global stabilization for a class of switched nonlinear feedforward systems abstract the problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper based on the integrator forwarding technique and the common lyapunov function method we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed loop system a common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

analysing repeated measurements with possibly missing observations by modelling marginal distributions suppose that subjects are observed repeatedly over a common set of time points with possibly time dependent covariates and possibly missing observations at each time point we model the marginal distribution of the response variable and the effect of the covariates on that distribution using a class of quasi likelihood models studied in mccullagh and nelder no parametric model of dependence of the repeated observations of the subject is assumed for large samples the quasi likelihood estimates of the time specific regression coefficients over the set of predetermined time points are shown to be approximately jointly normal this coupled with various inference procedures provides a global picture about the effects of the covariates on the response variable over the entire study period a lack of fit test for testing the adequacy of the assumed quasi likelihood model is also provided all the methods considered here are illustrated with real life examples

consistency and recovery in electroelasticity part ii equilibrium and mixed finite elements the first part of this paper establishes the concept of consistency for standard finite elements in electroelasticity this has permitted to trace the origin of certain spurious oscillations affecting the finite element response in terms of stress and electric flux density in this second part the consistency analysis is generalized to models which directly involve stress and electric flux density as independent variables the analysis shows that also these models can suffer from spurious outcomes however selecting the approximation functions on consistency basis allows to eliminate or at least reduce the undesired oscillations

consistency and recovery in electroelasticity part i standard finite elements developing finite elements for electroelastic analysis requires a special care as the coupling in the discrete equations depends on the matching between the approximations assumed for mechanical and electrical variables to provide a formal basis to this intuitive remark a notion of consistency is established and a rigorous consistency analysis is presented for the standard finite element model based on assumed displacement and electric potential in this way specific analytical requirements are obtained which serve as a guide to select the interpolation functions for primary variables moreover the analysis shows that violating consistency can be reflected as spurious outcomes upsetting the local distributions of secondary variables indeed this undesirable effect is shown to be typical of the standard approach if stress and electric flux density are computed via the constitutive equations to cure the trouble an alternative recovery procedure is devised based on the consistency analysis the procedure is variationally correct and reconstitutes in a consistent manner the distributions of stress and electric flux density

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

predicting longitudinal trajectories of health probabilities with random effects multinomial logit regression researchers often encounter longitudinal health data characterized with three or more ordinal or nominal categories random effects multinomial logit models are generally applied to account for potential lack of independence inherent in such clustered data when parameter estimates are used to describe longitudinal processes however random effects both between and within individuals need to be retransformed for correctly predicting outcome probabilities this study attempts to go beyond existing work by developing a retransformation method that derives longitudinal growth trajectories of unbiased health probabilities variances of the predicted probabilities are estimated by using the delta method additionally the covariates regression coefficients on the multinomial logit function not substantively meaningful are transformed to the conditional effects on the predicted probabilities the empirical illustration uses the longitudinal data from the asset and health dynamics among the oldest old ahead our analysis compares three sets of the predicted probabilities of three health states at six time points obtained from respectively the retransformation method the blup and the fixed effects approach the results demonstrate that neglect of retransforming random errors in the random effects multinomial logit model results in severely biased longitudinal trajectories of health probabilities as well as overestimated effects of covariates on the probabilities

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

some hybrid variational methods for linear electroelasticity problems two methods for linear electroelastic analysis are presented both supported by a variational formulation of hybrid type for stresses in the first formulation the field variables are stress and density of electric flux and mechanical and electrical equilibria are satisfied a priori in the field in the second formulation the field variables are stress and electric potential and mechanical equilibrium and electrical compatibility are satisfied a priori in the field in both cases the remaining field and boundary conditions are met weakly two finite element models are developed and their performance is examined and compared with the one of the compatible finite element approach in some test cases reported in the literature

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

backstepping design for time varying nonlinear systems with unknown parameters abstract a simple backstepping design procedure is proposed and sufficient conditions for global partial state and dynamic feedback stabilization for a class of triangular systems with unknown time varying parameters are derived

a finite element formulation for piezoelectric shell structures considering geometrical and material non linearities in this paper we present a non linear finite element formulation for piezoelectric shell structures based on a mixed multi field variational formulation an electro mechanical coupled shell element is developed considering geometrically and materially non linear behavior of ferroelectric ceramics the mixed formulation includes the independent fields of displacements electric potential strains electric field stresses and dielectric displacements besides the mechanical degrees of freedom the shell counts only one electrical degree of freedom this is the difference in the electric potential in the thickness direction of the shell incorporating non linear kinematic assumptions structures with large deformations and stability problems can be analyzed according to a reissner mindlin theory the shell element accounts for constant transversal shear strains the formulation incorporates a three dimensional transversal isotropic material law thus the kinematic in the thickness direction of the shell is considered the normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and the resultant dielectric displacement fields accounting for material non linearities the ferroelectric hysteresis phenomena are considered using the preisach model as a special aspect the formulation includes temperature dependent effects and thus the change of the piezoelectric material parameters due to the temperature this enables the element to describe temperature dependent hysteresis curves copyright 2011 john wiley sons ltd

barrier lyapunov functions for the output tracking control of constrained nonlinear switched systems abstract in this paper we investigate the output tracking control problem of constrained nonlinear switched systems in lower triangular form first when all the states are subjected to constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approach some finite limits to prevent the states from violating the constraints based on the simultaneous domination assumption we design a continuous feedback controller for the switched system which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed loop signals remain bounded provided that the initial states are feasible then we further consider the case of asymmetric time varying output constraints by constructing an appropriate blf finally the effectiveness of the proposed results is demonstrated with a numerical example

convexity and convex approximations of discrete time stochastic control problems with constraints we investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time we consider minimization of an expected value cost subject to probabilistic constraints we study the convexity of a finite horizon optimization problem in the case where the control policies are affine functions of the disturbance input we propose an expectation based method for the convex approximation of probabilistic constraints with polytopic constraint function and a linear matrix inequality lmi method for the convex approximation of probabilistic constraints with ellipsoidal constraint function finally we introduce a class of convex expectation type constraints that provide tractable approximations of the so called integrated chance constraints performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example

modelling transitional and joint marginal distributions in repeated categorical data when a repeated measures endpoint classifies people into several categories marginal and transitional models provide two distinct approaches for data analysis marginal models estimate the probabilities of being in different categories over time transitional models estimate the probability of changing between any two given states during follow up visits this paper develops transitional and marginal models and applies them to a clinical trial of treatments of opiate addiction the primary outcome was the presence or absence of opiates in a thrice weekly urine test administered for 17 weeks subjects frequently miss visits however and in effect respond in one of three ways to a visit missing opiates present or opiates absent thus we have three possible states our transitional model conditions on the current state and models the transition from state k to one of the other 0 k 1 states using a mutinomial logit model this model generalizes previous work of muenz and rubinstein significant covariates in this model are predictive of state changes our marginal model views the state at each time point rather than the transitions as the primary response here we model the probability of being in state k with a multinomial logit model correlation within individuals over visits can be handled by applying the approach of zeger and liang or the bootstrap significant covariates in this model can include more global summaries of a person such as extent of previous opiate use both marginal and transitional models are needed to provide a complete description of an individual s behaviour over time since global summaries might not affect transitions of particular substantive interest is how the opiate treatments affect both the marginal and transition probabilities

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

some general methods for the analysis of categorical data in longitudinal studies this paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs an expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets appropriate large sample tests of these hypotheses are developed through the application of weighted least squares to generate wald statistics these procedures are illustrated with extensive analyses of one of these data sets in some situations the resulting cross classification of the response variables leads to extremely sparse frequency data especially when the number of subjects is not large for such repeated measurement designs in which a single variable is measured repeatedly over time this paper considers the use of a generalized mantel haenszel strategy for tests of marginal homogeneity symmetry these randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale this paper also focuses on the available computing software to implement these methods within the version 5 release of the sas system the randomization model approach can be implemented within the freq procedure and a broad range of models and hypotheses can be investigated within the catmod procedure

on time optimal control of integrator switched systems with state constraints abstract in this paper time optimal control problems of a class of integrator switched systems with polyhedral state constraint subsets are studied we first develop a directed graph representation of the system discrete structure based on the graph representation we generate candidate solution paths and propose an algorithm for seeking the optimal solution a linear programming method for finding the optimal timing information for each path is then proposed finally we report preliminary results on some sufficient conditions and techniques which help reduce the number of candidate paths

brief paper backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings this paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings two classes of state feedback controllers and a common lyapunov function clf are simultaneously constructed by backstepping the first class uses the common state feedback controller which is independent of switching signals the other class utilizes individual state feedback controllers for the subsystems as an extension of the designed method the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied an example is given to show the effectiveness of the proposed method

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

brief paper swing up and stabilization of a twin pendulum under state and control constraints by a fast nmpc scheme in this paper a real time implementable nonlinear model predictive control scheme is proposed for the swing up and the stabilization of a twin pendulum system under control and state constraints the basic feature lies in a particular parametrization of the set of candidate control profiles leading to a decision variable that may take only 3 admissible values simulations are proposed to assess the efficiency of the proposed feedback

markov models for covariate dependence of binary sequences suppose that a heterogeneous group of individuals is followed over time and that each individual can be in state 0 or state 1 at each time point the sequence of states is assumed to follow a binary markov chain in this paper we model the transition probabilities for the 0 to 0 and 1 to 0 transitions by two logistic regressions thus showing how the covariates relate to changes in state with p covariates there are 2 p 1 parameters including intercepts which we estimate by maximum likelihood we show how to use transition probability estimates to test hypotheses about the probability of occupying state 0 at time i i 2 t and the equilibrium probability of state 0 these probabilities depend on the covariates a recursive algorithm is suggested to estimate regression coefficients when some responses are missing extensions of the basic model which allow time dependent covariates and nonstationary or second order markov chains are presented an example shows the model applied to a study of the psychological impact of breast cancer in which women did or did not manifest distress at four time points in the year following surgery

on converse lyapunov theorems for iss and iiss switched nonlinear systems abstract in this paper we present converse lyapunov theorems for iss and integral input to state stable iiss switched nonlinear systems their proofs are based on existing converse lyapunov theorems for input output to state stable and iiss nonlinear systems and on the association of the switched system with a nonlinear system with inputs and disturbances that take values in a compact set

testing whether an identified treatment is best summary we consider the problem of testing whether an identified treatment is better than each of k treatments suppose there are univariate test statistics si that contrast the identified treatment with treatment i for i 1 2 k the min test is defined to be the a level procedure that rejects the null hypothesis that the identified treatment is not best when for all i si rejects the one sided hypothesis at the a level that the identified treatment is not better than the ith treatment in the normal case where si are t statistics the min test is the likelihood ratio test for distributions satisfying mild regularity conditions if attention is restricted to test statistics that are monotone nondecreasing functions of si then regardless of their covariance structure the min test is an optimal a level test tables of the sample size needed to achieve power 5 8 90 and 95 are given for the min test when the si are student s t and wilcoxon

a transitional model of barrier methods compliance with unbalanced loss to follow up differential loss to follow up can substantially influence the evaluation of treatment effects on a dichotomous outcome of interest in longitudinal trials the use of transitional models incorporating loss to follow up as an additional category of response and the nature of the correlated responses can provide a comprehensive view of a trial with unbalanced loss to follow up under the markov assumption transitional models estimate the probability of changing from one outcome to another outcome between follow up visits patterns of the response variable can be described by the estimated transition probabilities the effects of intervention and covariates on the outcome of interest can also be estimated using a conditional likelihood function or a multinomial logit regression data from a randomized barrier method study designed to compare the proportion of participants using barrier methods consistently in two counselling groups are used to illustrate the proposed model

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

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

analyzing repeated measures on generalized linear models via the bootstrap the analysis of longitudinal data for which the response variables have nonnormal error distributions previously has been complex and or dependent on restrictive assumptions in this paper simple methods are introduced for the class of generalized linear models glms regressions are fit to the data at each observation time functions of the resulting coefficients may be bootstrapped or the coefficients combined through closed form estimation of their covariances application is made to a data set on xerophthalmia in indonesian children

barrier lyapunov functions for the control of output constrained nonlinear systems in this paper we present control designs for single input single output siso nonlinear systems in strict feedback form with an output constraint to prevent constraint violation we employ a barrier lyapunov function which grows to infinity when its arguments approach some limits by ensuring boundedness of the barrier lyapunov function in the closed loop we ensure that those limits are not transgressed besides the nominal case where full knowledge of the plant is available we also tackle scenarios wherein parametric uncertainties are present asymptotic tracking is achieved without violation of the constraint and all closed loop signals remain bounded under a mild condition on the initial output furthermore we explore the use of an asymmetric barrier lyapunov function as a generalized approach that relaxes the requirements on the initial conditions we also compare our control with one that is based on a quadratic lyapunov function and we show that our control requires less restrictive initial conditions a numerical example is provided to illustrate the performance of the proposed control