design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

nonquadratic stabilization of continuous t s fuzzy models lmi solution for a local approach this paper is concerned with nonquadratic stabilization design problem for continuous time nonlinear models in the takagi sugeno t s form obtained by sector nonlinearity approach most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function by changing the paradigm of global stabilization for something less restrictive a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper it is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous nonquadratic attempts moreover conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities lmis which can be efficiently solved by convex optimization techniques simulation examples are given to demonstrate the validity and applicability of the proposed approaches

delay dependent robust hbox it h _ infty control for uncertain discrete time fuzzy systems with time varying delays this paper deals with the robust h infin control problem for discrete time takagi sugeno t s fuzzy systems with norm bounded parametric uncertainties and interval time varying delays first based on a new lyapunov functional we present a sufficient condition guaranteeing that the resulting closed loop system is robustly stable and satisfies a prescribed h infin performance level the lyapunov functional used here depends on not only the fuzzy basis function but on the lower and upper bounds of the time varying delay as well second two classes of delay dependent conditions for the existence of the concerned h infin fuzzy controllers are given in terms of relaxed linear matrix inequalities lmis and a desired controller can be designed by using the solutions to these lmis finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

design of a polynomial fuzzy observer controller with sampled output measurements for nonlinear systems considering unmeasurable premise variables in this paper we propose a polynomial fuzzy observer controller for nonlinear systems where the design is achieved through the stability analysis of polynomial fuzzy model based pfmb observer control system the polynomial fuzzy observer estimates the system states using estimated premise variables the estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model the system stability of the pfmb observer control system is analyzed based on the lyapunov stability theory although using estimated premise variables in polynomial fuzzy observer can handle a wider class of nonlinear systems it leads to a significant drawback that the stability conditions obtained are nonconvex matrix decoupling technique is employed to achieve convex stability conditions in the form of sum of squares we further extend the design and analysis to polynomial fuzzy observer controller using a sampled data technique for nonlinear systems where only sampled output measurements are available simulation examples are presented to demonstrate the feasibility and validity of the design and analysis results

robustness properties of k means and trimmed k means abstract the generalized k means method is based on the minimization of the discrepancy between a random variable or a sample of this random variable and a set with k points measured through a penalty function as in the m estimators setting k 1 a penalty function with unbounded derivative naturally leads to nonrobust generalized k means however surprisingly the lack of robustness extends also to the case of bounded that is generalized k means do not inherit the robustness properties of the m estimator from which they came attempting to robustify the generalized k means method the generalized trimmed k means method arises from combining k means idea with a so called impartial trimming procedure in this article study generalized k means and generalized trimmed k means performance from the viewpoint of hampel s robustness criteria that is we investigate the influence function breakdown point and qualitative robustness confirming the superiority provided by the trimming we inc

constructing solutions of hamilton jacobi equations for 2d fields with one component by means of backlund transformations the hamilton jacobi formalism generalized to two dimensional field theories according to lepage s canonical framework is applied to several relativistic real scalar fields e g massless and massive klein gordon sinh and sine gordon liouville and 4 theories the relations between the euler lagrange and the hamilton jacobi equations are discussed in dedonder and weyl s and the corresponding wave fronts are calculated in caratheodory s formulation unlike mechanics one has to impose certain integrability conditions on the velocity fields to guarantee the transversality relations and especially the dynamical equivalence between hamilton jacobi wave fronts and fields of extremals embedded therein backlund transformations play a crucial role in solving the resulting system of coupled nonlinear pdes

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

new stability conditions based on piecewise fuzzy lyapunov functions and tensor product transformations improvements of recent stability conditions for continuous time takagi sugeno t s fuzzy systems are proposed the key idea is to bring together the so called local transformations of membership functions and new piecewise fuzzy lyapunov functions by relying on these special local transformations the associated linear matrix inequalities that are used to prove the system s stability can be relaxed without increasing the number of conditions in addition to enhance the usefulness of the proposed methodology one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives a standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

stabilization of networked stochastic time delay fuzzy systems with data dropout this paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout the plant in the networked control system ncs under consideration is a discrete stochastic time delay nonlinear system represented by a takagi sugeno fuzzy model exponential stability criteria of the ncs are developed by using a common quadratic lyapunov function and a fuzzy lyapunov function respectively a stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software three numerical examples are presented to demonstrate the effectiveness of the proposed methods

robust stabilization of the takagi sugeno fuzzy model via bilinear matrix inequalities quadratic stability has enabled mainly via the linear matrix inequality framework the analysis and design of a nonlinear control system from the local matrices of the system s takagi sugeno t s fuzzy model it is well known however that there exist stable differential inclusions hence t s fuzzy models whose stability is unprovable by a globally quadratic lyapunov function at present literature in the broader area of stability analysis suggests piecewise quadratic stability as a means to avoid such conservatism this paper generalizes the idea and proposes a framework that supports less conservative sufficient conditions for the stability of the t s model by using piecewise quadratic generalized lyapunov functions the advocated approach results in the formulation of the controller synthesis which herein aims for robust stabilization as a problem of bilinear rather than linear matrix inequalities simulation studies which include an algorithm for solution of bilinear matrix inequalities demonstrate the proposed method

an efficient approach for reducing the conservatism of lmi based stability conditions for continuous time t s fuzzy systems this paper deals with reducing the conservatism of stability conditions for continuous time t s fuzzy systems previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions some redundant terms are removed from the problem formulation furthermore more slack matrix variables are introduced to enlarge the design space consequently less conservative stability conditions are obtained finally a well known numerical example is provided to illustrate the effectiveness of the proposed result

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

h_ infty fuzzy control with randomly occurring infinite distributed delays and channel fadings in this paper the h output feedback control problem is investigated for a class of discrete time fuzzy systems with randomly occurring infinite distributed delays and channel fadings a random variable obeying the bernoulli distribution is introduced to account for the probabilistic infinite distributed delays the stochastic rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients the aim of this paper is to design an h output feedback fuzzy controller such that the closed loop takagi sugeno t s fuzzy control system is exponentially mean square stable and the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of desired output feedback controllers ensuring both the exponential mean square stability and the prescribed h performance the cone complementarity linearization algorithm is utilized to cast the controller design problem into a sequential minimization one that is solvable by the semi definite programming method a simulation result is exploited to illustrate the usefulness and effectiveness of the proposed design technique

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

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

stability analysis and design for a class of continuous time fuzzy control systems this paper presents a design method for a class of fuzzy control systems the class of fuzzy systems considered can be represented by the takagi sugeno fuzzy model which is a type of dynamic fuzzy model a constructive algorithm is developed to obtain the stabilizing feedback control law for the system the main contribution of this paper is the development of an equivalent principle that is the design of a fuzzy control system is equivalent to the design of a set of linear time invariant extreme systems thus any design method in linear control system theory can be used to design a fuzzy control system an example is given to illustrate the application of the method

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

h sub spl infin controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions and bilinear matrix inequalities this work presents an h sub spl infin controller design method for fuzzy dynamic systems based on techniques of piecewise smooth lyapunov functions and bilinear matrix inequalities it is shown that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities bmis two examples are given to illustrate the application of the proposed methods

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

h sub spl infin output feedback control of discrete time fuzzy systems with application to chaos control this paper presents an observer based h sub spl infin output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise lyapunov function the basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities lmis that are numerically feasible with commercially available software application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method

constructing a class of solutions for the hamilton jacobi equation in field theory a new approach leading to the formulation of the hamilton jacobi equation for field theories is investigated within the framework of jet bundles and multisymplectic manifolds an algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided the paper also puts into evidence the intrinsic limits of the hamilton jacobi method as an algorithm to determine families of solutions of the field equations showing how the choice of the boundary data is often limited by compatibility conditions

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

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

maximum lq likelihood estimation via the expectation maximization algorithm a robust estimation of mixture models we introduce a maximum lq likelihood estimation mlqe of mixture models using our proposed expectation maximization em algorithm namely the em algorithm with lq likelihood em lq properties of the mlqe obtained from the proposed em lq are studied through simulated mixture model data compared with the maximum likelihood estimation mle which is obtained from the em algorithm the mlqe provides a more robust estimation against outliers for small sample sizes in particular we study the performance of the mlqe in the context of the gross error model where the true model of interest is a mixture of two normal distributions and the contamination component is a third normal distribution with a large variance a numerical comparison between the mlqe and the mle for this gross error model is presented in terms of kullback leibler kl distance and relative efficiency

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

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

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

robust optimal reference tracking design method for stochastic synthetic biology systems t s fuzzy approach at present the development in the nascent field of synthetic gene networks is still difficult most newly created gene networks are nonfunctioning due to intrinsic parameter fluctuations uncertain interactions with unknown molecules and external disturbances of intra and extracellular environments on the host cell how to design a completely new gene network that is to track some desired behaviors under these intrinsic and extrinsic disturbances on the host cell is the most important topic in synthetic biology in this study the intrinsic parameter fluctuations uncertain interactions with unknown molecules and environmental disturbances are modeled into the nonlinear stochastic systems of synthetic gene networks in vivo four design specifications are introduced to guarantee the stochastic synthetic gene network which can achieve robust optimal tracking of a desired reference model in spite of these intrinsic and extrinsic disturbances on the host cell however the robust optimal reference tracking design problem of nonlinear synthetic gene networks is still hard to solve in order to simplify the design procedure of the robust optimal nonlinear stochastic tracking design for synthetic gene networks the takagi sugeno t s fuzzy method is introduced to solve the nonlinear stochastic minimum error tracking design problem hence the robust optimal reference tracking design problem under four design specifications can be solved by the linear matrix inequality lmi constrained optimization method using convex optimization techniques further a simple design procedure is developed for synthetic gene networks to meet the four design specifications to achieve robust optimal reference tracking finally an eigenvalue shifted design method is also proposed as an expedient scheme to improve the stochastic optimal tracking design method of synthetic gene oscillators

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

comments on controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this comment tries to describe a theoretical mistake made in the aforementioned paper g feng ieee trans fuzzy syst vol 11 no 5 pp 605 612 oct 2003 to formulate the inverse of matrices used to construct the piecewise quadratic lyapunov functions derivation of these inverse matrices is the most critical step toward transforming the design constraints into linear matrix inequalities lmis therefore the erroneous formulation essentially affects the validity of the approach and final results unfortunately it seems that there is no simple correction for this problem however some close alternative approaches are suggested by the same authors in their other works

generalized nonquadratic stability of continuous time takagi sugeno models this paper provides generalized nonquadratic stability conditions for continuous time nonlinear models in the takagi sugeno ts form obtained by sector nonlinearity approach should global quadratic stability fail for a given nonlinear model the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear matrix inequalities lmis which are efficiently solved by convex optimization techniques illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

non quadratic local stabilization for continuous time takagi sugeno models this paper is concerned with non quadratic stabilization of continuous time takagi sugeno ts models the well known problem of handling time derivatives of membership functions mfs as to obtain conditions in the form of linear matrix inequalities lmis is overcome by reducing global goals to the estimation of a region of attraction instead of parallel distributed compensation pdc a non pdc control law is proposed according to the non quadratic nature of the lyapunov function examples are provided to show the advantages over the quadratic and some non quadratic approaches

a membership function dependent approach for stability analysis and controller synthesis of takagi sugeno models this paper presents a new approach for stability analysis and controller design of takagi sugeno ts models the analysis considers information derived from existing or induced order relations among the membership functions partitioning of the state space and the use of piecewise lyapunov functions pwlf arise naturally as a consequence of induced order relations conditions under the novel approach can be expressed as linear matrix inequalities lmis facilitating the inclusion of performance design examples are provided to show the advantages over the classical quadratic approach

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

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

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

bayesian repulsive gaussian mixture model we develop a general class of bayesian repulsive gaussian mixture models that encourage well separated clusters aiming at reducing potentially redundant components produced by independent priors f

progressively better estimates of the domain of attraction for nonlinear systems via piecewise takagi sugeno models this paper introduces a novel approach for stability analysis and controller design of nonlinear models both continuous and discrete time based on an exact piecewise takagi sugeno representation which generalizes the sector nonlinearity methodology the motivation behind this work lies on the fact that piecewise induced takagi sugeno representations have smaller variations than single ones covering the whole modeling area thus increasing the chances of finding piecewise solutions for stability analysis or controller synthesis moreover this relaxation is shown to produce progressively better estimations of the domain of attraction via easy to implement algorithms that demand much less computational effort than other recent approaches in the literature examples are provided to highlight the advantages of the contributions over the existing methods

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

a novel approach to reliable output feedback control of fuzzy affine systems with time delays and sensor faults this paper proposes a novel system augmentation approach to the delay dependent reliable piecewise affine mathscr h infty static output feedback control for nonlinear systems with time varying delay and sensor faults in the piecewise markovian lyapunov functional based framework the nonlinear plant is described by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties and the sensor faults are characterized by a markov process specifically by applying a state input augmentation technique the original closed loop system is first reformulated into a descriptor fuzzy affine system based on a new piecewise markovian lyapunov krasovskii functional combined with a wirtinger based integral inequality improved reciprocally convex inequality and s procedure a novel bounded real lemma is then derived for the underlying closed loop system furthermore by taking advantage of the redundancy of descriptor system formulation together with a linearization procedure the piecewise affine controller synthesis is carried out it is shown that the desired piecewise affine controller gains can be attained by solving a linear matrix inequality based optimization problem finally simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach

piecewise fuzzy anti windup dynamic output feedback control of nonlinear processes with amplitude and rate actuator saturations in this paper a novel anti windup dynamic output compensator is developed to deal with the robust h infin output feedback control problem of nonlinear processes with amplitude and rate actuator saturations and external disturbances via fuzzy modeling of nonlinear systems the proposed piecewise fuzzy anti windup dynamic output feedback controller is designed based on piecewise quadratic lyapunov functions it is shown that with sector conditions robust output feedback stabilization of an input constrained nonlinear process can be formulated as a convex optimization problem subject to linear matrix inequalities simulation study on a strongly nonlinear continuously stirred tank reactor cstr benchmark plant is given to show the performance of the proposed anti windup dynamic compensator

existence of solutions for hamiltonian field theories by the hamilton jacobi technique the paper is devoted to prove the existence of a local solution of the hamilton jacobi equation in field theory whence the general solution of the field equations can be obtained the solution is adapted to the choice of the submanifold where the initial data of the field equations are assigned finally a technique to obtain the general solution of the field equations starting from the given initial manifold is deduced

h controller design for affine fuzzy systems based on piecewise lyapunov functions in finite frequency domain this paper studies the problem of state feedback controller design for a class of nonlinear systems described by continuous time affine fuzzy models based on a piecewise continuous lyapunov function combined with s procedure and some matrix decoupling techniques a novel control law is derived in the formulation of linear matrix inequalities lmis in finite frequency domain first a so called finite frequency h performance index is defined which extends the standard h performance then a sufficient condition is derived such that the fuzzy closed loop system satisfies a finite frequency h performance by introducing the s procedure and adding slack variables piecewise controllers are designed to deal with disturbances in the low middle and high frequency domain respectively the proposed piecewise controller design method can get a better disturbance attenuation performance when the frequency ranges of disturbances are known beforehand finally two examples are given to illustrate the effectiveness and superiority of the new results

analysis and design for a class of complex control systems part i fuzzy modelling and identification this paper is the first of two dealing with the analysis and design of a class of complex control systems this part deals with fuzzy modelling and identification the second paper is concerned with fuzzy controller design we believe that these two papers show a way to analyze and design complex control systems using a combination of fuzzy logic and modern control theory the complex systems studied in these two papers can be represented by a fuzzy aggregation of a set of local linear models the identification can be divided into two procedures the first procedure is the identification of the membership functions including the determination of the number of fuzzy rules and the estimation of the parameters in the membership functions the second is the identification of the local linear models including the determination of the structure and the parameters of the local rule maps and the global rule interpolation two examples are used to demonstrate the application of the modelling method

selective hbox scr h _2 and hbox scr h _ infty stabilization of takagi sugeno fuzzy systems this paper presents new results concerning the stability analysis and design of state feedback controllers for continuous time takagi sugeno t s fuzzy systems via fuzzy lyapunov functions the membership functions of the t s fuzzy systems are modeled in a space that is defined by the cartesian product of simplexes called a multisimplex if the time derivatives of the membership functions are bounded the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions linear matrix inequality lmi relaxations that are based on polynomial matrices are provided for stability analysis and controller design extensions for the design of control laws that minimize upper bounds to h2 and h norms are also given the main novelty of this method is that it allows one to synthesize control gains which depends only on some premise variables that are selected by the designer numerical experiments illustrate the flexibility and advantages of the proposed method

weighted fuzzy observer based fault detection approach for discrete time nonlinear systems via piecewise fuzzy lyapunov functions the main focus of this paper is on the analysis and integrated design of mathcal l 2 observer based fault detection fd systems for discrete time nonlinear industrial processes to gain a deeper insight into this fd framework the existence condition is introduced first then an integrated design of mathcal l 2 observer based fd approach is realized by solving the proposed existence condition with the aid of takagi sugeno fuzzy dynamic modeling technique and piecewise fuzzy lyapunov functions most importantly a weighted piecewise fuzzy observer based residual generator is proposed aiming at achieving an optimal integration of residual evaluation and threshold computation into fd systems the core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors in comparison with the standard norm based fuzzy observer based fd methods the proposed scheme may lead to a significant improvement of the fd performance in the end the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant

robust h control of takagi sugeno fuzzy systems with state and input time delays this paper addresses the robust h fuzzy control problem for nonlinear uncertain systems with state and input time delays through takagi sugeno t s fuzzy model approach the delays are assumed to be interval time varying delays and no restriction is imposed on the derivative of time delay based on lyapunov krasoviskii functional method delay dependent sufficient conditions for the existence of an h controller are proposed in linear matrix inequality lmi format illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

information ratios for validating mixture analyses abstract determining the number of components in a mixture of distributions is an important but difficult problem this article introduces a procedure called minimum information ratio estimation and validation mirev which is based on a ratio of fisher information matrices the smallest eigenvalue of the information ratio matrix is used to determine the number of components a measure of uncertainty may be obtained using a bootstrap technique simulations illustrate the effectiveness of the procedure for mixtures of exponential families an expression for the observed information ratio matrix provides insight to the success of the procedure cluster analysis attempts to identify and characterize subpopulations believed to be present in a population a wide variety of methods are available including criterion optimization hierarchical methods and various heuristic methods criterion optimization techniques such as mixture analysis fuzzy clustering and partitioning methods are popular because they

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods

robust estimation in the normal mixture model based on robust clustering summary we introduce a robust estimation procedure that is based on the choice of a representative trimmed subsample through an initial robust clustering procedure and subsequent improvements based on maximum likelihood to obtain the initial trimming we resort to the trimmed k means a simple procedure designed for finding the core of the clusters under appropriate configurations by handling the trimmed data as censored maximum likelihood estimation provides in each step the location and shape of the next trimming data driven restrictions on the parameters requiring that every distribution in the mixture must be sufficiently represented in the initial clustered region allow singularities to be avoided and guarantee the existence of the estimator our analysis includes robustness properties and asymptotic results as well as worked examples

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

stability analysis of polynomial fuzzy models via polynomial fuzzy lyapunov functions in this paper the stability of continuous time polynomial fuzzy models by means of a polynomial generalization of fuzzy lyapunov functions is studied fuzzy lyapunov functions have been fruitfully used in the literature for local analysis of takagi sugeno models a particular class of the polynomial fuzzy ones based on a recent taylor series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space it is shown that a refinement of the polynomial lyapunov function so as to make it share the fuzzy structure of the model proves advantageous conditions thus obtained are tested via available sos software

polynomial fuzzy model based control systems stability analysis via approximated membership functions considering sector nonlinearity of control input this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions in order to address the input nonlinearity the control signal is considered to be bounded by a sector with nonlinear bounds these nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account with the consideration of imperfectly matched membership functions and input nonlinearity the applicability of the pfmb control scheme can be further enhanced to facilitate the stability analysis a general form of approximated membership functions representing the original ones is introduced as a result approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions the sum of squares approach is employed to obtain the stability conditions based on lyapunov stability theory simulation examples are presented to demonstrate the feasibility of the proposed method

approaches to robust filtering design of discrete time fuzzy dynamic systems this paper presents two filter design methods for discrete time fuzzy dynamic systems based on a piecewise quadratic lyapunov function it is shown that the resulting filtering error system is globally stable with guaranteed hinfin or generalized h2 performance and the filter gains can be obtained by solving a set of linear matrix inequalities two simulation examples are also given to illustrate the performance of the proposed approaches

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available

a q parameterized deterministic annealing em algorithm based on nonextensive statistical mechanics we propose a q parameterized deterministic annealing expectation maximization q daem algorithm for parameter estimation motivated by the concept of tsallis entropy that originates from the nonextensive statistical mechanics the q daem algorithm combines the feature of annealing algorithms to reduce initialization sensitivity and that of q em algorithms to achieve fast convergence the q em algorithm is a one parameter generalized em algorithm that has been previously proposed by the authors by interpreting the em algorithm via likelihood lower bound maximization we build the fundamental interconnections among daem q daem and statistical mechanics to illustrate the benefits of using q daem we investigate two applications finite mixture model estimation in data clustering and joint channel estimation and data detection in communication systems where we show that the q daem algorithm achieves superior performance over the em algorithm for both applications