adaptive extensions of a two stage group sequential procedure for testing primary and secondary endpoints i unknown correlation between the endpoints in a previous paper we studied a two stage group sequential procedure gsp for testing primary and secondary endpoints where the primary endpoint serves as a gatekeeper for the secondary endpoint we assumed a simple setup of a bivariate normal distribution for the two endpoints with the correlation coefficient between them being either an unknown nuisance parameter or a known constant under the former assumption we used the least favorable value of 1 to compute the critical boundaries of a conservative gsp under the latter assumption we computed the critical boundaries of an exact gsp however neither assumption is very practical the 1 assumption is too conservative resulting in loss of power whereas the known assumption is never true in practice in this part i of a two part paper on adaptive extensions of this two stage procedure part ii deals with sample size re estimation we propose an intermediate approach that uses the sample correlation coefficient r from the first stage data to adaptively adjust the secondary boundary after accounting for the sampling error in r via an upper confidence limit on by using a method due to berger and boos we show via simulation that this approach achieves 5 11 absolute secondary power gain for 0 5 the preferred boundary combination in terms of high primary as well as secondary power is that of o brien and fleming for the primary and of pocock for the secondary the proposed approach using this boundary combination achieves 72 84 relative secondary power gain with respect to the exact gsp that assumes known we give a clinical trial example to illustrate the proposed procedure copyright 2012 john wiley sons ltd

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

a novel fuzzy framework for nonlinear system control nonlinear pid and gain scheduling controls have attracted much research interests in recent years these control strategies can accommodate some nonlinear characteristics by allowing the gains varied or rescheduled as a function of system states in this paper a novel fuzzy framework is developed to transfer this type of nonlinear controller to its fuzzy domain representation it is proved that the resulting fuzzy controller is functionally exactly identical to the original control system one of the benefits of the suggested approach is that it provides a well defined prototype for the design of fuzzy control system the resulting linguistic representation can facilitate investigation in linguistic terms into how the controller operates whereas expert knowledge can be effectively implemented to improve control performance the viability of the proposed mapping technique is demonstrated by using simulations corresponding to a flexible link robot

low rank based multi input multi output takagi sugeno fuzzy modeling for prediction of molten iron quality in blast furnace abstract for complex blast furnace smelting systems with large time delay accurate prediction of molten iron quality indicators plays an important guiding role in blast furnace control recently some data driven multi input multi output mimo modeling methods have been proposed to model multiple molten iron quality indicators including molten iron temperature mit silicon content si phosphorus content p and sulfur content s however those data driven mimo models do not consider the inter indicator correlation which leads to the suboptimal model for the estimation of multiple molten iron quality indicators this paper proposed a novel mimo takagi sugeno t s fuzzy model with taking full account of the inter indicator correlation in the novel method the inter indicator correlation was explicitly modeled by a low rank learning in a latent space that overcame the great challenge of jointly determining the fuzzy rules of mimo t s model and the inter indicator correlation for the corresponding optimization problem an effective alternating optimization algorithm is presented the validity of the proposed method is verified by simulation and comparison with some related methods on real blast furnace data

testing a primary and a secondary endpoint in a group sequential design summary we consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant the trial uses a group sequential procedure with two stages the familywise error rate fwer of falsely concluding significance on either endpoint is to be controlled at a nominal level the type i error rate for the primary endpoint is controlled by choosing any level stopping boundary e g the standard o brien fleming or the pocock boundary given any particular level boundary for the primary endpoint we study the problem of determining the boundary for the secondary endpoint to control the fwer we study this fwer analytically and numerically and find that it is maximized when the correlation coefficient between the two endpoints equals 1 for the four combinations consisting of o brien fleming and pocock boundaries for the primary and secondary endpoints the critical constants required to control the fwer are computed for different values of an ad hoc boundary is proposed for the secondary endpoint to address a practical concern that may be at issue in some applications numerical studies indicate that the o brien fleming boundary for the primary endpoint and the pocock boundary for the secondary endpoint generally gives the best primary as well as secondary power performance the pocock boundary may be replaced by the ad hoc boundary for the secondary endpoint with a very little loss of secondary power if the practical concern is at issue a clinical trial example is given to illustrate the methods

modeling and controller design for complex flexible nonlinear systems via a fuzzy singularly perturbed approach this paper investigates the problems of modeling and controller design for complex flexible nonlinear systems cfnss based on a fuzzy singularly perturbed model a standard discrete time fuzzy singularly perturbed model fspm is firstly constructed to estimate cfnss based on a matrix spectral norm approach a static output feedback controller is designed which guarantees the resulting closed loop system is asymptotically stable the gains of controllers are obtained by solving a set of e independent linear matrix inequalities lmis so the ill conditioned problems caused by e can be easily avoided finally the proposed approach is applied to modeling and attitude control of flexible satellites in contrast to the existing results the proposed method has the following advantages i flexible vibrations can be effectively suppressed and ii the control performance is greatly improved as well as iii the control inputs do not need to be limited in controller design two practical examples are provided to illustrate the effectiveness of the presented approach from the simulation results it can be seen that the proposed approach can also effectively overcome the external disturbances and noises

fuzzy input output controllers are universal approximators abstract in this paper we show that a fuzzy input output controller can approximate to any degree of accuracy a continuous fuzzy system this generalizes the known result that fuzzy controllers crisp input output can approximate continuous functions

shift variance measures for multirate lpsv filter banks with random input signals the linear periodically shift variant lpsv properties within critically sampled multirate fir filter banks are generally analysed using deterministic signals periodic shift variance is however closely related to cyclostationarities introduced by the lpsv system into originally wide sense stationary wss random signals passing through the system we provide first a unified framework to measure both shift variance of the lpsv system and the amount of cyclostationarity it generates in this respect the key concept is the covariance operator associated to a random variable cyclostationarity of the variable translates to lpsv properties of the operators and vice versa we study several related concepts for the quantification of shift variance in operators and their interpretation in the stochastic setting we then introduce a new concept called expected shift variance fourier analytic expressions for the various measures are given and subsequently used to derive explicit formulae for the case of critically sampled two channel filter banks as well as sharp upper bounds for unitary two channel filter banks numerical evaluations of the measures show that they provide largely consistent rankings between various critically sampled two channel filter banks

statistical tests for presence of cyclostationarity the presence of kth order cyclostationarity is defined in terms of nonvanishing cyclic cumulants or polyspectra relying upon the asymptotic normality and consistency of kth order cyclic statistics asymptotically optimal spl chi sup 2 tests are developed to detect the presence of cycles in the kth order cyclic cumulants or polyspectra without assuming any specific distribution on the data constant false alarm rate tests are derived in both time and frequency domain and yield consistent estimates of possible cycles present in the kth order cyclic statistics explicit algorithms for k spl les 4 are discussed existing approaches are rather empirical and deal only with k spl les 2 case simulation results are presented to confirm the performance of the given tests

finite time h_ infty filtering for t s fuzzy discrete time systems with time varying delay and norm bounded uncertainties in this paper we investigate the filtering problem of discrete time takagi sugeno t s fuzzy uncertain systems subject to time varying delays a reduced order filter is designed with the augmentation technique a filtering error system with delayed states is obtained in order to deal with time delays in system states the filtering error system is first transformed into two interconnected subsystems by using a two term approximation for the time varying delay sufficient delay dependent conditions of finite time boundedness and h infty performance of the filtering error system are derived with the lyapunov function based on these conditions the filter design methods are proposed and the filter gain matrices can be obtained by calculating a set of linear matrix inequalities a numerical example is used to illustrate the effectiveness of the proposed approaches

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

optimal design of multichannel equalizers for the structural similarity index the optimization of multichannel equalizers is studied for the structural similarity ssim criteria the closed form formula is provided for the optimal equalizer when the mean of the source is zero the formula shows that the equalizer with maximal ssim index is equal to the one with minimal mean square error mse multiplied by a positive real number which is shown to be equal to the inverse of the achieved ssim index the relation of the maximal ssim index to the minimal mse is also established for given blurring filters and fixed length equalizers an algorithm is also presented to compute the suboptimal equalizer for the general sources various numerical examples are given to demonstrate the effectiveness of the results

output feedback control for t s fuzzy delta operator systems with time varying delays via an input output approach in this paper the problem of induced l 2 disturbance attenuation control is investigated for discrete time takagi sugeno t s fuzzy delta operator systems with time varying delays and disturbance input via an input output approach a model transformation method is utilized to approximate the time varying delay in t s fuzzy delta operator systems by applying the scaled small gain ssg theorem and lyapunov krasovskii functional approach a sufficient condition is established to guarantee that the closed loop system is asymptotically stable and has an induced l 2 disturbance attenuation performance the existence condition of the dynamic output feedback controller can be solved via convex optimization problems finally simulation results are given to demonstrate the feasibility and effectiveness of the proposed method

bifrequency and bispectrum maps a new look at multirate systems with stochastic inputs in multirate digital signal processing we often encounter decimators interpolators and complicated interconnections of these with lti filters we also encounter cyclo wide sense stationary cwss processes and linear periodically time varying ptv systems it is often necessary to understand the effects of multirate systems on the statistical properties of their input signals some of these issues have been addressed earlier for example it has been shown that a necessary and sufficient addition for the output of an l fold interpolation filter to be wide sense stationary wss for all wss inputs is that the filter was an alias free l support however several questions of this nature remain unanswered for example what is the necessary and sufficient condition on a pair or more generally a bank of interpolation filters so that their outputs are jointly wss jwss for all jointly wss inputs what is the condition if only the sum of their outputs is required to be wss when is the output of an lptv system for example a uniform filter bank wss for all wss inputs some of these questions may appear to be simple generalizations of the above mentioned result for a single interpolation filter however the frequency domain approaches that proved this result are quite difficult to generalize to answer these questions the purpose of this paper is to provide these answers using analysis based on bifrequency maps and bispectra these tools are two dimensional 2 d fourier transforms that characterize linear time varying ltv systems and nonstationary random processes respectively we show that the questions raised above are addressed elegantly and in a geometrically insightful way using these tools we also derive a bifrequency characterization lossless ltv systems this may potentially lead to an increased understanding of these systems

dynamic output feedback h control synthesis for discrete time t s fuzzy systems via switching fuzzy controllers this paper studies the problem of dynamic output feedback h control of discrete time takagi sugeno t s fuzzy systems via a switched dynamic parallel distributed compensation dpdc scheme the considered switched dpdc control structure is determined based on the values of membership functions some new properties of membership functions are obtained and exploited to derive sufficient conditions for designing switching dpdc controllers that guarantee the stability and h performances of closed loop nonlinear systems the design conditions are given in terms of solvability of a set of linear matrix inequalities lmis it is shown that the new approach provides results at least as good as the corresponding dpdc methods a numerical example is given to illustrate the effectiveness of the proposed approach

p values maximized over a confidence set for the nuisance parameter abstract for testing problems of the form h 0 v v 0 with unknown nuisance parameter various methods are used to deal with the simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance in other problems such as the 2 2 contingency table one conditions on a sufficient statistic for 0 and proceeds as in fisher s exact test because neither of these standard methods is appropriate for all situations this article suggests a new method for handling the unknown this new method is a simple modification of the formal definition of a p value that involves taking a maximum over the nuisance parameter space of a p value obtained for the case when is known the suggested modification is to restrict the maximization to a confidence set for the nuisance parameter after giving a brief justification we give various examples to show how this new method gives improved results for 2 2 tabl

closed testing procedures for group sequential clinical trials with multiple endpoints summary a simple approach is given for conducting closed testing in clinical trials with multiple end points in which group sequential monitoring is planned the approach allows a flexible stopping time the earliest and latest stopping times are described the paradigm is applicable both to clinical trials with multiple endpoints and to the one sided multiple comparison problem of several treatments versus a control the approach leads to enhancements of previous methods and suggestions for new methods an example of a respiratory disease trial with four endpoints is given

on observer based fault detection for nonlinear systems abstract this paper addresses analysis and integrated design of observer based fault detection fd for nonlinear systems to gain a deeper insight into the observer based fd framework definitions and existence conditions for nonlinear observer based fd systems are studied first then a scheme for an integrated design of observer based fd systems for affine nonlinear systems is proposed our work is considerably inspired by the study on input output stability and stabilization of nonlinear systems examples are given at the end of the paper to illustrate the theoretical results

on spectral theory of cyclostationary signals in multirate systems this paper studies two problems in the spectral theory of discrete time cyclostationary signals the cyclospectrum representation and the cyclospectrum transformation by linear multirate systems four types of cyclospectra are presented and their interrelationships are explored in the literature the problem of cyclospectrum transformation by linear systems was investigated only for some specific configurations and was usually developed with inordinate complexities due to lack of a systematic approach a general multirate system that encompasses most common systems linear time invariant systems and linear periodically time varying systems is proposed as the unifying framework more importantly it also includes many configurations that have not been investigated before e g fractional sample rate changers with cyclostationary inputs the blocking technique provides a systematic solution as it associates a multirate system with an equivalent linear time invariant system and cyclostationary signals with stationary signals thus the original problem is elegantly converted into a relatively simple one which is solved in the form of matrix multiplication

robust control design for nonlinear stochastic partial differential systems with poisson noise fuzzy implementation abstract this study addresses the robust h control design problem for nonlinear stochastic partial differential systems nspdss with poisson noise under the environment of random external disturbance in the spatio temporal domain for nspdss with poisson noise the robust h control design needs to solve a complex hamilton jacobi integral inequality hjii for robust control despite random external disturbance in general it is very difficult to solve the nonlinear partial differential hjii in order to simplify the design procedure a fuzzy stochastic partial differential system is proposed to approximate the nspds based on fuzzy interpolation approach then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semi discretization finite difference scheme and the kronecker product based on this model the robust h control design is proposed to achieve the robust control of nspdss via solving linear matrix inequalities lmis instead of an hjii the proposed robust fuzzy h controller has an efficient ability to attenuate the effect of spatio temporal external disturbance on the controlled output of nspdss from the area energy point of view finally a robust h control of the nervous system is given to confirm the control performance of the proposed robust control design method for nspdss with poisson noise

toeplitz and hankel kernels for estimating time varying spectra of discrete time random processes for a nonstationary random process the dual time correlation function and the dual frequency loeve spectrum are complete theoretical descriptions of second order behavior that is each may be used to synthesize the random process itself according to the cramer loeve spectral representation when suitably transformed on one of its two variables each of these descriptions produces a time varying spectrum this spectrum is in fact the expected value of the rihaczek distribution in this paper we derive two large families of estimators for this spectrum one based on a diagonal toeplitz diagonal dtd factorization of smoothing kernels and the other based on a diagonal hankel diagonal dhd factorization the dtd factorization produces noncoherent averages of the time varying spectrogram and the dhd factorization produces coherent averages some of the dtd estimators may be called time varying power spectrum estimators and some of the dhd estimators may be called time varying wigner ville wv estimators the former may always be implemented as multiwindow spectrum estimators and in some casts they are true time variations on the blackman tukey rosenblatt grenander btgr spectrogram the latter are variations on the stankovic class of wv estimators

h sub spl infin output feedback control of discrete time fuzzy systems with application to chaos control this paper presents an observer based h sub spl infin output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise lyapunov function the basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities lmis that are numerically feasible with commercially available software application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method

challenge of multiple co primary endpoints a new approach there are many disorders where regulatory agencies have required a new treatment to demonstrate efficacy on multiple co primary endpoints all significant at the one sided 2 5 per cent level before accepting the treatment s effect for the disorder this requirement rooted in the intersection union iu test has led many researchers to increase the study sample size to make up for the reduction in the statistical power at the study level unfortunately the increase in sample size could be substantial when the endpoints are minimally correlated and the treatment effects on the multiple endpoints are comparable in this paper we demonstrate that the frequentist concept of controlling the maximum false positive rate even when applied to a restricted null space has only limited success in keeping the sample size increase at a reasonable level we therefore propose an approach that is based on the notion of controlling an average type i error rate by employing an upper bound for the average type i error rate the new approach provides an adjustment to the significance level that depends only on the correlation among the endpoints for the most common case of two or three co primary endpoints the adjusted significance level is at most 5 per cent one sided when the endpoints are moderately correlated we show how sample size could be calculated under the proposed approach and contrast the needed sample size with that required under the iu test we provide additional comments and discuss why the new approach is consistent with the principle requiring evidence of significance in the drug development and approval process

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

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

optimization of filter banks using cyclostationary spectral analysis this paper proposes a design method of optimal biorthogonal fir filter banks that minimize the time averaged mean squared error tamse when the high frequency subband signal is dropped to study filter banks from a statistical point of view cyclostationary spectral analysis is used since the output of the filter bank for a wide sense stationary input is cyclostationary first the cyclic spectral density of the output signal is derived and an expression for the tamse is presented then optimal filter banks are given by minimizing the tamse with respect to the coefficients of the filters under the biorthogonality condition by imposing the additional constraints on the coefficients the optimal biorthogonal linear phase filter bank can be obtained

hierarchical testing of multiple endpoints in group sequential trials we consider the situation of testing hierarchically a key secondary endpoint in a group sequential clinical trial that is mainly driven by a primary endpoint by mainly driven we mean that the interim analyses are planned at points in time where a certain number of patients or events have accrued on the primary endpoint and the trial will run either until statistical significance of the primary endpoint is achieved at one of the interim analyses or to the final analysis we consider both the situation where the trial is stopped as soon as the primary endpoint is significant as well as the situation where it is continued after primary endpoint significance to further investigate the secondary endpoint in addition we investigate how to achieve strong control of the familywise error rate fwer at a pre specified significance level alpha for both the primary and the secondary hypotheses we systematically explore various multiplicity adjustment methods starting point is a naive strategy of testing the secondary endpoint at level alpha whenever the primary endpoint is significant hung et al j biopharm stat 2007 17 1201 1210 have already shown that this naive strategy does not maintain the fwer at level alpha we derive a sharp upper bound for the rejection probability of the secondary endpoint in the naive strategy this suggests a number of multiple test strategies and also provides a benchmark for deciding whether a method is conservative or might be improved while maintaining the fwer at alpha we use a numerical example based on a real case study to illustrate the results of different hierarchical test strategies

adaptive extensions of a two stage group sequential procedure for testing primary and secondary endpoints ii sample size re estimation in this part ii of the paper on adaptive extensions of a two stage group sequential procedure gsp proposed by tamhane mehta and liu 1 referred to as tml hereafter for testing a primary and a secondary endpoint we focus on the second stage sample size re estimation based on thefirst stage data first we show that if we use the cui huang and wang 2 referred to as chw hereafter statistics at the second stage then we can use the same primary and the secondary boundaries as for the original procedure without sample size re estimation and still control the type i familywise error rate fwer this extends their result for the single endpoint case we further show that the secondary boundary can be sharpened in this case by taking the unknown correlation coefficient between the primary and secondary endpoints into account through the use of the confidence limit method proposed in part i of this paper 3 if we use the sufficient statistics instead of the chw statistics then we need to modify both the primary and secondary boundaries otherwise the error rate can get inflated we show how to modify the boundaries of the original gsp to control the fwer power comparisons between competing procedures are provided the procedures are illustrated with a clinical trial example copyright c 0000 john wiley sons ltd

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

identification of systems with cyclostationary input and correlated input output measurement noise an alternative approach to wiener s optimum filtering theory for stationary random time series that is applicable when the system input exhibits cyclostationarity is presented this alternative approach can in principle eliminate performance degradation due to input output corruption this method of system identification is called the speccorr spectral correlation ratio method since the cross spectra in the ratio are actually spectral correlation functions an application to interference tolerant time difference of arrival estimation is described and illustrated by simulation results showing its effectiveness for system identification with severely corrupted input output measurements a comparison of wiener s method to the speccorr method shows the superior performance of the latter

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

adaptive group sequential design with population enrichment in phase 3 randomized controlled trials with two binary co primary endpoints the use of co primary endpoints in drug development allows investigators to capture an experimental intervention s multidimensional effect more comprehensively than a single primary endpoint we propose the theoretical basis and development of an adaptive population enrichment design with co primary endpoints provide stage wise boundary values for futility and efficacy and discuss power under different efficacy configurations subgroup prevalence and analysis times using a pre specified decision criterion we considered a two arm two stage parallel group design where population enrichment occurs at the interim analysis by dropping any non responsive subgroups a test for efficacy is conducted only in the enriched population two binary endpoints are evaluated as co primary endpoints our trial objective is to determine whether the experimental intervention is superior to the control intervention with superiority required in both endpoints we define the stopping boundary using alpha spending functions using a 0 025 significance level for each endpoint we obtain the stage i threshold boundary values for futility and efficacy as 0 1040 and 2 2761 respectively and the stage ii boundary value for futility and efficacy is 2 2419 we show that in the presence of substantial heterogeneity of treatment effect we gain more power to observe an effect in the subgroup where the benefits are greater by allowing the dropping of non responsive subgroups at an early stage our design reduces the likelihood of obtaining false negative results due to inclusion of the heterogeneous treatment effects of both subgroups which would dilute the responsive subgroup s results

method of balanced adjustment in testing co primary endpoints in a clinical trial if there are three or more co primary endpoints the type ii error could increase depending on the correlation among the endpoints and their treatment effect sizes to keep the type ii error under control one may have to consider larger sample sizes however in cases where treatment effect size of at least one of the endpoints is likely to be small the required sample size estimates can exceed reasonable bounds patel 1991 proposed an approach that adjusts the significance level for testing each primary endpoint based on the idea of restricting the null space in chuang stein et al 2007 the upward adjustment to the significance levels is based on controlling an average type i error rate in the scenario that statistical significance of each individual hypothesis is not required we introduce a compromise testing approach in which the significance level for a co primary endpoint is adjusted upward only if the treatment shows high significance in one or more than one of the remaining co primary endpoints the adjustment depends on the correlation among the endpoints larger adjustment is needed for cases of smaller correlation the method is applicable for the scenario where the null space is restricted our testing approach controls maximum joint false positive rate over the restricted null space

sample size determination in group sequential clinical trials with two co primary endpoints we discuss sample size determination in group sequential designs with two endpoints as co primary we derive the power and sample size within two decision making frameworks one is to claim the test intervention s benefit relative to control when superiority is achieved for the two endpoints at the same interim timepoint of the trial the other is when superiority is achieved for the two endpoints at any interim timepoint not necessarily simultaneously we evaluate the behaviors of sample size and power with varying design elements and provide a real example to illustrate the proposed sample size methods in addition we discuss sample size recalculation based on observed data and evaluate the impact on the power and type i error rate copyright 2014 john wiley sons ltd

modification of sample size in group sequential clinical trials in group sequential clinical trials sample size reestimation can be a complicated issue when it allows for change of sample size to be influenced by an observed sample path our simulation studies show that increasing sample size based on an interim estimate of the treatment difference can substantially inflate the probability of type i error in most practical situations a new group sequential test procedure is developed by modifying the weights used in the traditional repeated significance two sample mean test the new test has the type i error probability preserved at the target level and can provide a substantial gain in power with the increase of sample size generalization of the new procedure is discussed

cyclo period estimation for discrete time cyclo stationary signals this paper presents a new method named as the variability method to estimate the cyclo period of a discrete time cyclo stationary signal the method is essentially based on the time varying correlation and or the time varying mean whose estimators are associated with some statistics of blocked signals a plot of variability of these statistics as a function of the blocking operator index visually reveals a periodic pattern from which the cyclo period is obtained properties of the variability method are analyzed and compared with three existing cyclo period estimation methods via simulation and real life examples

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

robust model predictive control for discrete time takagi sugeno fuzzy systems with structured uncertainties and persistent disturbances in this paper robust model predictive control for uncertain discrete time takagi sugeno t s fuzzy systems with input constraints and persistent disturbances is considered the robust positively invariant set for t s fuzzy systems is investigated based on this result computation of the terminal constraint set is proposed which is of crucial importance in the robust predictive controller design a zero step predictive controller is discussed first which has a time varying terminal constraint set the recursive feasibility and input to state stability can be ensured then a novel controller with n step prediction is further proposed which can be used to deal with the case of fixed terminal constraint set the implementation of the n step controller involves both online and offline computations it is shown that a sequence of approximating robust one step sets can be computed offline then bisection searches are carried out online as well as a constrained convex optimization problem the n step controller guarantees that the system state can be steered to the terminal constraint set in less than n steps if the initial state lies in a specific region simulation results are finally presented to show the effectiveness of the proposed controllers

universal fuzzy controllers a collection b of fuzzy controllers is a universal fuzzy controller if and only if given any controllable process p it can also be controlled by some fuzzy controller in b this paper identifies a new type of universal fuzzy controller

mamdani type fuzzy controllers are universal fuzzy controllers abstract this paper addresses the issues of universal fuzzy controllers and shows that the mamdani type fuzzy controllers are universal fuzzy controllers furthermore a constructive procedure is also presented to obtain the universal fuzzy controller if the reference fuzzy model is given

filter design for interval type 2 fuzzy systems with d stability constraints under a unified frame this paper investigates the problem of filter design for interval type 2 it2 fuzzy systems with d stability constraints based on a new performance index attention is focused on solving the h infty l 2 l infty passive and dissipativity fuzzy filter design problems for it2 fuzzy systems with d stability constraints in a unified frame under the new performance index frame using lyapunov stability theory a novel type of it2 filter is designed such that the filtering error system guarantees the prescribed h infty l 2 l infty passive and dissipativity performance levels with d stability constraints the existence condition of the it2 filter is expressed as the convex optimization problem and the filter parameters in the condition can be solved by the standard software the it2 fuzzy model and it2 fuzzy filter do not need to share the same lower and upper membership functions finally a numerical example is provided to show the effectiveness of the proposed results

mean based fuzzy identifier and control of uncertain nonlinear systems a mean based adaptive fuzzy control scheme with state estimation performance is proposed for a class of uncertain nonlinear systems in the presence of only output measurement in the control scheme a mean based fuzzy identifier without prior knowledge of membership functions is merged into direct adaptive controller with a linear state estimator the structure of the mean based fuzzy identifier is nonlinear in the adjusted parameters in order to diminish the unfavorable influence of initially designing membership functions on control performance for the nonlinear structure a mean method is used to derive adaptive laws compared with conventional methods the advantage of the mean method is that the computation burden can be effectively alleviated because finding the derivative of fuzzy systems is not required in addition for the linear state estimator the state estimation performance with beforehand given attenuation parameter is established by the design of a compensative controller finally two examples are provided to demonstrate the applicability of the proposed scheme

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

sample size determination in clinical trials with multiple co primary binary endpoints clinical trials often employ two or more primary efficacy endpoints one of the major problems in such trials is how to determine a sample size suitable for multiple co primary correlated endpoints we provide fundamental formulae for the calculation of power and sample size in order to achieve statistical significance for all the multiple primary endpoints given as binary variables on the basis of three association measures among primary endpoints we discuss five methods of power and sample size calculation the asymptotic normal method with and without continuity correction the arcsine method with and without continuity correction and fisher s exact method for all five methods the achieved sample size decreases as the value of association measure increases when the effect sizes among endpoints are approximately equal in particular a high positive association has a greater effect on the decrease in the sample size on the other hand such a relationship is not very strong when the effect sizes are different

approximately optimal one parameter boundaries for group sequential trials we present a class of group sequential tests indexed by a single parameter that yields approximately optimal results we also provide tables of key values to help in the design of group sequential tests that meet selected specifications

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

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

nonuniform multirate filter banks analysis and design with an spl hscr sub spl infin performance measure a general multirate filter bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst case energy gain spl hscr sub spl infin norm of the error system between the multirate system and a pure time delay system using blocking and polyphase decomposition we associate with the multirate system an equivalent linear time invariant lti system whose transfer matrix can be computed by a simple procedure based on this lti system the optimal design problem can be reduced to one of spl hscr sub spl infin optimization which can be solved by ready made software in many cases for illustration optimal synthesis filters are designed for a two channel example and their properties are studied in detail

universal fuzzy integral sliding mode controllers based on t s fuzzy models this paper addresses the universal fuzzy integral sliding mode controllers problem for continuous time multi input multi output nonlinear systems based on takagi sugeno t s fuzzy models by using the approximation capability of t s fuzzy models the nonlinear systems are expressed by uncertain t s fuzzy models with norm bounded approximation errors a novel fuzzy dynamic integral sliding mode control dismc scheme is then developed for the nonlinear systems based on their t s fuzzy approximation models one of the key features of the new dismc scheme is that the restrictive assumption that all local linear systems share a common input matrix which is required in most existing fuzzy integral sliding mode control ismc approaches is removed furthermore the results of universal fuzzy ismcs for two classes of nonlinear systems along with constructive procedures to obtain the universal fuzzy ismcs are provided respectively finally the advantages and effectiveness of the proposed approaches are illustrated via a numerical example

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

second order statistical characterization of the filter bank and its elements this correspondence proposes an alternative scheme for characterizing the wide sense cyclostationary wscs processes and applies it for the analysis of the filter banks whose output is wscs for wide sense stationary and wscs inputs the proposed representation clearly illustrates the kind of transformation taking place in multiscale stochastic systems these relationships are extended to the filter bank to make clear the effect of the various stages of the filter bank on wscs processes

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

a group sequential holm procedure with multiple primary endpoints we propose a group sequential holm procedure when there are multiple primary endpoints this method addresses multiplicities arising from multiple primary endpoints and from multiple analyses in a group sequential design it has been shown to be a closed testing procedure and preserves the familywise error rate in the strong sense when multiple endpoints are the only concern without an interim analysis the method simplifies to the weighted holm procedure the proposed method is more powerful than the parallel group sequential method and avoids the need to anticipate the testing order as in the fixed sequence testing scheme

design of multichannel nonuniform transmultiplexers using general building blocks the paper considers design of multichannel nonuniform band transmultiplexers it is well known that using traditional building blocks up and downsamplers and linear time invariant lti causal filters nonuniform transmultiplexers typically do not achieve perfect reconstruction to alleviate this we propose to build nonuniform transmultiplexers using general dual rate structures that provide more design freedom and hence perfect reconstruction can be achieved such general transmultiplexers have a new source of error called aliasing distortion in addition to the traditional cross talk magnitude and phase distortions we propose a composite error criterion that captures all four distortions in one using this error criterion as reconstruction performance measure we develop an optimal design procedure and apply it to a three channel nonuniform example yielding an fir transmultiplexer that has good frequency limiting properties in the synthesis end and is very close to perfect reconstruction

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