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

multi arm trials with multiple primary endpoints and missing values we present an extension of multiple contrast tests for multiple endpoints to the case of missing values the endpoints are assumed to be normally distributed and correlated and to have equal covariance matrices for the different treatments different multivariate t distributions will be applied differing in endpoint specific degrees of freedom in contrast to competing methods the familywise error type i is maintained in the strong sense in an admissible range and the problem of different marginal errors type i is avoided the information of all observations is exploited thereby enabling a gain in power compared with a complete case analysis

novel rule for quantizing chaos numerical tests of a novel semiclassical quantization rule are carried out for three strongly chaotic systems the hyperbolic billiard artin s billiard and the hadamard gutzwiller model the results demonstrate that this novel rule is very effective and capable of generalizing sensible approximations to the quantal energy levels

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

multivariate t nonlinear mixed effects models for multi outcome longitudinal data with missing values the multivariate nonlinear mixed effects model mnlmm has emerged as an effective tool for modeling multi outcome longitudinal data following nonlinear growth patterns in the framework of mnlmm the random effects and within subject errors are assumed to be normally distributed for mathematical tractability and computational simplicity however a serious departure from normality may cause lack of robustness and subsequently make invalid inference this paper presents a robust extension of the mnlmm by considering a joint multivariate t distribution for the random effects and within subject errors called the multivariate t nonlinear mixed effects model moreover a damped exponential correlation structure is employed to capture the extra serial correlation among irregularly observed multiple repeated measures an efficient expectation conditional maximization algorithm coupled with the first order taylor approximation is developed for maximizing the complete pseudo data likelihood function the techniques for the estimation of random effects imputation of missing responses and identification of potential outliers are also investigated the methodology is motivated by a real data example on 161 pregnant women coming from a study in a private fertilization obstetrics clinic in santiago chile and used to analyze these data

semiclassical form factor for chaotic systems with spin we study the properties of the two point spectral form factor for classically chaotic systems with spin in the semiclassical limit with a suitable semiclassical trace formula as our principal tool to this end we introduce a regularized form factor and discuss the limit in which the so called diagonal approximation can be recovered the incorporation of the spin contribution to the trace formula requires an appropriate variant of the equidistribution principle of long periodic orbits as well as the notion of a skew product of the classical translational and spin dynamics provided this skew product is mixing we show that generically the diagonal approximation of the form factor coincides with the respective predictions from random matrix theory

beyond the heisenberg time semiclassical treatment of spectral correlations in chaotic systems with spin 1 2 the two point correlation function of chaotic systems with spin 1 2 is evaluated using periodic orbits the spectral form factor for all times thus becomes accessible equivalence with the predictions of random matrix theory for the gaussian symplectic ensemble is demonstrated a duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established

a parametric family of correlation structures for the analysis of longitudinal data in epidemiological settings we are often faced with numerous short time series and a parsimonious parametrization of the correlation structure is desired in order to optimize the efficiency of the estimation procedure we propose a damped exponential correlation structure for modeling multivariate gaussian outcomes the correlation between two observations separated by s units of time is modeled as gamma s theta where gamma is the correlation between elements separated by one s unit and theta is a damping parameter for theta 0 theta 1 and theta infinity the correlation structures of compound symmetry first order autoregressive and first order moving average processes are obtained although the ar 2 dependency structure and the combination of random effects and ar 1 errors are not special cases of the proposed parametric family these structures can be well approximated within the family for short time series maximum likelihood methods for parameter estimation and interpretations of intermediate models 0 less than theta less than 1 are discussed in the context of modeling pulmonary function in an adult population in the netherlands and t cell subsets in homosexual men infected with human immunodeficiency virus type i

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

a random effects model for multiple characteristics with possibly missing data abstract the use of random effects models for the analysis of longitudinal data with missing responses has been discussed by several authors this article extends the random effects model for a single characteristic to the case of multiple characteristics allowing for arbitrary patterns of observed data two different structures for the covariance matrix of measurement error are considered uncorrelated error between responses and correlation of error terms at the same measurement times parameters for this model are estimated via the em algorithm the set of equations for this estimation procedure is derived these equations are appropriately modified to deal with missing data the methodology is illustrated with an example from clinical trials

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

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

two point correlations of the gaussian symplectic ensemble from periodic orbits we determine the asymptotics of the two point correlation function for quantum systems with half integer spin which show chaotic behaviour in the classical limit using a method introduced by bogomolny and keating for time reversal invariant systems we obtain the leading terms of the two point correlation function of the gaussian symplectic ensemble special attention has to be paid to the role of kramers degeneracy

numerical accuracy of bogomolny s semiclassical quantization scheme in quantum billiards we use the semiclassical quantization scheme of bogomolny to calculate eigenvalues of the limacon quantum billiard corresponding to a conformal map of the circle billiard we use the entire billiard boundary as the chosen surface of section and use a finite approximation for the transfer operator in coordinate space computation of the eigenvalues of this matrix combined with a quantization condition determines a set of semiclassical eigenvalues which are compared with those obtained by solving the schrodinger equation the classical dynamics of this billiard system undergoes a smooth transition from integrable circle to completely chaotic motion thus providing a test of bogomolny s semiclassical method in coordinate space in terms of the morphology of the wavefunction we analyse the results for billiards which exhibit both soft and hard chaos

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

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

discriminant analysis for longitudinal data with multiple continuous responses and possibly missing data multiple outcomes are often used to properly characterize an effect of interest this article discusses model based statistical methods for the classification of units into one of two or more groups where for each unit repeated measurements over time are obtained on each outcome we relate the observed outcomes using multivariate nonlinear mixed effects models to describe evolutions in different groups due to its flexibility the random effects approach for the joint modeling of multiple outcomes can be used to estimate population parameters for a discriminant model that classifies units into distinct predefined groups or populations parameter estimation is done via the expectation maximization algorithm with a linear approximation step we conduct a simulation study that sheds light on the effect that the linear approximation has on classification results we present an example using data from a study in 161 pregnant women in santiago chile where the main interest is to predict normal versus abnormal pregnancy outcomes

semiclassical theory of spectral rigidity the spectral rigidity l of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of l mean level spacings in the semiclassical limit 0 formulae are obtained giving l as a sum over classical periodic orbits when l l max where l max n 1 for a system of n freedoms l is shown to display the following universal behaviour as a result of properties of very long classical orbits if the system is classically integrable all periodic orbits filling tori l 1 5 l as in an uncorrelated poisson eigenvalue sequence if the system is classically chaotic all periodic orbits isolated and unstable and has no symmetry l in l 2 2 d if 1 l l max as in the gaussian unitary ensemble of random matrix theory if the system is chaotic and has time reversal symmetry l in l 2 e if 1 l l max as in the gaussian orthogonal ensemble when l l max l saturates non universally at a value determined by short classical orbits of order n 1 for integrable systems and in 1 for chaotic systems these results are obtained by using the periodic orbit expansion for the spectral density together with classical sum rules for the intensities of long orbits and a semiclassical sum rule restricting the manner in which their contributions interfere for two examples l is studied in detail the rectangular billiard integrable and the riemann zeta function assuming its zeros to be the eigenvalues of an unknown quantum system whose unknown classical limit is chaotic

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

the semiclassical origin of the logarithmic singularity in the symplectic form factor sieber and richter achieved a breakthrough towards a proof of the universality of spectral fluctuations of chaotic quantum systems conjectured by bohigas giannoni and schmidt by calculating semiclassically the first term beyond the diagonal approximation of the orthogonal form factor in this letter the semiclassical origin of the logarithmic singularity of the symplectic form factor is deduced perturbatively by combining this result with the contribution that arises due to the spin this approach stands in contrast to the duality approach introduced by bogomolny and keating which is essentially non perturbative and where the structure around the heisenberg time is related to the structure for very small time which can be deduced using the diagonal approximation

controlling linear systems with nonlinear perturbations under sampled data output feedback digital redesign approach this article develops a digital redesign dr technique for sampled data observer based output feedback control of a continuous time linear system with nonlinear perturbation it is assumed that the nonlinear perturbation is a locally lipschitz function to deal with the discrete time modelling error in nonlinear systems as opposed to the previous approach the dr problem is configured as a stabilisation one for error dynamics between the closed loop system of nominal linear model under an analogue state feedback controller and that of the linear system with the nonlinear perturbation under a sampled data output feedback controller a constructive dr condition is formulated in the format of linear matrix inequalities the stability of the actual sampled data control system is guaranteed within the dr procedure the effectiveness of the proposed dr methodology is demonstrated through a numerical simulation

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

analysis of incomplete multivariate data using linear models with structured covariance matrices incomplete and unbalanced multivariate data often arise in longitudinal studies due to missing or unequally timed repeated measurements and or the presence of time varying covariates a general approach to analysing such data is through maximum likelihood analysis using a linear model for the expected responses and structural models for the within subject covariances two important advantages of this approach are 1 the generality of the model allows the analyst to consider a wider range of models than were previously possible using classical methods developed for balanced and complete data and 2 maximum likelihood estimates obtained from incomplete data are often preferable to other estimates such as those obtained from complete cases from the standpoint of bias and efficiency a variety of applications of the model are discussed including univariate and multivariate analysis of incomplete repeated measures data analysis of growth curves with missing data using random effects and time series models and applications to unbalanced longitudinal data

ga based intelligent digital redesign of fuzzy model based controllers intelligent digital redesign involves converting a continuous time fuzzy model based controller into an equivalent discrete time counterpart for the digital control of continuous time nonlinear systems by using the takagi sugeno ts fuzzy models in this paper the authors present a new global state matching intelligent digital redesign method for nonlinear systems by using genetic algorithms gas more precisely the intelligent digital redesign problem is converted to an equivalent optimization problem and then gas are adopted to find a solution the search space in which each problem variable is defined for gas are systematically obtained by the interval arithmetic operations the proposed method results in global matching of the states of the analogously controlled system with those of the digitally controlled system while the conventional intelligent digital redesign method does not the chen s chaotic system is used as an illustrative example to show the effectiveness and the feasibility of the developed method the proposed method provides a new approach for the digital redesign of a class of fuzzy model based controllers

periodic orbits and a correlation function for the semiclassical density of states through the rule that there is one quantum state per planck cell in phase space classical mechanics supplies an average semiclassical density of states for a system with bound motion can it supply more refined averages such as the correlation function for the density of states i shall argue that for the two extreme cases of integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this but a closely related correlation function the results for the two types of motion are markedly different