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

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

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

adjoint active surfaces for localization and imaging this paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries as opposed to imaging the entirety of the volume active surfaces are used to directly reconstruct the shape of the region of interest we describe the procedure for finding the optimal surface which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface in doing so we introduce the adjoint model to compute the sensitivity and in this respect the method shares common ground with several other disciplines such as optimal control finally we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar helmholtz equation potential applications include electromagnetics acoustics geophysics nondestructive testing and medical imaging

on the stability of fuzzy systems studies the global asymptotic stability of a class of fuzzy systems it demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant lti switching systems a necessary and sufficient condition for the stability of such systems are given and it is shown that under the sufficient condition a common lyapunov function exists for the lti subsystems a particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic lyapunov function a constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided

on the generalization of single input rule modules connected type fuzzy reasoning method yubazaki have proposed a ldquosingle input rule modules connected type fuzzy reasoning method sirms method rdquo in which its final output is obtained by summarizing the product of importance degree and inference result from single input fuzzy rule modules this paper proposes a ldquofunctional type sirms method rdquo which is an extended version of the sirms method and clarifies the relationship between the takagi sugeno t s reasoning method and the functional type sirms method the functional type sirms method can be shown to be transformed to the t s reasoning method but generally the conversion to functional type sirms method from the t s reasoning method is impossible it is shown however that the t s reasoning method can be transformed to the functional type sirms method when the t s reasoning method fills some conditions for this reason it is shown that the functional type sirms method is the subset of the t s reasoning method

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

fuzzy controls under various fuzzy reasoning methods abstract a fuzzy logic controller consists of linguistic control rules tied together by means of two concepts fuzzy implications and a compositional rule of inference most of the existing fuzzy logic controllers are based on the approximate reasoning method due to mamdani this paper introduces other fuzzy implications such as the arithmetic rule and maximin rule for linguistic control rules and compares control results for a plant model with first order delay under various approximate reasoning methods moreover control results are compared when the widths of fuzzy sets of linguistic control rules are changed

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 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

decentralized techniques for the analysis and control of takagi sugeno fuzzy systems this paper discusses decentralized parallel distributed compensator design for takagi sugeno fuzzy systems the fuzzy system is viewed as an interconnection of subsystems some of which are strongly connected while others being weakly connected the necessary theory is developed so that one can associate this fuzzy system with another one in a higher dimensional space the so called expanded space design decentralized parallel distributed compensators in the expanded space then contract the solution for implementation on the original fuzzy system in this respect connective stability of the open loop and closed loop of the interconnected system is analyzed via the concepts of vector lyapunov functions and m matrices different lyapunov functions generate different results for the discrete time fuzzy system quadratic lyapunov generating the superior of the two following a similar approach stabilization of the closed loop fuzzy system using local parallel distributed compensators is investigated

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

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

sirms connected fuzzy inference method adopting emphasis and suppression the single input rule modules connected fuzzy inference method sirms method can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods however the inference results obtained by the sirms method is generally simple compared with those of the conventional fuzzy inference methods for example the sirms method may be not equivalent to the product sum gravity method and fuzzy singleton type inference method if the fuzzy sets of the antecedent parts are limited to normal fuzzy sets in this paper we propose a fuzzy singleton type sirms method which weights the rules of the sirms method in order to solve the above problem this paper also clarifies the property of the fuzzy singleton type sirms method from the view point of equivalence and monotonicity moreover the fuzzy singleton type sirms method is shown to be superior to the conventional sirms method by applying to a medical diagnosis system

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

coupled complex adjoint sensitivities for frequency domain fluorescence tomography theory and vectorized implementation we present a computationally efficient and accurate adjoint method for calculating coupled sensitivities of complex frequency domain excitation and emission fluence to any underlying optical parameters in highly scattering media the method is shown to be general and accurate novel vectorized implementations for finite element global matrix assembly and adjoint sensitivity calculations are shown to speed up calculations by orders of magnitude over traditional loop implementations thereby making least squares approaches to fluorescence tomography computationally practical

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

overlapping decompositions expansions contractions and stability of hybrid systems inclusion and extension principles are defined and studied for hybrid systems the controller design problem for hybrid systems is then considered within the framework of the extension principle it is shown that if the extension principle is used then any controller designed in the expanded spaces is contractible to the original spaces for implementation the stability of hybrid systems is also considered a number of definitions of stability for hybrid systems are given and it is shown that if a system which includes another system is stable then the included system is also stable furthermore it is shown that if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system decentralized controller design with overlapping decompositions is also discussed within the framework of extension an example is provided to illustrate the proposed approach

realization of nonlinear and linear pid controls using simplified indirect fuzzy inference method abstract in this paper we propose a more practical method for realizing nonlinear and linear pid controls using fuzzy inference methods than previous ones this proposed method is based on the fact that not only nonlinear but also linear pid control can be easily realized by applying the simplified indirect fuzzy inference method for fuzzy control to few fuzzy control rules with a simple structure therefore we first show that nonlinear pid control which is based on a conventional pid controller can be realized using this proposed method secondly we show that linear pid control can also be realized simply by replacing the arctan with the linear membership function in the antecedent part of the fuzzy control rules

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

a comparison of exact and approximate adjoint sensitivities in fluorescence tomography many approaches to fluorescence tomography utilize some form of regularized nonlinear least squares algorithm for data inversion thus requiring repeated computation of the jacobian sensitivity matrix relating changes in observable quantities such as emission fluence to changes in underlying optical parameters such as fluorescence absorption an exact adjoint formulation of these sensitivities comprises three terms reflecting the individual contributions of 1 sensitivities of diffusion and decay coefficients at the emission wavelength 2 sensitivities of diffusion and decay coefficients at the excitation wavelength and 3 sensitivity of the emission source term simplifying linearity assumptions are computationally attractive in that they cause the first and second terms to drop out of the formulation the relative importance of the three terms is thus explored in order to determine the extent to which these approximations introduce error computational experiments show that while the third term of the sensitivity matrix has the largest magnitude the second term becomes increasingly significant as target fluorophore concentration or volume increases image reconstructions from experimental data confirm that neglecting the second term results in overestimation of sensitivities and consequently overestimation of the value and volume of the fluorescent target whereas contributions of the first term are so low that they are probably not worth the additional computational costs

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

sequential stability analysis and observer design for distributed ts fuzzy systems many complex physical systems are the interconnection of lower dimensional subsystems for such systems distributed stability analysis and observer design presents several advantages with respect to centralized approaches such as modularity easier analysis and design and reduced computational complexity applications include distributed process control traffic and communication networks and economic systems in this paper we propose sequential stability analysis and observer design for distributed systems where the subsystems are represented by takagi sugeno ts fuzzy models the analysis and design are done sequentially for the subsystems allowing for the online addition of new subsystems the conditions are formulated as lmis and are therefore easy to solve the approach is illustrated on simulation examples

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

a proposal of sirms dynamically connected fuzzy inference model for plural input fuzzy control single input rule modules sirms dynamically connected fuzzy inference model is proposed for plural input fuzzy control for each input item a sirm is constructed and a dynamic importance degree is defined the dynamic importance degree consists of a base value insuring the role of the input item through a control process and a dynamic value changing with control situations to adjust the dynamic importance degree each dynamic value can be easily tuned based on the local information of current state the model output is obtained by summarizing the products of the dynamic importance degree and the fuzzy inference result of each sirm the controller constructing method for constant value control systems is given and constant value controls of typical first and second order lag plants are tested the simulation results show that by using the proposed mode the reaching time can be reduced by more than 15 without any steady state error overshoot or vibration compared with the sirms fixed importance degree connected fuzzy inference model the proposed model is further successfully applied to stabilization control of an inverted pendulum system including the position control of the cart

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

on the equivalence conditions of fuzzy inference methods part 1 basic concept and definition this paper addresses equivalence of fuzzy inference methods it first presents several well known fuzzy inference methods the product sum gravity method the simplified fuzzy inference method the fuzzy singleton type inference method the single input rule modules connected type fuzzy inference method sirms method and the single input connected fuzzy inference method sic method second three fuzzy inference methods of the product sum gravity method simplified fuzzy inference method and fuzzy singleton type inference method which are all widely used as fuzzy control methods are shown to be equivalent to each other third the equivalence conditions between the sirms method and the sic method known as single input type fuzzy inference method are shown finally it also gives the equivalence conditions between the single input type fuzzy inference methods and the previous three fuzzy inference methods investigating the equivalence among various fuzzy inference methods would help to understand the relationship of those fuzzy inference methods

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

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

lyapunov like stability theorems for continuous time fuzzy control systems the essential characteristics of fuzzy logic control are analysed in this paper the locality of fuzzy control and the interpolation among fuzzy rules may be the most important characteristics of fuzzy control systems based on these two characteristics a new lyapunov like stability analysis approach is developed for both mamdani and takagi sugeno type fuzzy control systems in this approach we apply the theory of generalized dynamical systems and contingent equations thus the method can be used for both model free and model based fuzzy controller designs finally an example is given to illustrate the application of the method

analysis and design of functionally weighted single input rule modules connected fuzzy inference systems the single input rule modules sirms connected fuzzy inference method can efficiently solve the fuzzy rule explosion phenomenon which usually occurs in the multivariable modeling and or control applications however the performance of the sirms connected fuzzy inference system sirm fis is limited due to its simple input output mapping in this paper to further enhance the performance of sirm fis a functionally weighted sirm fis fwsirm fis which adopts multivariable functional weights to measure the important degrees of the sirms is presented then in order to show the fundamental differences of the sirms methods properties of the traditional sirm fis the type 2 sirm fis t2sirm fis the functional sirm fis fsirm fis the sirms model with single variable functional weights sirm fw and fwsirm fis are explored these properties demonstrate that the proposed fwsirm fis has more general and complex input output mapping than the existing sirms methods such properties theoretically guarantee that better performance can be achieved by fwsirm fis furthermore based on the least squares method a novel data driven optimization method is presented for the parameter learning of fwsirm fis it can also be used to optimize the parameters of sirm fis t2sirm fis fsirm fis and sirm fw due to the properties of the least squares method the proposed parameter learning algorithm can overcome the drawbacks of the gradients based parameter learning methods and obtain both smallest training errors and smallest parameters finally to show the effectiveness and superiority of fwsirm fis and the proposed optimization method six examples and detailed comparisons are given simulation results show that fwsirm fis can obtain better performance than the other sirms methods and compared with some well known methods fwsirm fis can achieve similar or better performance but has much less parameters and faster training speed

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

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

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

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

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

a new fuzzy controller for stabilization of parallel type double inverted pendulum system a new fuzzy controller with 6 input items and 1 output item for stabilizing a parallel type double inverted pendulum system is presented based on the single input rule modules sirms dynamically connected fuzzy inference model each input item is assigned with a sirm and a dynamic importance degree the sirms and the dynamic importance degrees are designed such that the angular control of the longer pendulum takes the highest priority over the angular control of the shorter pendulum and the position control of the cart when the angle of the longer pendulum is big by using the sirms and the dynamic importance degrees the priority orders of the three controls are automatically adjusted according to control situations the proposed fuzzy controller has a simple and intuitively understandable structure and executes the three controls entirely in parallel simulation results show that the proposed fuzzy controller can stabilize completely a parallel type double inverted pendulum system within 10 0 s for a wide range of the initial angles of the two pendulums this is the first result for a fuzzy controller to achieve successfully complete stabilization control of a parallel type double inverted pendulum system

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

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

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

a systematic study of fuzzy pid controllers function based evaluation approach a function based evaluation approach is proposed for a systematic study of fuzzy proportional integral derivative pid like controllers this approach is applied for deriving process independent design guidelines from addressing two issues simplicity and nonlinearity to examine the simplicity of fuzzy pid controllers we conclude that direct action controllers exhibit simpler design properties than gain scheduling controllers then we evaluate the inference structures of direct action controllers in five criteria control action composition input coupling gain dependency gain role change and rule parameter growth three types of fuzzy pid controllers using one two and three input inference structures are analyzed the results according to the criteria demonstrate some shortcomings in mamdani s two input controllers for keeping the simplicity feature like a linear pid controller a one input fuzzy pid controller with one to three mapping inference engine is recommended we discuss three evaluation approaches in a nonlinear approximation study function estimation based generalization capability based and nonlinearity variation based approximations the study focuses on the last approach a nonlinearity evaluation is then performed for several one input fuzzy pid controllers based on two measures nonlinearity variation index and linearity approximation index using these quantitative indices one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information from the study we observed that the zadeh mamdani s max min gravity scheme produces the highest score in terms of nonlinearity variations which is superior to other schemes such as mizumoto s product sum gravity and takagi sugeno kang schemes

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

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

fuzzy mixed h 2 h infty optimization based decentralized model reference control and application to piezo driven xy table systems in this paper a decentralized model reference control via fuzzy mixed h2 hinfin optimization design was developed each subsystem contained l linear pulse transfer function systems lptfss the reference model for every lptfs was first designed to shape the response of the ith closed loop subsystem then the h2 norm of the output error i e the difference between the output of the reference model and the system and weighted control input of the jth lptfs was minimized to obtain a control such that smaller energy consumption with bounded tracking error of the jth lptfs was achieved however an output disturbance of the jth lptfs caused by the interactions among the lptfss the interconnections among the subsystems modeling errors and external loads deteriorated system performance or even resulted in instability in this situation the h infin norm of weighted sensitivity between output disturbance and output error of the jth lptfs was minimized to attenuate its effect a nonlinear control based on output error for every lptfs was also established to improve robust performance the stability of the overall system was then verified by lyapunov stability criterion the application to piezo driven xy table system pd xy ts was carried out to confirm the usefulness of the proposed control

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

overlapping vs partitioning in block iteration methods application in large scale system theory abstract the concept of overlapping decomposition in splitting theory is introduced matrix splitting hamiltonian operator splitting and riccati operator splitting are successively considered for the case of block overlapping and are compared with classical corresponding splitting methods based on block partitioning numerical simulations are given overlapping decomposition is shown to succeed where classical partitioning decomposition fails

three dimensional bayesian optical image reconstruction with domain decomposition most current efforts in near infrared optical tomography are effectively limited to two dimensional reconstructions due to the computationally intensive nature of full three dimensional 3 d data inversion previously we described a new computationally efficient and statistically powerful inversion method apprize automatic progressive parameter reducing inverse zonation and estimation the apprize method computes minimum variance estimates of parameter values here spatially variant absorption due to a fluorescent contrast agent and covariance while simultaneously estimating the number of parameters needed as well as the size shape and location of the spatial regions that correspond to those parameters estimates of measurement and model error are explicitly incorporated into the procedure and implicitly regularize the inversion in a physically based manner the optimal estimation of parameters is bounds constrained precluding infeasible values in this paper the apprize method for optical imaging is extended for application to arbitrarily large 3 d domains through the use of domain decomposition the effect of subdomain size on the performance of the method is examined by assessing the sensitivity for identifying 112 randomly located single voxel heterogeneities in 58 3 d domains also investigated are the effects of unmodeled heterogeneity in background optical properties the method is tested on simulated frequency domain photon migration measurements at 100 mhz in order to recover absorption maps owing to fluorescent contrast agent this study provides a new approach for computationally tractable 3 d optical tomography

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

a fuzzy decentralized variable structure tracking control with optimal and improved robustness designs theory and applications to begin with each subsystem of a nonlinear interconnected system was approximated by a weighted combination of l linear pulse transfer function systems lptfss for every nominal lptfs of the mth subsystem a dead beat to its switching surface was first designed the output disturbance of the mth lptfs included the interconnections coming from the other subsystems the approximation error of the mth subsystem and the interactions resulting from the other lptfss in general this output disturbance was not small and contains various frequencies under this circumstances the h sup spl infin norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized in addition an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance although the effect of the output disturbance is attenuated and partially rejected a better performance could be enhanced by a switching control based on the lyapunov redesign in addition the stability of the overall system was verified by lyapunov stability theory the simulations for the lptfss with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control finally the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control

new delay dependent stability criteria for t s fuzzy systems with time varying delay this paper is concerned with the stability problem of uncertain t s fuzzy systems with time varying delay by employing a further improved free weighting matrix approach by taking the relationship among the time varying delay its upper bound and their difference into account some less conservative lmi based delay dependent stability criteria are obtained without ignoring any useful terms in the derivative of lyapunov krasovskii functional finally two numerical examples are given to demonstrate the effectiveness and the merits of the proposed methods

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

improved stability criteria for time varying delayed t s fuzzy systems via delay partitioning approach this paper focuses on the stability analysis for uncertain takagi sugeno t s fuzzy systems with interval time varying delay the uncertainties of system parameter matrices are assumed to be time varying and norm bounded some new lyapunov krasovskii functionals lkfs are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different lyapunov functionals to different segments in the lkfs by employing these lkfs some new delay derivative dependent stability criteria are established for the nominal and uncertain t s fuzzy systems in a convex way these stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay by employing the new delay partitioning approach the obtained stability criteria are stated in terms of linear matrix inequality lmi they are equivalent or less conservative while involving less decision variables than the existing results finally numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results

approximate reasoning on a basis of z number valued if then rules approximate reasoning is about reasoning with imperfect information nowadays a large diversity of approaches to approximate reasoning with fuzzy information and fuzzy type 2 information exists it should be stressed however that real world imperfect information is characterized by combination of fuzzy and probabilistic uncertainties which is referred to as bimodal information in view of this zadeh introduced the concept of a z number regarded as an ordered pair z a b of fuzzy numbers a and b where a is a linguistic value of a variable of interest and b is a linguistic value of probability measure of a playing a role of its reliability unfortunately up to day there is no research on approximate reasoning realized on the basis of if then rules with z number valued antecedents and consequents briefly z rules zadeh addressed this problem as related to an uncharted territory in this paper a new approach is developed to study approximate reasoning with z rules on a basis of linear interpolation we provide an application of the approach to job satisfaction evaluation and to students educational achievement evaluation problems related to psychological and perceptual issues naturally characterized by imperfect information the obtained results show applicability and validity of the proposed approach

discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography part ii for imaging problems in which numerical solutions need to be computed for both the inverse and the underlying forward problems discretization can be a major factor that determines the accuracy of imaging in this work we analyze the effect of discretization on the accuracy of fluorescence diffuse optical tomography we model the forward problem by a pair of diffusion equations at the excitation and emission wavelengths and consider a finite element discretization method for the numerical solution of the forward problem for the inverse problem we use an optimization framework which allows incorporation of a priori information in the form of zeroth and first order tikhonov regularization terms next we convert the inverse problem into a variational problem and use galerkin projection to discretize the inverse problem following the discretization we analyze the error in reconstructed images due to the discretization of the forward and inverse problems and present two theorems which point out the factors that may lead to high error such as the mutual dependence of the forward and inverse problems the number of sources and detectors their configuration and their positions with respect to fluorophore concentration and the formulation of the inverse problem finally we demonstrate the results and implications of our error analysis by numerical experiments in the second part of the paper we apply our results to design novel adaptive discretization algorithms

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

robust stability of discrete systems the objective of this paper is to show how to choose a liapunov function to obtain the best and sometimes exact estimates of the degree of exponential stability for linear time invariant discrete systems the choice is interesting because it is also shown that it provides the largest robustness bounds on non linear time varying perturbations which can be established by either norm like or quadratic liapunov functions by applying the results obtained to large scale systems where the role of perturbations is played by the interconnections among the subsystems the least conservative stability conditions are derived for the overall system which are available in the context of vector liapunov functions and m matrices

decentralized pdc for large scale t s fuzzy systems this paper studies the decentralized stabilization problem for a large scale system the considered large scale system comprises of a number of subsystems and each subsystem is represented by a takagi sugeno t s fuzzy model the interconnection between any two subsystems may be nonlinear and satisfies some matching condition by the concept of parallel distributed compensation pdc the decentralized fuzzy control for each subsystem is synthesized in which the control gain depends on the strength of interconnections maximal number of the fired rules in each subsystem and the common positive matrix p sub i based on lyapunov criterion and riccati inequality some sufficient conditions are derived and the common p sub i is solved by linear matrix inequalities lmi so that the whole closed loop large scale fuzzy system with the synthesized fuzzy control is asymptotically stable finally a numerical example is given to illustrate the control synthesis and its effectiveness

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

on the monotonicity of fuzzy inference methods related to t s inference method yubazaki et al have proposed a single input rule modules connected type fuzzy inference method sirms method whose final output is obtained by combining the products of the importance degrees and the inference results from single input fuzzy rule modules moreover seki et al have proposed a functional type sirms method whose consequent parts are generalized to functions from real numbers it is expected that inference results from the functional type sirms method are monotone if the antecedent parts and the consequent parts of fuzzy rules in the functional type sirms rule modules are monotone however this paper points out that even if consequent parts in the functional type sirms rule modules are monotone the inference results are not necessarily monotone when the antecedent parts are noncomparable fuzzy sets and it clarifies the conditions for the monotonicity of inference results from the functional type sirms method moreover for the takagi sugeno t s inference method the monotonicity condition is clarified in the case of two inputs by using the equivalence relation of fuzzy inference

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

upswing and stabilization control of inverted pendulum system based on the sirms dynamically connected fuzzy inference model abstract a new fuzzy controller is presented based on the single input rule modules sirms dynamically connected fuzzy inference model for upswing and stabilization control of inverted pendulum system the fuzzy controller takes the angle and angular velocity of the pendulum and the position and velocity of the cart as its input items and the driving force as its output item each input item is assigned with a sirm and a dynamic importance degree when the pendulum locates at the pending domain the fuzzy controller becomes an upswing controller by using the saturation feature of the membership functions of the pendulum angle when the pendulum locates at the upright domain the fuzzy controller then becomes a stabilization controller and realizes smoothly the pendulum angular control and the cart position control in parallel by using the sirms and the dynamic importance degrees the fuzzy controller has a simple structure and is easily understandable compared with the other approaches simulation results show that the fuzzy controller can swing up the pendulum from the pending position and then stabilize the whole system in about 3 0 s

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

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