direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

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

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

theory and application of a novel fuzzy pid controller using a simplifier takagi sugeno rule scheme we first present a novel general purpose nonlinear pid controller realized via fuzzy pid control that uses our newly introduced simplified takagi sugeno ts rule scheme analytical structure of the fuzzy pid controller is derived and its structure is analyzed in relation to the linear pid controller the unique features of the fuzzy controller are as follows first the proportional integral and derivative gains constantly vary with the output of the system under control the gain variation leads to a shorter rise time a less overshoot and a smaller settling time as compared to a comparable linear pid controller second the characteristics of the gain variation are determined by the fuzzy rules and can intuitively be designed we have also investigated the local stability of the fuzzy pid control systems as an application demonstration we have developed a fuzzy pid control system to regulate in computer simulation blood pressure in postsurgical patients we have chosen this particular control problem because the studies in the literature have established that in order to achieve satisfactory control results using a nonlinear controller with variable gains is necessary the simulation results show that the fuzzy pid controller significantly outperforms its linear counterpart and is safer and more robust over a wide range of patient condition 2000 published by elsevier

stabilization of takagi sugeno models with non measured premises input to state stability approach abstract this work deals with the observer based output stabilization problem for takagi sugeno models with non measured premises it aims at providing efficient design methods for the controller observer pair with minimal constrained hypothesis on the model non linear functions the main idea is to consider the closed loop and the error dynamic as two interacting subsystems and study them in the input to state stability framework this paper provides also some results about the existence of a stabilizing output feedback for all models of a sub class of takagi sugeno models to illustrate the efficiency of the proposed design procedures illustrative examples and a comparative study with existing results in the literature based on more restrictive hypothesis are presented

multiple dnn identifier for uncertain nonlinear systems based on takagi sugeno inference in nature most systems show nonlinear complex behaviors among other characteristics plants present a high degree of oscillation over time adaptive algorithms used to approximate such difficult behaviors show some important deficiencies many adaptive non parametric methods cannot reconstruct the trajectories of such complex dynamics differential neural networks dnns are no exception when just one dnn is applied to achieve an approximation the identification error may significantly differ from zero a natural trick to overcome this difficulty is to increase the number of neurons or to increase the number of layers another possible suggestion is to define a set of neural networks working together usually in parallel the members of such a set each work on well defined trajectories contained in specific subspaces in which the uncertain system may evolve nevertheless a decision system is required to define the contribution of each dnn in the final identification scheme one of the most successful methodologies for constructing this selector is based on a takagi sugeno ts inference system this paper discusses how to combine the identification properties offered by a continuous neural network and the characteristic decision capabilities of fuzzy methods the selection of which neural network is activated depends on the decision achieved by a ts fuzzy system the convergence of this algorithm is proved using a quadratic lyapunov function a complete description of the learning laws used for the set of dnn identifiers is also obtained the chen circuit and the rabinovich fabrikant system are used to demonstrate the superior performance achieved by this mixed dnn and fuzzy system usually called a neuro fuzzy 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

hierarchical ts fuzzy system and its universal approximation an efficient tool to deal with the rule explosion problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low dimensional systems in this paper a generalized hierarehical tagaki sugeno ts system is built it is shown that the input output i o relationship of this generalized hierarehical system can be represented as one of a standard ts fuzzy system and the system approximation capability is analyzed by taking piecewise linear functions as a bridge by constructive method it is proven that the hierarchical fuzzy systems hfs s can be universal approximators for the given approximation accuracy an estimation formula about the number of the rules needed in the hfs is established finally some simulation examples confirm that the hfs s with smaller size rule base can approximate the given functions with high accuracy the results obtained here provide us with the theoretical basis for various applications of hfs s

positive periodic solutions of functional differential equations with impulses and a parameter by applying the well known leggett williams multiple fixed point theorem this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter

a new proof of an inequality of bohr for hilbert space operators in this note we present a new proof and an extension of the hilbert space operators version of an inequality by bohr

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

inequalities for absolute value operators abstract we present refinements of an inequality which is due to saito and tominaga linear algebra appl 432 2010 3258 3264 and other inequalities for absolute value operators

neural network based approximate reasoning principles and implementation instead of seeking a structure mapping from a fuzzy reasoning system to a neural network this paper is intended to find a functional mapping from a fuzzy logic based algorithm to the network based approach by viewing the given rule base as defining a global linguistic association constrained by fuzzy sets approximate reasoning is implemented here by a backpropagation neural network bnn with the aid of fuzzy set theory by paying particular attention to the generalization capability of the bnn the underlying principles have been examined in detail using two examples a small demonstration at the linguistic level and a more realistic problem of multivariable fuzzy control of blood pressure the simulation results not only indicate the feasibility of the bnn based approach but also reveal some deeper similarities which exist in the two methods which may have some important implications for future studies into fuzzy control in addition this work may be considered as another application example of t

constructing nonlinear variable gain controllers via the takagi sugeno fuzzy control we investigated the analytical structure of the takagi sugeno ts type of fuzzy controllers which was unavailable in the literature the ts fuzzy controllers we studied employ a new and simplified ts control rule scheme in which all the rule consequent use a common function and are proportional to one another greatly reducing the number of parameters needed in the rules other components of the fuzzy controllers are general arbitrary input fuzzy sets any type of fuzzy logic and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case we proved that all these ts fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality we conducted an in depth analysis on a class of nonlinear variable gain proportional derivative pd controllers we present the results to show 1 how to analyze the characteristics of the variable gains in the context of control 2 why the nonlinear variable gain pd controllers can outperform their linear counterpart and 3 how to generate various gain variation characteristics through the manipulation of the rule proportionality

positive periodic solutions of first order singular systems abstract we establish a complete structure for the existence of positive periodic solutions of first order non autonomous singular system u i t a i t u i t b i t f i u t i 1 n the methods employed are fixed point index theorems leray schauder degree and lower and upper solutions method

pragmatical adaptive synchronization new fuzzy model of two different and complex chaotic systems by new adaptive control abstract in this paper 1 a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and 2 a new adaptive approach and a new control lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors by using this new model the numbers of fuzzy rules of chaotic systems can be reduced from 2 n to 2 n and only 2 subsystems are needed where n is the number of nonlinear terms the fuzzy systems become much simpler in addition through the new fuzzy model the new fuzzy systems are much simpler than t s fuzzy systems when nonlinear systems are complicated and can be used to any other kind of application in fuzzy logic control or fuzzy modeling mathieu van der pol system which is called m v system in this paper and quantum cellular neural networks nanosystem which is called q cnn system in this paper are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control lyapunov function the t s fuzzy modeling and traditional adaptive control are also given in appendix b t s fuzzy model of chaotic systems appendix c traditional adaptive method for comparison

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

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

estimating the concentration of optically active constituents of sea water by takagi sugeno models with quadratic rule consequents determining the concentrations of chlorophyll suspended particulate matter and coloured dissolved organic matter in the sea water is basic to support the monitoring of upwelling phenomena algae blooms and changes in the marine ecosystem since these concentrations affect the spectral distribution of the solar light back scattered by the water body their estimation can be computed by using a set of remotely sensed multispectral measurements of the reflected sunlight in this paper the relation between the concentrations of interest and the average subsurface reflectances is modelled by means of a set of second order takagi sugeno ts fuzzy rules unlike first order ts rules which adopt linear functions as consequent second order ts rules exploit quadratic functions thus improving the modelling capability of the rule in the subspace determined by the antecedent first we show how we can build a second order ts model through a simple transformation which allows estimating the consequent parameters using standard linear least squares algorithms and by adopting one of the most used methods proposed in the literature to generate first order ts models then we compare first order and second order ts models against mean square error and interpretability of rules we highlight how second order ts models allow us to achieve better approximation than first order ts models though maintaining interpretability of the rules finally we show how second order ts models perform considerably better the mean square error is lower by two orders of magnitude than the specific implementations of radial basis function networks and multi layer perceptron networks used in previous papers for the same application domain

identification of non linear systems using empirical data and prior knowledge an optimization approach abstract the choice of a parametric model structure in empirical and semi empirical non linear modeling is usually viewed as an important and critical step however it is known that by augmenting the least squares identification criterion with a term that imposes a penalty on the non smoothness of the model an optimal non parametric model can be found explicitly the optimal non parametric model will depend on the particular form of the penalty which can be looked upon as a priori knowledge or the desired properties of the model in this paper these results are extended in several directions i we show how useful types of prior knowledge other than smoothness can be included as a term in the criterion or as a constraint and how this influences the optimal model ii dynamic models and a general prediction error penalty are considered iii we present a practical numerical procedure for the identification of a close to optimal semi parametric model the numerical approach is motivated by the difficulty of deriving the optimal non parametric model if there are complicated constraints or penalty terms in the criterion and finally iv we discuss determination of the appropriate model complexity through selecting weights on the different penalties on the basis of empirical data since the optimal non parametric model is identified using an augmented optimization criterion and all prior knowledge and desired model properties may be specified through the augmented optimization criterion it is the choice of this criterion that is critical in this approach this elevates the empirical and semi empirical modeling problems to a more transparent and engineering friendly level than is achieved by directly specifying a parametric model structure hence our results shed some more light on modern non linear empirical modeling approaches like radial basis functions splines and neural networks in addition to providing a fundamental insight into the role of different kinds of prior knowledge this high level formulation is also attractive from a practical point of view as it lies closer to engineering thinking and less guesswork is required the flexibility and power of this approach are illustrated with a semi realistic simulation example

effective optimization for fuzzy model predictive control this paper addresses the optimization in fuzzy model predictive control when the prediction model is a nonlinear fuzzy model nonconvex time consuming optimization is necessary with no guarantee of finding an optimal solution a possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control i e quadratic programming for long range predictive control however the influence of the linearization error may significantly deteriorate the performance in our approach this is remedied by linearizing the fuzzy model along the predicted input and output trajectories one can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories four different methods for the construction of the optimization problem are proposed making difference between the cases when a single linear model or a set of linear models are used by choosing an appropriate method the user can achieve a desired tradeoff between the control performance and the computational load the proposed techniques have been tested and evaluated using two simulated industrial benchmarks ph control in a continuous stirred tank reactor and a high purity distillation column

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

pid type fuzzy controller and parameters adaptive method abstract the authors of this paper try to analyze the dynamic behavior of the product sum crisp type fuzzy controller revealing that this type of fuzzy controller behaves approximately like a pd controller that may yield steady state error for the control system by relating to the conventional pid control theory we propose a new fuzzy controller structure namely pid type fuzzy controller which retains the characteristics similar to the conventional pid controller in order to improve further the performance of the fuzzy controller we work out a method to tune the parameters of the pid type fuzzy controller on line producing a parameter adaptive fuzzy controller simulation experiments are made to demonstrate the fine performance of these novel fuzzy controller structures

on the bohr inequality of operators abstract this paper is focused on the operator inequalities of the bohr type we will give a new and transparent proof for the operator bohr inequality through an absolute value operator identity show some related operator inequalities by means of 2 2 block operator matrices and finally we will present a generalization of the operator bohr inequality for multiple operators

sufficient conditions on general fuzzy systems as function approximators abstract in a constructive way we have found sufficient conditions under which general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy more importantly we have revealed the underlying mechanism of such function approximation the fuzzy systems can uniformly approximate any polynomials which according to the weierstrass approximation theorem can uniformly approximate any continuous function on a compact domain these findings lead to the following practical results 1 explicit fuzzy rules of fuzzy systems can now be easily obtained according to functions to be approximated and 2 formulas are derived which can calculate the number of input fuzzy sets output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy the number increases as required approximation error decreases and as approximation error approaches zero the number approaches these formulas also reveal that the number is minimal when the maximum number of intersection between adjacent input fuzzy sets is one practical implications of these results will be discussed especially in the context of fuzzy control and fuzzy modeling two examples are provided to demonstrate how to design fuzzy systems to approximate given functions with required approximation accuracy

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

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

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

building a model based fuzzy controller a new form of fuzzy model based controller is introduced the new controller is based on a conventional predictive controller design but utilises a fuzzy relational model the controller is described and compared with existing fuzzy controllers practical advice is given on generating suitable relational models for control purposes and an appropriate identification algorithm is recommended the controller is tested on a liquid level process and its performance compared to another fuzzy model based controller which has been previously reported

positive periodic solutions of second order nonlinear differential systems with two parameters by employing the deimling fixed point index theory we consider a class of second order nonlinear differential systems with two parameters l m r 2 0 0 we show that there exist three nonempty subsets of r 2 0 0 c d 1 and d 2 such that r 2 0 0 c d 1 d 2 and the system has at least two positive periodic solutions for l m d 1 one positive periodic solution for l m c and no positive periodic solutions for l m d 2 meanwhile we find two straight lines l 1 and l 2 such that c lies between l 1 and l 2

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

adaptive fuzzy sliding mode control of nonlinear system in this paper the fuzzy approximator and sliding mode control smc scheme are considered we propose two methods of adaptive smc schemes that the fuzzy logic systems approximators are used to approximate the unknown system functions in designing the smc of nonlinear system in the first method a fuzzy logic system is utilized to approximate the unknown function f of the nonlinear system x sup n f x t b x t u and the robust adaptive law is proposed to reduce the approximation errors between the true nonlinear functions and fuzzy approximators in the second method two fuzzy logic systems are utilized to approximate the f and b respectively and the control law which is robust to approximation error is also designed the stabilities of proposed control schemes are proved and these schemes are applied to an inverted pendulum system the comparisons between the proposed control schemes are shown in simulations

regular paper the takagi sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers takagi sugeno ts for short fuzzy controllers have been used and treated as black box controllers and there exists no explicit structure of any ts fuzzy controller in the literature in this paper we investigate the analytical structure of the ts fuzzy controllers that use our newly introduced simplified ts control rule scheme our scheme requires that all the rule consequent employ a common linear function and be proportional to one another the scheme drastically reduces the number of adjustable parameters required by the original ts rule scheme product fuzzy logic and was employed in the rule antecedents we theoretically proved that the ts controllers using the simplified rule scheme were nonlinear variable gain controllers the proportionality of the rule consequent parameterized the gain variation characteristics as special cases the ts controllers with three or two input variables and the simplified linear rule consequent were nonlinear variable gain pid pi or pd controllers as an illustration we mathematically analyzed the nonlinear variable gain pi controllers and revealed that the gain variation empowered the controllers to outperform their linear counterparts stability of the nonlinear pi control systems was also addressed a practical example is given to show how to achieve the desired characteristics of the gain variation by properly designing the simplified rules

characterization of equality in a generalized dunkl williams inequality abstract we establish a generalization of the dunkl williams inequality and its inverse in the framework of hilbert c modules and characterize the equality case as applications we get some new results and some known results due to j e pecaric and r rajic the dunkl williams equality in pre hilbert c modules linear algebra appl 425 1 2007 16 25

control of ph processes using fuzzy modeling of titration curve abstract model based ph control is a difficult problem due to its inherent nonlinearity and time varying characteristics this is specially the case when the ph regulation of streams consisting hundreds of constituents with varying concentrations is desired the ph process can be modeled by using conservation laws and neutrality condition an alternative to this mechanistic modeling is using nonlinear empirical modeling such as fuzzy modeling this paper proposes a new approach of fuzzy modeling of titration curves which can be used for control purposes the takagi sugeno model was used for the modeling of titration curve two control algorithms which are designed based on the titration curve namely strong acid equivalent sae and multiple model switching and tuning mmst have been used the efficacy of the proposed approach is demonstrated via simulation and experimental study of a ph control system

robust stability constraints for fuzzy model predictive control this paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the takagi sugeno t s type resulting in a stable closed loop control system conditions are given that guarantee closed loop robust asymptotic stability for open loop bounded input bounded output bibo stable processes with an additive l sub 1 norm bounded model uncertainty the idea is closely related to small gain based l sub 1 control theory but due to the time varying approach the resulting robust stability constraints are less conservative therefore the fuzzy model is viewed as a linear time varying system rather than a nonlinear one the goal is to obtain constraints on the control signal and its increment that guarantee robust stability robust global asymptotic stability and offset free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances

kernel shapes of fuzzy sets in fuzzy systems for function approximation the shapes of if part fuzzy sets affect the approximating capability of fuzzy systems in this paper the fuzzy systems with the kernel shaped if part fuzzy sets are built directly from the training data it is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single input single output siso case on the basis of these rates the relationships between the approximating capability and the shapes of if part fuzzy sets are developed for the fuzzy systems furthermore the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions the theoretical results are confirmed from the simulation data in addition the estimations of the uniform approximation rates are extended to the multi input single output miso case

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

fuzzy constrained min max model predictive control based on piecewise lyapunov functions this paper proposes two novel stable fuzzy model predictive controllers based on piecewise lyapunov functions and the min max optimization of a quasi worst case infinite horizon objective function the main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction and thus to obtain the optimal transient control performance which is of great importance in industrial process control moreover in both of these predictive controllers piecewise lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common lyapunov functions it is shown that the asymptotic stability of the resulting closed loop discrete time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities moreover the controller designs of the closed loop control systems with desired decay rate and input constraints are also considered simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

takagi sugeno fuzzy model based indirect adaptive fuzzy observer and controller design this paper proposes the design scheme of the alternative adaptive observer and controller based on the takagi sugeno t s fuzzy model the t s fuzzy modeling and the state feedback control technique are adopted for the simple structure the proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators in addition with the simple adaptive state feedback controller it solves the singularity problem which occurs in the inverse dynamics based on the feedback linearization method using lyapunov theory and lipschitz condition the stability analysis is conducted and the adaptive law is derived the proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance

indirect adaptive fuzzy sliding mode control part i fuzzy switching in this paper by using the concept of sliding mode control design and lyapunov synthesis approach we propose an indirect adaptive fuzzy sliding mode control iafsmc scheme for a class of nonlinear systems in contrast to the existing sliding mode fuzzy control system designs where the sliding mode control law is directly substituted by a fuzzy controller in our approach both the equivalent control term and switching type control term in the sliding mode control law are approximated by fuzzy systems respectively an on line adaptive tuning algorithm for the consequent parameters in the fuzzy rules is also designed the sliding mode based design procedure ensures the stability and robustness of the proposed iafsmc we prove that the proposed adaptive scheme can achieve asymptotically stable tracking of a reference input with a guarantee of the bounded system signals the chattering phenomena in the sliding mode control is attenuated and the steady error is also alleviated simulation studies have shown that the presented adaptive design of fuzzy sliding mode controller performs very well in the presence of an unknown disturbance

adaptive fuzzy controller application to the control of the temperature of a dynamic room in real time this paper presents a direct adaptive fuzzy controller for unknown monotonic nonlinear systems thus not requiring the system model but only a little information about it the plant monotonicity and its delay without any off line pre training the algorithm achieves very high control performance through a three stage algorithm 1 output scale factor 2 adaptation of the fuzzy rule consequents and 3 optimization of the position of the membership functions the design is simple in the sense that both the membership functions and the rule base can be initialized from arbitrary values it can be applied to a large class of monotonic dynamic or static plants due the fact that the system is able to modify its behaviour in real time i e during the control process

a unified real time approximate reasoning approach for use in intelligent control part 1 theoretical development taking account of the fuzzy nature of human decision making processes and real time properties this paper establishes a unified approximate reasoning model based on possibility theory rather than on relational matrix computation both fuzzy and random uncertainties can be coped with in the model in the case of sensor based situations a simpler reasoning scheme is derived by introducing the concepts of matching measures the proposed models may provide another possibility for on line reasoning in real time expert system applications in part 1 the theoretical foundations are provided while in part 2 their application to multivariate blood pressure control is described

bohr s inequalities for hilbert space operators abstract the classical bohr s inequality states that z w 2 p z 2 q w 2 for all z w c and all p q 1 with 1 p 1 q 1 in this paper bohr s inequality is generalized to the context of hilbert space operators for all positive conjugate exponents p q r in particular the parallelogram law is recovered and some other interesting operator inequalities and established

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

existence of positive periodic solutions of nonlinear first order delayed differential equations abstract we consider the existence of positive periodic solutions for the equation u t a t g u t u t b t f u t t where a b c r 0 are periodic functions with 0 a t d t 0 0 b t d t 0 f g c 0 0 and f s 0 for s 0 is a continuous periodic function 0 is a parameter the proofs of our main results are based upon fixed point index theory

a self organizing neural network based fuzzy system abstract a neural network based fuzzy system nnfs is proposed in this paper it is a self organizing neural network which can partition the input spaces in a flexible way based on the distribution of the training data in order to reduce the number of rules without any loss of modeling accuracy associated with the nnfs is a two phase hybrid learning algorithm which utilizes a nearest neighborhood clustering scheme for both structure learning and initial parameters setting and a gradient descent method for fine tuning the parameters of the nnfs by combining the above two methods the learning speed converges much faster than the original back propagation algorithm simulation results suggest that the nnfs has merots of simple structure fast learning speed few fuzzy logic rules and relatively high modeling accuracy finally the nnfs is applied to the construction of the soft sensor for a distillation column

necessary conditions for some typical fuzzy systems as universal approximators abstract we investigate necessary conditions for general single input single output fuzzy systems and a class of typical multiple input single output fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds considering the case where the only available data about the continuous function to be approximated are a finite set of its extrema we have established some necessary conditions for the fuzzy systems to be universal approximators of the function the conditions can be used practically to determine input fuzzy sets output fuzzy sets and fuzzy rules of the fuzzy systems furthermore these necessary conditions provide a basis for insightful analysis of the strengths as well as the limitations of the fuzzy systems the main strength is that only a small number of fuzzy rules may be needed to uniformly approximate continuous functions that have a complicated formulation but a relatively small number of extrema the limitation is that in order to approximate highly oscillatory continuous functions the number of fuzzy rules must be large 1997 elsevier science ltd

general takagi sugeno fuzzy systems with simplified linear rule consequent are universal controllers models and filters abstract takagi sugeno ts fuzzy systems have successfully been employed mainly in a trial and error manner to solve many control and modeling problems but their applications as signal filters remain to be fully explored compared to their nonfuzzy counterparts ts fuzzy controllers and models are difficult to be efficiently constructed because there is a large number of design parameters in the rule consequent the number grows dramatically with the increase of the number of input fuzzy sets and input variables furthermore there exists little published result on relationship between ts fuzzy controllers models filters and their nonfuzzy counterparts in this paper we investigate in relation to some popular nonfuzzy controllers models and filters analytical structure of a general class of multi input single output miso ts fuzzy systems that use arbitrary fuzzy rules with our recently introduced simplified linear rule consequent other components of the fuzzy systems in this study are general arbitrary continuous input fuzzy sets any type of fuzzy logic and and the generalized defuzzifier containing the widely used centroid defuzzifier as a special case we prove that the general miso ts fuzzy systems are 1 nonlinear variable gain controllers when implemented as controllers or 2 nonlinear time varying auto regressive with the extra input arx models when implemented as models or 3 nonlinear infinite impulse response iir or finite impulse response fir filters when implemented as filters furthermore we constructively prove that the general ts fuzzy systems with the simplified linear rule consequent are universal approximators and can approximate any continuous function in closed domain arbitrarily well the practical implication of these results is that these fuzzy systems with much less design parameters are always able to produce solutions to various control modeling and filtering problems we also establish sufficient conditions that can be used to calculate the number of input fuzzy sets and rules needed for achieving prespecified approximation accuracy

fuzzy control as a universal control tool abstract it is known that fuzzy control is a universal control tool because an arbitrary control strategy in particular a control strategy that is in some sense optimal can be obtained in principle by applying a fuzzy control methodology to some set of rules this result has already been proved e g 2 7 20 21 for the case when a plant is described by finitely many parameters and a special type of fuzzy control methodology is used in this paper we prove it for arbitrary plants including plants that are distributed systems i e plants whose state requires infinitely many parameters to describe and arbitrary fuzzy control methodologies we also prove that there exists a universal fuzzy controller that generates an appropriate control from an input description of a plant and the desired objective mathematically we prove that fuzzy systems can approximate arbitrary continuous functionals thus generalizing a known result about continuous functions

modeling ph neutralization processes using fuzzy neural approaches abstract this paper is concerned with the modeling and identification of ph processes via fuzzy neural approaches a simplified fuzzy model acting as an approximate reasoner is used to deduce the model output on the basis of the identified rule base which is derived by using one of the following three network based self organizing algorithms unsupervised self organizing counter propagation network usocpn supervised self organizing counter propagation network ssocpn and self growing adaptive vector quantization sgavq three typical ph processes were treated including a strong acid strong base system a weak acid strong base system and a two output system with buffering taking part in reaction extensive simulations including on line modeling have shown that these nonlinear ph processes can be modeled reasonably well by the present schemes which are simple but efficient

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

a comparative study on sufficient conditions for takagi sugeno fuzzy systems as universal approximators universal approximation is the basis of theoretical research and practical applications of fuzzy systems studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years in this paper linear takagi sugeno ts fuzzy systems that use linear functions of input variables as rule consequent and their special case named simplified fuzzy systems that use fuzzy singletons as rule consequent are investigated on condition that overlapped fuzzy sets are employed new sufficient conditions for simplified fuzzy systems and linear ts fuzzy systems as universal approximators are given respectively then a comparative study on existing sufficient conditions is carried out with numeric examples

design of fuzzy logic controllers based on generalized t operators abstract since zadeh first proposed the basic principle of fuzzy logic controllers in 1968 the min and max operators have been popular in the design of fuzzy logic controllers in this paper the general concept of t operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available then by computer simulations studies are made so as to determine the relations between the various t operators and the performance of a fuzzy logic controller it is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the t operators

approximation theory of fuzzy systems spl minus siso case in this paper the approximation properties of mimo fuzzy systems generated by the product inference are discussed we first give an analysis of fuzzy basic functions fbf s and present several properties of fbf s based on these properties of fbf s we obtain several basic approximation properties of fuzzy systems 1 basic approximation property which reveals the basic approximation mechanism of fuzzy systems 2 uniform approximation bounds which give the uniform approximation bounds between the desired control or decision functions and fuzzy systems 3 uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions and 4 universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect the similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds

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

application of statistical information criteria for optimal fuzzy model construction theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy however constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple a simpler model is not only easily understood but also less likely to overfit the training data even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed few principled approaches exist in the literature due to the lack of a well defined optimality criterion in this paper we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria 1 the akaike information criterion aic 1974 2 the bhansali downham information criterion bdic 1977 and 3 the information criterion of schwarz 1978 and rissanen 1978 sric we then describe a principled approach to explore the fitness complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition svd the role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example

novel determination of differential equation solutions universal approximation method in a conventional approach to numerical computation finite difference and finite element methods are usually implemented to determine the solution of a set of differential equations des this paper presents a novel approach to solve des by applying the universal approximation method through an artificial intelligence utility in a simple way in this proposed method neural network model nnm and fuzzy linguistic model flm are applied as universal approximators for any nonlinear continuous functions with this outstanding capability the solutions of des can be approximated by the appropriate nnm or flm within an arbitrary accuracy the adjustable parameters of such nnm and flm are determined by implementing the optimization algorithm this systematic search yields sub optimal adjustable parameters of nnm and flm with the satisfactory conditions and with the minimum residual errors of the governing equations subject to the constraints of boundary conditions of des the simulation results are investigated for the viability of efficiently determining the solutions of the ordinary and partial nonlinear des

a dunkl williams type inequality for absolute value operators abstract dunkl and williams showed that for any nonzero elements x y in a normed linear space x x x y y 4 x y x y pecaric and rajic gave a refinement and moreover a generalization to operators a b b h such that a b are invertible as follows a a 1 b b 1 2 a 1 p a b 2 q a b 2 a 1 where p q 1 with 1 p 1 q 1 in this note we shall investigate the inequality and also equality conditions under the assumption that the existence of a 1 and b 1 is not required moreover we give a refinement of the equality conditions

hybrid fuzzy modeling of chemical processes fuzzy models have been proved to have the ability of modeling all plants without any priori information however the performance of conventional fuzzy models can be very poor in the case of insufficient training data due to their poor extrapolation capacity in order to overcome this problem a hybrid grey box fuzzy modeling approach is proposed in this paper to combine expert experience local linear models and historical data into a uniform framework it consists of two layers the expert fuzzy model constructed from linguistic information the local linear model and the t s type fuzzy model constructed from data are all put in the first layer layer 2 is a fuzzy decision module that is used to decide which model in the first layer should be employed to make the final prediction the output of the second layer is the output of the hybrid fuzzy model with the help of the linguistic information the poor extrapolation capacity problem caused by sparse training data for conventional fuzzy models can be overcome simulation result for ph neutralization process demonstrates its modeling ability over the linear models the expert fuzzy model and the conventional fuzzy model

representation of digital image by fuzzy neural network a multilayer feedforward fuzzy neural network fnn by which the predetermined fuzzy system can be realized is constructed to express a given two dimensional 2 d digital image it is shown that such a network is universal approximator the fnn approach provides us with the representation model of the 2 d discrete image in noise environment some given fuzzy numbers are employed to describe gray levels of a digital image and the deviation of corrupted image to its noise free one a class of fuzzy rules for removing impulse noise in degraded image are presented the corresponding fnn may work as a filter which improves the performances of median and rank conditioned rank selection filters especially such a filter may to a greatest extent maintain the fine structure of the image under the minimum mean absolute error criterion the membership functions of fuzzy numbers are adaptively adjusted and an optimal fnn for image representation is derived in noise environment simultaneously some real image examples are systemically analyzed to show that the fnn may result in higher quality global restoration

non affine nonlinear adaptive control of decentralized large scale systems using neural networks this paper introduces a new decentralized adaptive neural network controller for a class of large scale nonlinear systems with unknown non affine subsystems and unknown interconnections represented by nonlinear functions a radial basis function neural network is used to represent the controller s structure the stability of the closed loop system is guaranteed through lyapunov stability analysis the effectiveness of the proposed decentralized adaptive controller is illustrated by considering two nonlinear systems a two inverted pendulum and a turbo generator the simulation results verify the merits of the proposed controller

periodic solutions for scalar functional differential equations suf ficient criteria are established f or the existence ofpositive periodic solutions ofscalar f tional differential equations which improve and generalize some related results in the literature the approach is based on the krasnoselskii s fixed point theorem numerical simulations are presented to support the analytical analysis 2005 elsevier ltd all rights reserved msc 34k13 92d25

fuzzy model based predictive control by instantaneous linearization a linearization technique for product sum crisp type fuzzy model and a multistep predictive control strategy for the construction of a model based predictive fuzzy controller is presented in this paper a model based predictive controller is based on a local linear model generated by using the proposed linearization technique that linearizes the product sum crisp type fuzzy process model around the current operating point the control of ph in a continuous stirred tank reactor is chosen as a realistic nonlinear case study for the demonstration of the proposed control algorithm the controller is shown to be capable of controlling the nonlinear processes that operate over a wide range and of providing better overall system performance than the optimal pi controller

non commutative operator bohr inequality abstract it is shown that if a b x are hilbert space operators such that x i for the positive real number and p q 1 with 1 p 1 q 1 then a b 2 p a 2 q b 2 with equality if and only if 1 p a b and a b 2 p a 2 x qx b 2 for every unitarily invariant norm moreover if in addition a b are normal and x is any hilbert schmidt operator then a b 2 x 2 p a 2 x qx b 2 2 with equality if and only if 1 p ax xb