a new algorithm for constructing approximate transformations for nonlinear systems an algorithm is provided for constructing an approximating transformation for a feedback linearizable system and for a system that is not feedback linearizable instead of approximating the given nonlinear system the authors approximate the transformation in a proper sense they assume that the lead variables of a transformation have a certain form with unknown parameters substitute these variables into the required equations and determine the unknown parameters through linear algebraic equations there is a tremendous savings in terms of number of equations and unknowns and it is sometimes possible to find exact or best possible transformations in a surprisingly small number of steps

a direct method for the construction of nonlinear discrete time observer with linearizable error dynamics we provide a direct method for the design of nonlinear discrete time observers by a construction of a change of variables an explicit expression of the change of variables is given some simulations for chaotic systems such as lozi system and he spl acute non system are provided to illustrate the proposed method

nonlinear control via uniform system approximation abstract we introduce the notion of uniform system approximation and use it to solve the following problem given a single input nonlinear system f g x f x g x u that is linearly controllable on a manifold e of equilibrium points find vector fields f g such that f g and f g agree to first order on e and f g is input to state linearizable on a neighborhood of e the solution proceeds by constructing a linearizable uniform system approximation and yields as a by product a feedback control law that can be used to guarantee stable operation of the given system in a neighborhood of e this includes for example smooth transitions between operating points that are not necessarily close to each other a simple example is given to illustrate the approach

normal forms and approximated feedback linearization in discrete time abstract the paper discusses approximated feedback linearization of nonlinear discrete time dynamics which are controllable in first approximation and introduces two types of normal forms the study is set in the context of differential difference representations of discrete time dynamics proposed in monaco normand cyrot in normand cyrot ed perspectives in control a tribute to ioan dore landau springer londres 1998 pp 191 205

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

bias analysis and simex approach in generalized linear mixed measurement error models abstract we consider generalized linear mixed models glmms for clustered data when one of the predictors is measured with error when the measurement error is additive and normally distributed and the error prone predictor is itself normally distributed we show that the observed data also follow a glmm but with a different fixed effects structure from the original model a different and more complex random effects structure and restrictions on the parameters this characterization enables us to compute the biases that result in common glmms when one ignores measurement error for instance in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases both for regression coefficients and for variance components parameter estimation is described using the simex method a relatively new functional method that makes no assumptions about the structure of the unobservable predictors simulations and an example illustrate the results

laplace s approximation for nonlinear mixed models summary an approximation to laplace s method for integrals is applied to marginal distributions of data arising from models in which both fixed and random effects enter nonlinearly the approach provides alternative derivations of some recent algorithms for fitting such models and it has direct ties with gaussian restricted maximum likelihood and the accompanying mixed model equations

approximate linearization by state feedback and coordinate change a nonlinear system can always be approximated to first order by linear systems it has been shown by jakubczyk and respondek 4 and hunt and su 3 that certain nonlinear systems are the exact transforms of linear systems under nonlinear state coordinate change and nonlinear state feedback in this paper we give necessary and sufficient conditions for a nonlinear system to be approximated to higher order by the transform of a linear system the use of this technique in the design of nonlinear compensators has been suggested recently by the author 6

one qubit reduced states of a pure many qubit state polygon inequalities we show that a necessary and sufficient condition for a set of n one qubit mixed states to be the reduced states of a pure n qubit state is that their smaller eigenvalues should satisfy polygon inequalities each of them must be no greater than the sum of the others

sampled data state feedback stabilization of boolean control networks in this letter we investigate the sampled data state feedback control sdsfc problem of boolean control networks bcns some necessary and sufficient conditions are obtained for the global stabilization of bcns by sdsfc different from conventional state feedback controls new phenomena observed the study of sdsfc based on the controllability matrix we derive some necessary and sufficient conditions under which the trajectories of bcns can be stabilized to a fixed point by piecewise constant control pcc it is proved that the global stabilization of bcns under sdsfc is equivalent to that by pcc moreover algorithms are given to construct the sampled data state feedback controllers numerical examples are given to illustrate the efficiency of the obtained results

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

feedback classification of multi input nonlinear control systems we study the feedback group action on multi input nonlinear control systems with uncontrollable mode we follow slightly an approach proposed in kang and krener w kang and a j krener siam j control optim 30 1992 pp 1319 1337 which consists of analyzing the system and the feedback group step by step we construct a normal form which generalizes on one hand the results obtained in the single input case and on the other hand those recently obtained by the same author in the controllable case we illustrate our results by studying the caltech multi vehicle wireless testbed mvwt and the prototype of planar vertical takeoff and landing aircraft pvtol we also study the notion of bifurcation of controllability for systems with one nonzero uncontrollable mode we first show that the equilibria for those systems is a p dimensional submanifold p equals number of inputs provided that one term in their normal form is nonzero we show that these systems are linearly controllable hence stabilizable at any nearby equilibrium point of the origin

a note on the use of laplace s approximation for nonlinear mixed effects models the asymptotic properties of estimates obtained using laplace s approximation for nonlinear mixed effects models are investigated unlike the restricted maximum likelihood approach e g wolfinger 1993 here the laplace approximation is applied only to the random effects of the integrated likelihood this results in approximate maximum likelihood estimation the resulting estimates are shown to be consistent with the rate of convergence depending on both the number of individuals and the number of observations per individual conditions under which the leading term laplace approximation should be avoided are discussed

on the existence of quantum representations for two dichotomic measurements under which conditions do outcome probabilities of measurements possess a quantum mechanical model this kind of problem is solved here for the case of two dichotomic von neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics the solution uses methods from the theory of operator algebras and the theory of moment problems the ensuing conditions reveal surprisingly simple relations between certain quantum mechanical probabilities it also shown that generally none of these relations holds in general probabilistic models this result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

exact and approximate feedback linearization without the linear controllability assumption the feedback linearization problem of nonlinear control systems has been solved in the literature under the assumption that the nonlinear system is linearly controllable in this paper the assumption of linear controllability is removed necessary and sufficient conditions are given through lie orbital symmetries thus giving a geometric characterization of the problem in the analytic case both the exact and the approximate linearization problems are considered in the analytic case

random effects logistic regression analysis with auxiliary covariates summary we study a semiparametric estimation method for the random effects logistic regression when there is auxiliary covariate information about the main exposure variable we extend the semiparametric estimator of pepe and fleming 1991 journal of the american statistical association86 108 113 to the random effects model using the best linear unbiased prediction approach of henderson 1975 biometrics31 423 448 the method can be used to handle the missing covariate or mismeasured covariate data problems in a variety of real applications simulation study results show that the proposed method outperforms the existing methods we analyzed a data set from the collaborative perinatal project using the proposed method and found that the use of ddt increases the risk of preterm births among us children

transition probabilities and measurement statistics of postselected ensembles it is well known that a quantum measurement can enhance the transition probability between two quantum states such a measurement operates after preparation of the initial state and before postselecting for the final state here we analyze this kind of scenario in detail and determine which probability distributions on a finite number of outcomes can occur for an intermediate measurement with postselection for given values of the following two quantities i the transition probability without measurement and ii the transition probability with measurement this is done for both the cases of projective measurements and of generalized measurements among other constraints this quantifies a trade off between high randomness in a projective measurement and high measurement modified transition probability an intermediate projective measurement can enhance a transition probability such that the failure probability decreases by a factor of up to 2 but not by more

regression calibration for models with two predictor variables measured with error and their interaction using instrumental variables and longitudinal data regression calibration provides a way to obtain unbiased estimators of fixed effects in regression models when one or more predictors are measured with error recent development of measurement error methods has focused on models that include interaction terms between measured with error predictors and separately methods for estimation in models that account for correlated data in this work explicit and novel forms of regression calibration estimators and associated asymptotic variances are derived for longitudinal models that include interaction terms when data from instrumental and unbiased surrogate variables are available but not the actual predictors of interest the longitudinal data are fit using linear mixed models that contain random intercepts and account for serial correlation and unequally spaced observations the motivating application involves a longitudinal study of exposure to two pollutants predictors outdoor fine particulate matter and cigarette smoke and their association in interactive form with levels of a biomarker of inflammation leukotriene e4 lte4 outcome in asthmatic children since the exposure concentrations could not be directly observed measurements from a fixed outdoor monitor and urinary cotinine concentrations were used as instrumental variables and concentrations of fine ambient particulate matter and cigarette smoke measured with error by personal monitors were used as unbiased surrogate variables the derived regression calibration methods were applied to estimate coefficients of the unobserved predictors and their interaction allowing for direct comparison of toxicity of the different pollutants simulations were used to verify accuracy of inferential methods based on asymptotic theory

stabilization of single input nonlinear systems using piecewise constant controllers the purpose of this note is to present a new approach for stabilizing single input control affine systems for which the robust relative degree equals the dimension of the state space in contrast to the method used in approximate feedback linearization we employ piecewise constant controllers which allows us to account for higher order terms

quadratic forms and approximate feed back linearization in discrete time quadratic feedback linearization is discussed for discrete time systems i e approximate feedback linearization up to the second order with respect to input and state variables after introducing in discrete time two equivalence classes invariant under quadratic static state feedback and diffeomorphism two canonical quadratic representations are proposed then it is shown that any nonlinear discrete time dynamics which are controllable in their first approximations can be linearized up to the second order under dynamic feedback the results stated here can be considered as the general discrete time analogues of the continuous time ones kang and krener 1992

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

a neural approach for control of nonlinear systems with feedback linearization several schemes for feedback linearization using neural networks have been investigated and compared then an approach to design a neurocontroller in the sense of feedback linearization is introduced the contents include 1 full input output linearization when a system has relative degree n 2 partial input output linearization when a system has relative degree r r n and 3 approximate linearization when the involutivity condition does not hold corresponding programs and examples are given to illustrate the proposed methodology

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

controllability distributions and systems approximations a geometric approach given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a taylor series approximation of it the value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant controllability distributions the relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation

correcting for measurement error in individual level covariates in nonlinear mixed effects models summary the nonlinear mixed effects model is used to represent data in pharmacokinetics viral dynamics and other areas where an objective is to elucidate associations among individual specific model parameters and covariates however covariates may be measured with error for additive measurement error we show substitution of mismeasured covariates for true covariates may lead to biased estimators for fixed effects and random effects covariance parameters while regression calibration may eliminate bias in fixed effects but fail to correct that in covariance parameters we develop methods to take account of measurement error that correct this bias and may be implemented with standard software and we demonstrate their utility via simulation and application to data from a study of hiv dynamics