequent associated to the tsk fuzzy model in our case using fuzzy clustering algorithms that look for linear behaviours in the product space of the input output data we analyse different methods to generate the associated fuzzy rules using in some cases multidimensional reference fuzzy sets in the product space of the input variables and in other cases fuzzy sets in each of the different dimensions in any case the rules being generated correspond to a tsk fuzzy model

robust h control of multiple time delay uncertain nonlinear system using fuzzy model and adaptive neural network in this paper a robust control method which combines fuzzy model based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time delay the fuzzy t s model with multiple time delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties and fuzzy model based h control law is designed by means of lmi method a full adaptive rbf neural network is added to the fuzzy h control in order to guarantee the robust stability of the controlled system the effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights centers and widths of the rbf neural network on line and no constraint or matching conditions are required the stability of the designed closed loop system is thus proved the proposed method is applied to a multiple time delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems but has strong robustness against uncertainties and external disturbance

fuzzy network model based fuzzy state controller design the performance of model based controller design relies heavily on the quality and suitability of the utilized process model this contribution proposes a fuzzy network based nonlinear controller design methodology fuzzy networks are a model approach combining high approximation quality with high interpretability the input output i o models commonly used for identification are transformed to fuzzy state space models transferring and adjusting methods from linear state space theory a control concept consisting of a fuzzy state controller and an adaptive set point filter for nonlinear dynamic processes is deduced the capability of the method is demonstrated for a hydraulic drive

a general fuzzy scheme for nonlinear processes with stability analysis abstract in this paper we develop a general fuzzy control scheme for nonlinear processes assuming little knowledge about the dynamics of the controlled process the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation a simple local controller is then designed at each fuzzy locality a fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm by employing a newly developed structure adaptive fuzzy modelling scheme the appropriate fuzzy rule base for the inference mechanism can be extracted stably and efficiently the conditions for the stability of the global controller are rigourously established simulation results are presented to illustrate the effectiveness of the scheme

robust tsk fuzzy modeling for function approximation with outliers the takagi sugeno kang tsk type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications most approaches for modeling tsk fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions besides training data sets algorithms often contain outliers which seriously affect least square error minimization clustering and learning algorithms a robust tsk fuzzy modeling approach is presented in the approach a clustering algorithm termed as robust fuzzy regression agglomeration rfra is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers to obtain a more precision model a robust fine tuning algorithm is then employed various examples are used to verify the effectiveness of the proposed approach from the simulation results the proposed robust tsk fuzzy modeling indeed showed superior performance over other approaches

a hierarchical fuzzy clustering approach to fuzzy modeling abstract this paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy clustering scheme the method consists of a sequence of steps aiming towards developing a takagi sugeno ts fuzzy model of optimal structure where the fuzzy sets in the premise part are of gaussian type starting from an initial ordinary fuzzy partition of the input space the algorithm performs a nearest neighbor search and groups the original input training data into a number of clusters the centers of these clusters are further processed using an optimal fuzzy clustering technique which is based on the weighted fuzzy c means algorithm the resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters which in a next step are fine tuned using the well known gradient descend algorithm the proposed method is successfully applied to three test examples where the produced fuzzy models prove to be very accurate as well as compact in size

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

a type 2 fuzzy c regression clustering algorithm for takagi sugeno system identification and its application in the steel industry this paper proposes a new type 2 fuzzy c regression clustering algorithm for the structure identification phase of takagi sugeno t s systems we present uncertainties with fuzzifier parameter m in order to identify the parameters of interval type 2 fuzzy sets two fuzzifiers m 1 and m 2 are used then by utilizing these two fuzzifiers in a fuzzy c regression clustering algorithm the interval type 2 fuzzy membership functions are generated the proposed model in this paper is an extended version of a type 1 fcrm algorithm 25 which is extended to an interval type 2 fuzzy model the gaussian mixture model is used to create the partition matrix of the fuzzy c regression clustering algorithm finally in order to validate the proposed model several numerical examples are presented the model is tested on a real data set from a steel company in canada our computational results show that our model is more effective for robustness and error reduction than type 1 nfcrm and the multiple regression

pseudoholomorphic curves in symplectizations with applications to the weinstein conjecture in dimension three l in t roduct ion 515 1 1 the weinstein conjecture 515 1 2 the main results 517 1 3 sketch of the proof 522 2 local f redho lm theory 525 2 1 similar i ty principle and consequences 525 2 2 n m as a lmost complex manifold and local fillings 529 2 3 local propert ies of ho lomorphic curves 531 3 bubbl ing off analysis and global fredholm theory 533 3 l grad ien t bounds imply ca bounds 533 3 2 bubbing off analysis of ho lomorphic planes 534 3 3 grad ien t bounds near the boundary 537 4 proof of the main results 544 4 1 set up for a global fredholm theory 544 4 2 bishop s theorem 545 4 3 proof of theorem 5 546 4 4 proof of theorems 8 and 11 547 4 5 uniqueness results for foliations 547 5 appendix 550 5 1 per turbing surfaces 550 5 2 ki l l ing crit ical points of hypersurfaces 552 5 3 adding a thin tube to a sphere 560

stability and the fuzzy controller abstract this paper corrects a part of the main result theorem 1 in buckley fuzzy sets and systems 77 1996 167 173

identification of functional fuzzy models using multidimensional reference fuzzy sets abstract most commonly fuzzy systems for modelling and control use one dimensional orthogonal reference ffuzzy sets such as triangular or trapezoidal ones in this article a new description of functional fuzzy models by fuzzy rules with premises evaluating point affinities is presented this results in multidimensional reference fuzzy sets an algorithm to identify such systems using cluster algorithms is proposed two algorithms the fuzzy c means and the gustafson and kessel algorithm with locally varying distance measures are applied the performance of the identification algorithm is demonstrated by applying it to the identification of two nonlinear systems one of them is a gas furnace described by the well known box jenkins data

delay dependent stabilization for stochastic fuzzy systems with time delays this paper is concerned with the delay dependent stabilization problem for a class of time delay stochastic fuzzy systems the time delays are assumed to appear in both the state and the control input the purpose is the design of a state feedback fuzzy controller such that the resulting closed loop system is asymptotically stable in the mean square a delay dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities lmis by solving these lmis a desired controller can be obtained finally a numerical example is given to demonstrate the effectiveness of the present results

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

a methodology to design stable nonlinear fuzzy control systems the stability of nonlinear systems has to be investigated without making linear approaches in order to do this there are several techniques based on lyapunov s second method for example krasovskii s method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems this method requires the calculation of the jacobian matrix in this paper an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed later this model is used to compute the jacobian matrix of a closed loop fuzzy system next an algorithm to solve the jacobian matrix is proposed the algorithm uses a methodology based on the extension of the state vector the developed algorithm is completely general it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models and it allows the compound of different membership functions in a same model we have developed a matlab s function that implements the improved algorithm together with a series of additional applications for its use the designed software provides complementary functions to facilitate the reading and writing of fuzzy systems as well as an interface that makes possible the use of all the developed functions from the matlab s environment which allows to complement and to extend the possibilities of the matlab s fuzzy logic toolbox an example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented the work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems

a new approach to fuzzy modeling and control of discrete time systems we present a new approach to fuzzy modeling and control of discrete time systems which is based on the formulation of a novel state space representation using the hyperbolic tangent function the new representation designated the hyperbolic model combines the advantages of fuzzy system theory and classical control theory on the one hand the hyperbolic model is easily derived from a set of mamdani type fuzzy rules on the other hand classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of mamdani type fuzzy rules thus this new approach combines the best of two worlds it enables linguistic interpretability of both the model and the controller and guarantees closed loop stability and robustness

t s fuzzy model identification with a gravitational search based hyperplane clustering algorithm in order to improve the performance of the fuzzy clustering algorithm in fuzzy space partition in the identification of the takagi sugeno t s fuzzy model a hyperplane prototype fuzzy clustering model is proposed to solve the clustering objective function which could not be handled by the gradient method as the traditional clustering method fuzzy c means does a newly developed excellent global search method which is the gravitational search algorithm gsa is employed then the gsa based hyperplane clustering algorithm gshpc is proposed and illuminated gshpc is used to partition the fuzzy space and identify premise parameters of the t s fuzzy model and orthogonal least squares is exploited to identify the consequent parameters comparative experiments are designed to verify the validity of the proposed clustering algorithm and the t s fuzzy model identification method and the results show that the new method is effective in describing a complicated nonlinear system with significantly high accuracies compared with approaches in the literature

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

a new approach to robust and non fragile h control for uncertain fuzzy systems this paper investigates the robust h control and non fragile control problems for takagi sugeno t s fuzzy systems with linear fractional parametric uncertainties the robust h control problem is to design a state feedback controller such that the robust stability and a prescribed h performance of the resulting closed loop system is ensured and the non fragile h control problem is to design a state feedback controller with parameter uncertainties based on the linear matrix inequality lmi approach new sufficient conditions for the solvability of the two problems are obtained it is shown that the desired state feedback fuzzy controller can be constructed by solving a set of lmis numerical examples are also provided to demonstrate the effectiveness of the proposed design method

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

stability analysis of the simplest takagi sugeno fuzzy control system using circle criterion in this paper we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest takagi sugeno t s fuzzy control system based on the circle criterion and its graphical interpretation these conditions are significant in graphically designing the simplest t s fuzzy controller in the frequency domain four numerical examples are provided to demonstrate the efficiency of our two frequency domain based conditions furthermore this t s fuzzy controller and the linear proportional controllers are also compared it is concluded that the simplest t s fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances

a descriptor system approach to non fragile h control for uncertain fuzzy neutral systems in this paper the problem of non fragile h control for a class of uncertain takagi sugeno t s fuzzy neutral systems with linear fractional parametric uncertainties is considered the non fragile h control problem is to design a state feedback controller with parameter uncertainties such that the l 2 induced gain of the mapping from the exogenous input to the controlled output is less than some prescribed level based on lyapunov krasovskii functional the descriptor model transformation and lmi approach new sufficient conditions for solvability of this problem are obtained it is shown that by a novel controller design method the desired state feedback fuzzy controller can be constructed by solving a set of lmis and the minimum h disturbance attenuation level can be obtained via using the lmi algorithm mincx finally an illustrative numerical example is provided to demonstrate correctness and effectiveness of the theoretical results

analysis and design of an affine fuzzy system via bilinear matrix inequality a novel analysis and design method for affine fuzzy systems is proposed both continuous time and discrete time cases are considered the quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities bmis two diffeomorphic state transformations one is linear and the other is nonlinear are introduced to convert the plant into more tractable affine form the conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality lmi technique the bias terms of the fuzzy controller are solved simultaneously together with the gains finally the applicability of the suggested method is demonstrated via an example and computer simulation

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

geodesics on s2 and periodic points of annulus homeomorphisms we show that an area preserving homeomorphism of the open or closed annulus which has at least one periodic point must in fact have infinitely many interior periodic points a consequence is the theorem that every smooth riemannian metric ons2 with positive gaussian curvature has infinitely many distinct closed geodesics

a poincare birkhoff theorem for tight reeb flows on s 3 we consider reeb flows on the tight 3 sphere admitting a pair of closed orbits forming a hopf link if the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition then there exist infinitely many periodic trajectories distinguished by their linking numbers with the components of the link this result admits a natural comparison to the poincare birkhoff theorem on area preserving annulus homeomorphisms an analogous theorem holds on so 3 and applies to geodesic flows of finsler metrics on s 2

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

modeling nonlinear dynamic biological systems with human readable fuzzy rules optimized by convergent heterogeneous particle swarm abstract it is an important issue to model the dynamic biological networks from their time course response datasets which is critical to understand the system behaviors this task includes two sub tasks network structure identification and associated parameters estimation in most existing methods the two sub tasks are dealt with step by step which may result in inconsistence between them and hence inaccuracy of the final model another challenge is how to transparently understand the derived model which cannot be achieved by the traditional black box methods a human readable fuzzy rule based model denoted as mopath is developed for the identification of both structure topology and associated parameters simultaneously of a biological network within an optimization framework mopath encodes the fuzzy rules into particles of heterogeneous particle swarm optimization chpso algorithm to generate the optimal model theoretically we demonstrate that the cooperation in chpso can maintain a balance between exploration and exploitation to guarantee the particles converge to stable points which is greatly helpful for finding the optimal model consisting of both the network topology and parameters we demonstrate mopath on two dynamic biological networks and successfully generate a few human readable rules that can well represent the network with high accuracy and good robustness

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

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

on burnett coefficients in periodic media the aim of this work is to demonstrate a curious property of general periodic structures it is well known that the corresponding homogenized matrix is positive definite we calculate here the next order burnett coefficients associated with such structures we prove that these coefficients form a tensor which is negative semidefinite we also provide some examples showing degeneracy in multidimension

a dynamical characterization of universally tight lens spaces we give necessary and sufficient conditions for a closed connected co orientable contact 3 manifold m to be a standard lens space based on assumptions on the reeb flow associated to a defining contact form our methods also provide rational global surfaces of section for non degenerate reeb flows on l p q std with prescribed binding orbits

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

analysis and design of fuzzy control systems using dynamic fuzzy state space models a discrete time fuzzy control system which is composed of a dynamic fuzzy model and a fuzzy state feedback controller is proposed stability of the fuzzy control system is discussed and two sufficient conditions to guarantee the stability of the system are given in terms of uncertain linear system theory an algorithm is developed to check the stability condition the controller design method is divided into two procedures one is to get the state feedback matrix by linear system theory in every local rule map the other is to determine conditions of global stability by using a nonlinear analysis method two examples are used to show the design method

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

a dispersive effective medium for wave propagation in periodic composites the problem of wave propagation through a periodic medium is considered it is assumed that the ratio between the cell size and the shortest wavelength of the initial disturbance is small within this regime an effective medium model of the propagation phenomena is obtained using the bloch expansion the effective medium obtained is shown to be dispersive it is known that a dominant feature of the transient wave train in a periodic medium is that of dispersion it is shown that our model recovers homogenization formally when the cell size approaches zero explicit formula for the constants appearing in the effective medium equation is derived for the case of one dimension the accuracy of the resulting approximation is assessed in numerical simulations

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

cluster centric fuzzy modeling in this study we propose a cluster oriented development of fuzzy models an overall design process is focused on an efficient usage of fuzzy clustering fuzzy c means fcm in particular to form information granules clusters that are used in the construction of the fuzzy model fuzzy models are regarded as mappings from information granules expressed in the input and output spaces this position motivates us to look at the development of the models through the perspective of the construction and efficient usage of information granules this study directly associates fuzzy clustering with fuzzy modeling both in terms of conceptual and algorithmic linkages the augmented fcm method is formed predominantly for modeling purposes so that a balance between the structural content present in the input and output spaces is achieved and this way the performance of the resulting fuzzy model is optimized it is shown that the cluster oriented modeling gives rise to the mamdani like fuzzy rules and a zero order takagi sugeno model under a certain decoding scheme we identify an interesting and direct linkage between the developed fuzzy models and a fundamental idea of encoding decoding or granulation degranulation encountered in processing fuzzy sets and granular computing in general furthermore refinements of zero order fuzzy models are investigated leading to first order fuzzy models with linear functions standing in the conclusions of the rules a series of experiments is reported where we used synthetic and real world data using which an issue of generalization capabilities is elaborated in detail

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

first bloch eigenvalue in high contrast media this paper deals with the asymptotic behavior of the first bloch eigenvalue in a heterogeneous medium with a high contrast y periodic conductivity when the conductivity is bounded in l1 and the constant of the poincare wirtinger weighted by the conductivity is very small with respect to 2 the first bloch eigenvalue converges as 0 to a limit which preserves the second order expansion with respect to the bloch parameter in dimension two the expansion of the limit can be improved until the fourth order under the same hypotheses on the contrary in dimension three a fibers reinforced medium combined with a l1 unbounded conductivity leads us to a discontinuity of the limit first bloch eigenvalue as the bloch parameter tends to zero but remains not orthogonal to the direction of the fibers therefore the high contrast conductivity of the microstructure induces an anomalous effect since for a given low contrast conductivity the first bloch eigenvalue is known to be analytic with respect to the bloch

t s fuzzy model identification based on a novel hyperplane shaped membership function the fuzzy membership function is a crucial factor that may affect the model structure and modeling accuracy although hyperplane shaped clustering hpsc has been widely used in takagi sugeno t s fuzzy model identification there is no well designed membership function in these approaches the commonly used bell shaped gaussian function is actually inappropriate to employ together with hpsc in fuzzy modeling in this paper a hyperplane shaped fuzzy membership function is designed to match hpsc for t s fuzzy model identification for the first time experimental results on several benchmark problems indicate that modeling accuracies have been greatly improved from the original modeling approach by replacing the proposed membership function

stability and stabilizability of fuzzy neural linear control systems this paper discusses stability analysis of fuzzy neural linear fnl control systems which consist of combinations of fuzzy models neural network nn models and linear models the authors consider a relation among the dynamics of nn models those of fuzzy models and those of linear models it is pointed out that the dynamics of linear models and nn models can be perfectly represented by takagi sugeno t s fuzzy models whose consequent parts are described by linear equations in particular the authors present a procedure for representing the dynamics of nn models via t s fuzzy models next the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of lyapunov the stability criteria is reduced to the problem of finding a common lyapunov function for a set of lyapunov inequalities the stability conditions are employed to analyze stability of fnl control systems finally stability analysis for four types of fnl control systems is demonstrated

robust fuzzy logic control of mechanical systems an approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed the approach employs the framework of lyapunov s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances the proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper the large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation a number of fuzzy implementations of the proposed control methodology are provided all implementations guarantee tracking error convergence to within prespecified performance limits an extensive simulation study using a model of a two degree of freedom robot manipulator was conducted fuzzy and non fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods simulation study results indicate a superiority of the proposed control methodology compared to other approaches the study also demonstrates better performance of the fuzzy control implementation compared to its non fuzzy counterpart

designing fuzzy controllers from a variable structures standpoint a procedure is presented for designing fuzzy controllers based upon variable structures techniques three such controllers are presented the fuzzy equivalents of sliding mode controllers saturating controllers and tanh controllers by using an approach based upon variables structures vss techniques the stability of each of these controllers is assured by using a sliding surface the order of the rule base is reduced to size r spl times m where r is the number of inputs and m is the number of fuzzification levels this combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties to illustrate the proposed design procedure fuzzy controllers are designed for a ball and beam system it is demonstrated that in spite of this system being a fourth order unstable system the proposed design procedure results in simple stable fuzzy controllers

homogenization of periodic structures via bloch decomposition in this paper the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered using bloch wave decomposition a new proof of convergence is furnished it sheds new light and offers an alternate way to view the classical results in a natural way this method leads us to work in the fourier space and thus in a framework dual to the one used by l tartar problemes d homogeneisation dans les equations aux derivees partielles cours peccot au college de france 1977 in his method of homogenization further this technique offers a nontraditional way of calculating the homogenized coefficients which is easy to implement in the computer

a characterization of the tight 3 sphere ii recall that every closed oriented connected 3 manifold m admits a contact form we shall give conditions on a periodic orbit p0 of the reeb vector field defined by that allows the construction of an open book decomposition of m p0 into embedded planes asymptotic to p0 such that p0 is the binding orbit of the decomposition it follows that m is the tight 3 sphere as a by product a new dynamical criterion for the tightness of a contact structure is derived in the proof the results extend earlier results 1999 john wiley sons inc

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

approximative fuzzy rules approaches for classification with hybrid ga techniques abstract in this paper the use of different methods from the fuzzy modeling field for classification tasks is evaluated and the potential of their integration in producing better classification results is investigated the methods considered approximative in their nature consider different integrations of techniques with an initial rule generation step and a following rule tuning approach using different evolutionary algorithms we analyse the adaptation of existing techniques in the fuzzy modeling context for the classification problem and the integration of these techniques in order to improve the classifiers performance finally a genetic algorithm ga for translation from approximative rules to similar descriptive ones trying to preserve the accuracy of the approximative classifier is presented the classical iris and cancer data set are used throughout the evaluation process to form a common ground for comparison and performance analysis

a three dimensional fuzzy control methodology for a class of distributed parameter systems the traditional fuzzy set is two dimensional 2 d with one dimension for the universe of discourse of the variable and the other for its membership degree this 2 d fuzzy set is not able to handle the spatial information the traditional fuzzy logic controller flc developed from this 2 d fuzzy set should not be able to control the distributed parameter system that has the tempo spatial nature a three dimensional 3 d fuzzy set is defined to be made of a traditional fuzzy set and an extra dimension for spatial information based on concept of the 3 d fuzzy set a new fuzzy control methodology is proposed to control the distributed parameter system similar to the traditional flc it still consists of fuzzification rule inference and defuzzification operations different to the traditional flc it uses multiple sensors to provide 3 d fuzzy inputs and possesses the inference mechanism with 3 d nature that can fuse these inputs into a so called ldquospatial membership function rdquo thus a simple 2 d rule base can still be used for two obvious advantages one is that rules will not increase as sensors increase for the spatial measurement the other is that computation of this 3 d fuzzy inference can be significantly reduced for real world applications using only a few more sensors the proposed flc is able to process the distributed parameter system with little complexity increased from the traditional flc the 3 d flc is successfully applied to a catalytic packed bed reactor and compared with the traditional flc the results demonstrate its effectiveness to the nonlinear unknown distributed parameter process and its potential to a wide range of engineering applications