controlling chaotic dynamical systems we review the major ideas involved in the control of chaos we present the ott grebogi yorke ogy method of controlling chaos which is a particular case of the pole placement technique but which is the one leading to the shortest time to achieve the control of chaotic systems implementation using only measured time series in experimental settings is also described

h_ infty filtering for nonlinear discrete time systems subject to quantization and packet dropouts this paper investigates the problem of h filtering for a class of nonlinear discrete time systems with measurement quantization and packet dropouts each output is transmitted via an independent communication channel and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution while the quantization errors are treated as sector bound uncertainties based on a piecewise lyapunov function an approach to the design of h piecewise filter is pro posed such that the filtering error system is stochastically stable with a guaranteed h performance some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the lyapunov matrices and the system matrices the filter parameters can be obtained by solving a set of linear matrix inequalities lmis which are numerically tractable with commercially available software finally two illustrative examples are provided to show the effectiveness of the proposed method

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

disturbance observer based robust mixed h2 h fuzzy tracking control for hypersonic vehicles this paper introduces a disturbance observer do based mixed h2 h robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle hv with modeled and unmodeled disturbances a takagisugeno ts fuzzy model is firstly employed to approximate the nonlinear dynamics of hv subsequently based on the fuzzy model a do is constructed to estimate the modeled disturbance next by integrating the hv dynamics the tracking error integral and the disturbance estimation error dynamics an augmented system is established for the control design then a do based mixed h2 h robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed h2 h control performance of the augmented system the proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error and a do based compensator for the modeled disturbance cancellation the outcome of the do based mixed h2 h robust fuzzy control problem is formulated in terms of linear matrix inequalities lmis furthermore by utilizing the existing lmi optimization technique a suboptimal controller is obtained in the sense of minimizing an upper bound of h2 performance finally simulation results on an hv demonstrate the effectiveness of the proposed design method

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

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

fuzzy model based piecewise mathscr h _ infty static output feedback controller design for networked nonlinear systems this paper investigates the problem of robust h output feedback control for a class of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s uncertain fuzzy model and the communication links between the plant and controller are assumed to be imperfect i e data packet dropouts occur intermittently which is often the case in a network environment stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon and the attention is focused on the design of a piecewise static output feedback sof controller such that the closed loop system is stochastically stable with a guaranteed h performance based on a piecewise lyapunov function combined with some novel convexifying techniques the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are also provided to illustrate the effectiveness of the proposed approaches

h sub spl infin state feedback controller design for discrete time fuzzy systems using fuzzy weighting dependent lyapunov functions for discrete time takagi sugeno ts fuzzy systems we propose an h sub spl infin state feedback fuzzy controller associated with a fuzzy weighting dependent lyapunov function the controller which is designed via parameterized linear matrix inequalities plmis employs not only the current time but also the one step past information on the time varying fuzzy weighting functions appropriately selecting the structures of variables in the plmis allows us to find an lmi formulation as a special case

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

communication delay distribution dependent networked control for a class of t s fuzzy systems this paper investigates a robust networked control for a class of takagi sugeno t s fuzzy systems the controller design specifically takes probabilistic interval distribution of the communication delay into account a general framework of networked control is first proposed the two main features are 1 the zero order hold can choose the latest control input signal when the packets received are out of order and 2 as the result of 1 the models of the all kinds of uncertainties in networked signal transfer including network induced delay and data packet dropout are under a unified framework next if the probability distribution of communication delay is known or specified in a design process sufficient stability conditions for networked t s fuzzy systems are derived which are based on the lyapunov theory following this a stabilizing controller design method is developed which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well finally a numerical example is used to show the application of the theoretical results obtained in this paper

stability analysis and synthesis of fuzzy singularly perturbed systems in this paper we investigate the stability analysis and synthesis problems for both continuous time and discrete time fuzzy singularly perturbed systems for continuous time case both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities lmis for discrete time case only the analysis problem can be cast in lmis while the derived stability conditions for controller design are nonlinear matrix inequalities nmis furthermore a two stage algorithm based on lmi and iterative lmi ilmi techniques is developed to solve the resulting nmis and the stabilizing feedback controller gains can be obtained for both continuous time and discrete time cases the reduced control law which is only dependent on the slow variables is also discussed finally an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures

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

robustness of the latent variable model for correlated binary data the marginal regression model offers a useful alternative to conditional approaches to analyzing binary data liang zeger and qaqish 1992 journal of the royal statistical society series b 54 3 40 instead of modelling the binary data directly as do liang and zeger 1986 biometrika 73 13 22 the parametric marginal regression model developed by qu et al 1992 biometrics 48 1095 1102 assumes that there is an underlying multivariate normal vector that gives rise to the observed correlated binary outcomes although this parametric approach provides a flexible way to model different within cluster correlation structures and does not restrict the parameter space it is of interest to know how robust the parameter estimates are with respect to choices of the latent distribution we first extend the latent modelling to include multivariate t distributed latent vectors and assess the robustness in this class of distributions then we show through a simulation that the parameter estimates are robust with respect to the latent distribution even if latent distribution is skewed in addtion to this empirical evidence for robustness we show through the iterative algorithm that the robustness of the regression coefficents with respect to misspecifications of covariance structure in liang and zeger s model in fact indicates robustness with respect to underlying distributional assumptions of the latent vector in the latent variable model

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

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

border collision bifurcations an explanation for observed bifurcation phenomena recently physical and computer experiments involving systems describable by continuous maps that are nondifferentiable on some surface in phase space have revealed novel bifurcation phenomena these phenomena are part of a rich new class of bifurcations which we call border collision bifurcations a general criterion for the occurrence of border collision bifurcations is given illustrative numerical results including transitions to chaotic attractors are presented these border collision bifurcations are found in a variety of physical experiments

assessing interrater agreement from dependent data estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods we investigate the use of a latent model proposed by qu piedmonte and medendorp 1995 biomerics 51 268 275 to estimate the correlation between raters for each method and test for their equality for each of the assessment methods these correlations can be interpreted as the variance components of random effects representing subject and rater this method is applied to an hiv study in which the amount of ectopy on a woman s cervix is measured by both direct visual assessment and a computer planimetry method

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

brief paper an ilmi approach to robust h2 static output feedback fuzzy control for uncertain discrete time nonlinear systems this paper studies the problem of robust h 2 static output feedback sof fuzzy control for discrete time nonlinear systems with parametric uncertainties the takagi and sugeno fuzzy model is employed to represent an uncertain discrete time nonlinear system a sufficient condition for the existence of robust h 2 sof fuzzy controllers is presented in terms of a set of matrix inequalities which not only guarantees the stability of the closed loop fuzzy system but also provides an upper bound on the quadratic cost function a suboptimal robust h 2 sof fuzzy control problem is addressed in the sense of minimizing the bound an iterative linear matrix inequality ilmi algorithm is proposed to compute the feedback gain matrices of the suboptimal fuzzy controller finally two numerical examples are also provided to demonstrate the effectiveness of the proposed method

border collision bifurcations in two dimensional piecewise smooth maps recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle node pitchfork or hopf bifurcations occurring in smooth maps in this paper we first present experimental results to establish the need for the development of a theoretical framework and classification of the bifurcations resulting from border collision we then present a systematic analysis of such bifurcations by deriving a normal form the piecewise linear approximation in the neighborhood of the border we show that there can be eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form and these are classified under six cases we present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur this theoretical framework will help in explaining bifurcations in all systems which can be represented by two dimensional piecewise smooth maps

fuzzy static output feedback may be possible in lmi framework takagi sugeno t s fuzzy model based static output feedback controller design is a challenging issue due to the nonconvexity in the lyapunov stability condition recently a convexified linear matrix inequality lmi condition was proposed for the problem by additionally importing as many equality constraints as the number of the fuzzy rules with a variable in the paper from the study of fang et al however numerical experiences seem to imply the infeasibility of the proposed lmi this letter shows that their lmi problem may be feasible

design of observer based h_ infty control for fuzzy time delay systems this paper addresses the problem of observer based hinfin control for nonlinear systems with time varying delay represented by takagi sugeno t s fuzzy model it presents a single step linear matrix inequality lmi method for the fuzzy control design which overcomes the drawback of the two step lmi approach often encountered in the literature the derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict lmis when restricted to delay free fuzzy systems the present results improve or reduce to existing ones illustrative examples show the effectiveness and merits of the present results

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

border collision bifurcations including period two to period three for piecewise smooth systems abstract we examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter in the simplest case there is a surface in phase space along which the map has no derivative or has two one sided derivatives is the border of two regions in which the map is smooth as the parameter is varied a fixed point e may collide with the border and we may assume that this collision occurs at 0 a variety of bifurcations occur frequently in such situations but never or almost never occur in smooth systems in particular e may cross the border and so will exist for 0 but it may be a saddle in one case say 0 for 0 there may be a stable period 3 orbit which similarly shrinks to e0 as 0 hence one observes the following stable periodic orbits a stable period 2 orbit collapses to a point and is reborn as a stable period 3 orbit we also see analogously stable period 2 to stable period p orbit bifurcations with p 5 11 52 or period 2 to quasi periodic or even to a chaotic attractor we believe this phenomenon will be seen in many applications

effect of smoothing on robust chaos in piecewise smooth dynamical systems situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic e g no periodic windows this is the phenomenon of robust chaos previous works have established that robust chaos can occur through the mechanism of border collision bifurcation where border is the phase space region where discontinuities in the derivatives of the dynamical equations occur we investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present we introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter regardless of the details of the smoothing function numerical support and a heuristic theory are provided to establish the scaling relation experimental evidence of periodic windows in a supposedly piecewise linear dynamical system which has been implemented as an electronic circuit is also provided

marginally specified logistic normal models for longitudinal binary data summary likelihood based inference for longitudinal binary data can be obtained using a generalized linear mixed model breslow n and clayton d g 1993 journal of the american statistical association88 9 25 wolfinger r and o connell m 1993 journal of statistical computation and simulation48 233 243 given the recent improvements in computational approaches alternatively fitzmaurice and laird 1993 biometrika80 141 151 molenberghs and lesaffre 1994 journal of the american statistical association89 633 644 and heagerty and zeger 1996 journal of the american statistical association91 1024 1036 have developed a likelihood based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and or marginal higher moment assumptions each of these marginal approaches is computationally intense and currently limited to small cluster sizes in this manuscript an alternative parameterization of the logistic normal random effects model is adopted and both likelihood and estimating equation approaches to parameter estimation are studied a key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual level predictions or contrasts an example is presented where scientific interest is in both the mean response and the covariance among repeated measurements

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

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

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

latent variables measurement error and methods for analysing longitudinal binary and ordinal data we explore structural equations with latent variables for modelling between individual variability and measurement error in the analysis of longitudinal binary and ordinal data the structural equation formulation provides insight into the assumptions and differences in interpretation of methods that are popular for longitudinal data analysis introducing the concept of continuous latent variables makes it clear that marginal and cluster specific models differ because their predicted variables are scaled to different standard deviations and that adjustment for measurement error in the outcome involves a change in scale as well we apply both structural equation modelling and common longitudinal modelling approaches to data from a study of sleep disorders in the process we compare results from marginal modelling using an sas gee routine karim and zeger 1988 qu s gauss program qu 1992 for generalized mixed models using gee the mixor package for cluster specific mixed effects models hedeker and gibbons 1994 and liscomp for structural models muthen 1988

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

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

joint modeling of multiple ordinal adherence outcomes via generalized estimating equations with flexible correlation structure jiang z reprint author univ pittsburgh grad sch publ hlth dept biostat pittsburgh pa 15261 usa zhen jiang fda hhs gov

latent variable models for clustered dichotomous data with multiple subclusters summary regression models for clustered binary data are derived from nonlinear mixed models in terms of latent normal variables the marginal response probabilities are functions of covariates through generalized linear models within a cluster the pairwise tetrachoric correlations are all equal and are not restricted by marginal probabilities this approach accommodates hierarchically nested binary data an algorithm for estimation using generalized estimating equations is proposed an example illustrates the application of this approach

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

nonsynchronized state estimation of multichannel networked nonlinear systems with multiple packet dropouts via t s fuzzy affine dynamic models this paper investigates the problem of robust h state estimation for a class of multichannel networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables with general probability distributions are adopted to characterize the data missing phenomenon in output channels the objective is to design an admissible state estimator guaranteeing the stochastic stability of the resulting estimation error system with a prescribed h disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the estimator implementation with state space partition may not be synchronized with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexifying techniques two different approaches are developed to robust filtering design for the underlying t s fuzzy affine systems with unreliable communication links all the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

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

effect of omitted confounders on the analysis of correlated binary data summary marginal analysis using the generalized estimating equation approach is widely applied to correlated observations as occur in studies with clusters and in longitudinal follow up of individuals in this article we investigate the effect of confounding in such models we assume that a risk factor x and a confounder z are related by a generalized linear model to the outcome y which can be binary or ordinal in order to investigate confounding arising from the omission of z a joint structure for x and z must be specified modeling normally distributed x z as sums of between and within individual or cluster components allows us to incorporate different degrees of betweenand within individual correlation such a structure includes as special cases cohort and period effects in longitudinal settings and random intercept models the latter situation corresponds to allowing z to vary only on the between individual or cluster level and to be uncorrelated with x and leads to attenuation of the coefficient of x in marginal models with the logit and probit links more complex situations occur when z is allowed to also vary on the within individual or cluster level and when z is correlated with x we examine the model specification and the expected bias when fitting a marginal model in the presence of the omitted confounder z we derive general formulas and interpret the parameters and results in an ongoing cohort study testing for omitted covariates is also discussed

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

use of quasi least squares to adjust for two levels of correlation this article considers data with two levels of association our motivating example is an international intervention trial with repeated observations on subjects who reside within geographically defined clusters to account for the potential correlation within clusters and within the repeated measurements that pertain to each subject we apply a method based on generalized estimating equations for a correlation structure proposed by lefkopoulou moore and ryan 1989 journal of the american statistical association 84 810 815

a random effects ordinal regression model for multilevel analysis a random effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data this model is developed for both the probit and logistic response functions the threshold concept is used in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects a maximum marginal likelihood mml solution is described using gauss hermite quadrature to numerically integrate over the distribution of random effects an analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random effects analysis of clustered ordinal data while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random effects approach for longitudinal ordinal data

nonlinear state feedback controller for nonlinear systems stability analysis and design based on fuzzy plant model this paper presents the stability analysis of a fuzzy model based control system consisting of a nonlinear plant and a nonlinear state feedback controller and the design of the nonlinear gains of the controller the nonlinear plant is represented by a fuzzy model having p rules a nonlinear state feedback controller is designed to close the feedback loop under this design the stability condition is reduced to p linear matrix inequalities an application example on stabilizing a mass spring damper system will be given

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

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

a mixed model procedure for analyzing ordered categorical data a mixed model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables this procedure resembles the best linear unbiased procedure of henderson 1975 biometrics 31 423 447 for predicting the value of a quantitative response the approach is based on a mixed model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model the results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf

likelihood inference in a correlated probit regression model correlated binary observations arise in a variety of applications for example in animal studies the term litter effect is used to describe the greater alikeness of responses within a litter as compared to that between litters at a given set of experimental conditions in a setting that motivated this work cells on individual atomic bomb survivors were scored as to the presence or absence of chromosomal aberrations the number of aberrant cells varied among subjects at a specified radiation exposure estimate age at exposure city of exposure and sex in a manner that substantially exceeds that consistent with a binomial error structure otake prentice 1984 this extra binomial variation or overdispersion reflects the fact that the binary response of cells from a given survivor tend to be more alike than are the responses of cells from distinct survivors having the same estimated radiation exposure level and other covariate values such overdispersion may result from individual differences in susceptibility to radiation damage from omitted covariates or most plausibly in this setting from substantial random errors in the estimated radiation exposure levels failure to acknowledge overdispersion may lead to serious underestimation of the standard errors associated with regression parameter estimates and to unduly precise inferences

a new design of delay dependent robust cal h _ bm infty filtering for discrete time t s fuzzy systems with time varying delay this paper investigates the problem of delay dependent robust h infin filtering design for a class of uncertain discrete time state delayed takagi sugeno t s fuzzy systems the state delay is assumed to be time varying and of an interval like type which means that both the lower and upper bounds of the time varying delay are available the parameter uncertainties are assumed to have a structured linear fractional form based on a novel fuzzy basis dependent lyapunov krasovskii functional combined with finsler s lemma and an improved free weighting matrix technique for delay dependent criteria a new sufficient condition for robust h infin performance analysis is first derived and then the filter synthesis is developed it is shown that by using a simple linearization technique incorporating a bounding inequality a unified framework can be developed such that both the full order and reduced order filters can be obtained by solving a set of linear matrix inequalities lmis which are numerically efficient with commercially available software finally simulation examples are provided to illustrate the advantages and less conservatism of the proposed approach

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

autonomous coupled oscillators with hyperbolic strange attractors abstract we propose several examples of smooth low order autonomous dynamical systems which have apparently uniformly hyperbolic attractors the general idea is based on the use of coupled self sustained oscillators where due to certain amplitude nonlinearities successive epochs of damped and excited oscillations alternate because of additional phase sensitive coupling terms in the equations the transfer of excitation from one oscillator to another is accompanied by a phase transformation corresponding to some chaotic map in particular an expanding circle map or anosov map of a torus the first example we construct is a minimal model possessing an attractor of the smale williams type it is a four dimensional system composed of two oscillators the underlying amplitude equations are similar to those of the predator pray model the other three examples are systems of three coupled oscillators with a heteroclinic cycle this scheme presents more variability for the phase manipulations in the six dimensional system not only the smale williams attractor but also an attractor with arnold cat map dynamics near a two dimensional toral surface and a hyperchaotic attractor with two positive lyapunov exponents are realized

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

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

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures