h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

effective digital implementation of fuzzy control systems based on approximate discrete time models this paper addresses an effective digital implementation of fuzzy control systems via an intelligent digital redesign idr approach the purpose of idr is to effectively convert an existing continuous time fuzzy controller to an equivalent sampled data fuzzy controller in the sense of the state matching the authors show that under reasonable assumptions the idr based on the exact discrete time models can be reduced to the idr based on the approximate discrete time models the state matching error between the closed loop trajectories is carefully analyzed using the integral quadratic functional approach the estimation of the state matching error is presented using the linear matrix inequality lmi techniques the problem of designing the sampled data fuzzy controller to minimize the estimation as well as to guarantee the stability is formulated and solved as the convex optimization problem with lmi constraints it is also shown that the resulting sampled data fuzzy controller recovers the performance of the continuous time fuzzy controller as the sampling period approaches zero a numerical example is used to demonstrate the effectiveness of the proposed design technique

sampled data h h fault detection and isolation for nonlinear systems in t s form a direct discrete time design methodology for the sampled data fault detection and isolation fdi problem is proposed for a nonlinear system in takagi sugeno form the generalized observer scheme is adopted accompanied by a bank of the sensors number of observers a sufficient condition to find observer and residual gains based on an accessible approximate rather than unavailable exact discrete time model is proposed in terms of matrix inequalities so that it exhibits h h performance and asymptotic stability an algorithm involving a convex optimization is presented using the cone complementary linearization technique we show that the fdi observer ensures modified h h performance and lagrange stability when it is connected to the actual nonlinear system

a stability property of nonlinear sampled data systems with slowly varying inputs a stability analysis is presented that deals with the response of a nonlinear sampled data system to a slowly varying exogenous input signal the main result similar to existing results for purely continuous time and discrete time systems establishes that if the system possesses a manifold of exponentially stable constant operating points equilibria corresponding to constant values of the input signal then an initial state close to this manifold and a slowly varying input signal yield a trajectory that remains close to the manifold the analysis involves casting the sampled data system as a continuous time system with discrete jumps at the sampling instants

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

brief analysis and design of gain scheduled sampled data control systems the existence of gain scheduled sampled data controllers that meet an important linearization requirement about a family of equilibria is investigated

sampled data observer based output feedback fuzzy stabilization of nonlinear systems exact discrete time design approach this paper presents a new direct discrete time design methodology of a sampled data observer based output feedback fuzzy controller for a class of nonlinear system that is exactly modeled in takagi sugeno s form at least locally a fundamental yet challenging issue in this direction is the unavailability of the exact discrete time model of the nonlinear plant in a closed form in contrast to the earlier works that are based on an approximate discrete time model thus the stability obtained in the design step is not preserved in the implementation step we employ an exact discrete time fuzzy model in an integral form sufficient asymptotic stabilization conditions are investigated in the discrete time lyapunov sense we then show that the resulting sampled data controller indeed asymptotically stabilizes the nonlinear plant an example is provided to illustrate the effectiveness of the proposed methodology

a stability property in this note we obtain a stability property not for a point of equilibrium but for a certain family of asymptotically stable equilibria of a dynamical system with an input we show that this property depends not only on the initial condition but also on the time derivative of the input function we suggest possible applications of this result to some control problems

brief paper stability connection between sampled data fuzzy control systems with quantization and their approximate discrete time model this paper concerns the stability of a sampled data takagi sugeno t s fuzzy control system with quantization when a controller design is based on an approximate discrete time model of the plant without quantization the motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete time model of the t s fuzzy system is generally not amenable to synthesis process we show that the concerned system is lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete time model a constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities

robust digital control of fuzzy systems with parametric uncertainties lmi based digital redesign approach this paper presents a new intelligent digital redesign idr method for uncertain nonlinear systems which are represented by a takagi sugeno t s fuzzy model the term idr involves converting an analog controller into an equivalent digital one in the sense of state matching the idr problem can be reduced to finding the digital fuzzy gains minimizing the norm distance between the closed loop states of the analog and digital control systems the uncertainties in the plant dynamics are considered in the idr condition that plays an important role in the performance improvement also the robust stability is well guaranteed in the proposed idr procedure its constructive conditions are expressed as linear matrix inequalities lmis two numerical examples the chaotic lorenz system and the qi system are demonstrated to visualize the feasibility of the proposed methodology

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

fuzzy stabilization of nonlinear systems under sampled data feedback an exact discrete time model approach this paper addresses stabilization problems for a nonlinear system via a sampled data fuzzy controller the nonlinear system is assumed to be exactly modeled in takagi sugeno s form at least locally unlike the conventional direct discrete time design approach based on an approximate discrete time model the sampled data fuzzy controllers are designed based on an exact discrete time model sufficient design conditions are formulated in terms of linear matrix inequalities it is shown that whenever the exact discrete time fuzzy model is asymptotically stabilizable via the sampled data fuzzy controller uniformly bounded in the state then so is the original nonlinear system a numerical example is given to illustrate the effectiveness of the proposed methodology

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

nonquadratic lyapunov function for continuous ts fuzzy models through their discretization since the beginning of the fuzzy control theory results have been obtained independently for continuous and discrete models it is still quite difficult to use nonquadratic lyapunov functions for the continuous case while this is much easier for the discrete case this approach tries to put a bridge between the continuous and discrete cases for the class of continuous takagi sugeno fuzzy models that can be exactly discretized indeed for this particular class once the stability of the discrete model is ensured the same control law applied to the continuous model will ensure the stability too the interest of such an approach is that complex control laws and complex lyapunov functions can be easily used simulation examples show that stabilizing feedbacks may be obtained with discrete control laws when purely continuous ones fail

a stability property and its application to discrete time nonlinear system control an inequality on the solution of discrete time nonlinear systems is established a special case of this inequality leads to a stability result that is the counterpart of the kelemen theorem on continuous time systems application of this inequality gives some results on stability regulation and tracking of the discrete time nonlinear systems

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

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

assessing goodness of fit of parametric regression models for lifetime data graphical methods graphical methods are often used to check goodness of fit of models to data it is common to plot residuals against a reference distribution so that when the model fits the data the configuration should be close to a straight line since the resemblance to a straight line is often unclear it has been suggested to add simulated envelopes within which the configuration is expected to lie the implementation of this method for survival data analysis is not straightforward in this paper we point out the difficulties which arise in constructing envelopes on residual plots for randomly censored data methods are suggested to deal with the problems and evaluated they are illustrated by simulated data and on a follow up study of myeloma

integration on supermanifolds and a generalized cartan calculus a suggestion by berezin for a method of integration on supermanifolds is given a precise differential geometric meaning by assuming that a supermanifold is the total space of a fibre bundle with connection the relevant objects for integration are identified as suitable horizontal vertical projections of hyperforms the latter are generalizations of differential forms having both covariant and contravariant indices the exterior calculus of these projected hyperforms is developed analogously to the cartan calculus by introducing appropriate derivations and determining their commutators respectively anticommutators

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

fuzzy model based control of complex plants in the field of fuzzy modeling the takagi sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants the paper addresses two control design problems associated with state space realizations of such fuzzy models first we treat the stability robustness of fuzzy model based controllers against modeling uncertainty second we develop observer based control schemes and further investigate the behavior of estimated state feedback in both cases we provide sufficient conditions that guarantee stability of the closed loop the results are demonstrated on the fuzzy model of a gas furnace process

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

graphical generalized residuals in fitting distributions applications to epidemiological follow up data three kinds of generalized residuals based on probability integral transformation are defined and their roles in graphical goodness of fit testing are discussed although they are useful in fitting parametric distributions their value is questionable however in fitting cox s proportional hazard rate phr models they almost always appear to give a good fit because of a almost non parametric nature of the phr models b heavy right hand censoring in epidemiological data and c scale adjustment in graphical presentation thus the apparent overall fit has little inferential meaning but the residuals are useful in exploratory analysis a simple method based on non parametric stratified residual plots for selection of risk factors is discussed it is in fact equivalent to comparison of several empirical survival functions one for each set of values stratum of a covariable under consideration it is also suggested that for the preliminary phr model the continuous variables should be discretized and indicator variables used in the model to check analytically the graphical perception of the possible functional form of the contribution of each covariable to the phr model

technical communique theoretical justification of approximate norm minimization method for intelligent digital redesign this paper investigates the theoretical justification of intelligent digital redesign idr methods based on the approximate discrete time models its main purpose is to design the digital fuzzy controller achieving the minimum norm distance between the trajectories of the approximate closed loop systems under the analog and the digital controls it is verified that if there exist the digital gains such that the approximate norm distance is sufficiently small the redesigned controller makes the trajectories of the exact closed loop systems close or at least asymptotically stabilizes the plant

digitalizing a fuzzy observer based output feedback control intelligent digital redesign approach this paper concerns an intelligent digital redesign idr technique for a takagi sugeno fuzzy observer based output feedback control fobofc system the term idr involves converting an existing analog control into an equivalent digital counterpart in the sense of state matching the idr problem is herein viewed as a minimization problem of the norm distances between nonlinearly interpolated linear operators to be matched its constructive condition with global rather than local state matching is formulated in terms of bilinear matrix inequalities the main features of the proposed method are that the state estimation error in the plant dynamics is considered in the idr condition that plays a crucial role in the performance improvement the stability property is preserved by the proposed idr algorithm the separation principle is shown when the premise variables are measurable finally the idr condition for a more general fobofc an estimated premise variable case is conducted a numerical example is demonstrated to visualize the feasibility of the developed methodology

design of robust fuzzy model based controller with sliding mode control for siso nonlinear systems in this paper we present the design of a new type of fuzzy controllers for controlling complex single input single output systems by incorporating sliding mode control theory with fuzzy control technology first a fuzzy model of the given nonlinear system is constructed to represent the local dynamic behaviors of the given nonlinear system a global controller is then constructed by combining all local state feedback controllers and a global supervisory sliding mode controller improved robustness and tracking performance are obtained by a seamless integration of fuzzy model based control and sliding mode control in addition stability of controlling the original underlying nonlinear systems is guaranteed owing to the robustness of the sliding mode control method to system parameter uncertainties two simulation examples are included to show the effectiveness and feasibility of the developed integrated controller

group theoretical foundations of fractional supersymmetry fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized grassmann variable n 0 for arbitrary integer n 2 3 an explicit formula is given in the case of general n for the transformations that leave the theory invariant and it is shown that these transformations possess interesting group properties it is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group careful attention is paid to some technically important issues including differentiation that arise as a result of the peculiar nature of quantities such as

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

intelligent digital redesign revisited approximate discretization and stability limitation this paper sharpens the recently developed intelligent digital redesign idr technique in regard of stability a major assumption in the previous result was that the firing strength of each fuzzy rule is approximated as its sampled value during a sampling period for efficient discretization of the takagi sugeno t s fuzzy system by which some unexpected stability might be experienced for certain sampling period as large as the assumption is unrealistic to clarify results for that case we refine the idr condition and prove that the uniformly semiglobal practical asymptotic stability of the sampled data t s fuzzy control system by the intelligently redesigned digital fuzzy controller rather than the global exponential stability shown in the previous result

technical communique an lmi approach to guaranteed cost control of linear uncertain time delay systems the guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time delay systems with norm bounded time varying parametric uncertainty and a given quadratic cost function sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities lmis furthermore a convex optimization problem with lmi constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed loop uncertain system

hybrid state space fuzzy model based controller with dual rate sampling for digital control of chaotic systems we develop a hybrid state space fuzzy model based controller with dual rate sampling for digital control of chaotic systems a takagi sugeno ts fuzzy model is used to model the chaotic dynamic system and the extended parallel distributed compensation technique is proposed and formulated for designing the fuzzy model based controller under stability conditions the optimal regional pole assignment technique is also adopted in the design of the local feedback controllers for the multiple ts linear state space models the proposed design procedure is as follows an equivalent fast rate discrete time state space model of the continuous time system is first constructed by using fuzzy inference systems to obtain the continuous time optimal state feedback gains the constructed discrete time fuzzy system is then converted into a continuous time system the developed optimal continuous time control law is finally converted into an equivalent slow rate digital control law using the proposed intelligent digital redesign method the main contribution of the paper is the development of a systematic and effective framework for fuzzy model based controller design with dual rate sampling for digital control of complex such as chaotic systems the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic chua circuit

some examples of compact supermanifolds with non abelian fundamental group a detailed construction is given of a supermanifold which is compact and has far from trivial topology higher dimensional examples are also described the grassmann algebra from which the supermanifolds are constructed may have finite or infinite dimension

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

a note on the meaning of covariant derivatives in supersymmetry we analyze in this paper the group theoretical meaning of the covariant derivatives and show that they are horizontal left invariant vector fields on superspace obtained from a super lie group which at the same time exhibits the structure of a principal bundle with a canonical connection the geometrical construction is general and not restricted to the super poincare group

an improved digital redesign for sampled data fuzzy control systems this paper proposes an improved digital redesign dr technique for sampled data fuzzy controllers in nonlinear systems based on a takagisugeno ts fuzzy model to improve the performance of the dr technique two methodologies are used a state matching error cost function and a continuous time fuzzy lyapunov function using these two methodologies a novel dr technique is proposed to guarantee both the stability and state matching conditions of the sampled data fuzzy control system further the proposed dr technique is represented as an optimal problem using the linear matrix inequality lmi format finally some simulation examples are provided to verify the effectiveness of the proposed technique in comparison with previous techniques

brief paper a velocity algorithm for the implementation of gain scheduled controllers a new method is proposed to implement gain scheduled controllers for nonlinear plants given a family of linear feedback controllers designed for linearizations of a nonlinear plant about constant operating points a nonlinear gain scheduled controller is derived that preserves the input output properties of the linear closed loop systems locally about each equilibrium point the key procedures in the proposed method are to provide integral action at the inputs to the plant and differentiate some of the measured outputs before they are fed back to the scheduled controller for a fairly general class of systems the nonlinear gain scheduled controllers are easy to obtain and their structure is similar to that of the original linear controllers

gain scheduling dynamic linear controllers for a nonlinear plant abstract for a general type of nonlinear tracking problem we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points a necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented using this condition the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed and ad hoc approaches to scheduling can be analyzed

a new intelligent digital redesign for t s fuzzy systems global approach this paper proposes a novel and efficient global intelligent digital redesign technique for a takagi sugeno t s fuzzy system the term of intelligent digital redesign involves converting an existing analog fuzzy model based controller into an equivalent digital counterpart in the sense of state matching the proposed method should be notably discriminated from the previous works in that it allows us to globally match the states of the overall closed loop t s fuzzy system with the predesigned analog fuzzy model based controller and those with the digitally redesigned fuzzy model based controller and further to examine the stabilizability by the redesigned controller in the sense of lyapunov the key idea is that the global intelligent digital redesign problem is viewed as a convex minimization problem of the norm distance between nonlinearly interpolated linear operators to be matched sufficient conditions for the global state matching and the stability of the digitally controlled system are formulated in terms of linear matrix inequalities lmis a complex nonlinear system duffing like chaotic oscillator is simulated and demonstrated to validate the feasibility and effectiveness of the proposed digital redesign technique which implies the safe applicability to the digital control system