a robust observer for discrete time nonlinear systems abstract this paper extends the results developed in ciccarella et al 1993 and presents a robust observer for discrete time nonlinear systems a simple robust and easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems combined parameter and state estimation is made for a numerical example which compares the robust observer to the observer given in ciccarella et al 1993

remarks on linearization of discrete time autonomous systems and nonlinear observer design abstract this paper presents necessary and sufficient conditions under which a discrete time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form krener and isidori 1983 in particular an open problem raised in lee and nam 1991 namely the observer linearization problem is solved for a nonlinear system which may not be invertible i e the mapping f may not be a local diffeomorphism as a consequence the nonlinear observer design problem is solved by means of exact linearization techniques

a donsker varadhan type of invariance principle letx 1 x 2 h be i i d random variables in the domain of attraction of a stable lawg and denote sn x1 xn ln a n 1 l n omega a n 1 sum limits j 0 n 1 chi a s j mathord left vphantom s j a n right kern nulldelimiterspace a n satisfiesa n 1 s n g large deviation probability estimates of donsker varadhan type are obtained forl n and these are then used to study the behavior of small values of s n a n these latter results are analogues of strassen s results which described the behavior of large values of s n a n when the limit law was gaussian the limiting constants are seen to depend only on the limit lawg and not on the distribution ofx 1 the techniques used are those developed by donsker and varadhan in their theory of large deviations

observer design for autonomous discrete time nonlinear systems abstract we obtain a necessary and sufficient condition for a discrete time nonlinear system to be locally state equivalent to the nonlinear observer form the result looks similar to the continuous counterpart except for the fact that ad operation is utilized instead of ad operation

nonlinear discrete time observer design with linearizable error dynamics a necessary and sufficient condition for the existence of a discrete time nonlinear observer with linearizable error dynamics is provided the result can be applied to any real analytic nonlinear system whose linear part is observable the necessary and sufficient condition is the solvability of a nonlinear functional equation furthermore the well known siegel s theorem on the linearizability of a mapping is naturally reproduced in a corollary the proposed observer design method is constructive and can be applied approximately to any sufficiently smooth linearly observable system yielding a local observer with approximately linear error dynamics

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

restricted dynamic observer error linearizability following the general dynamic observer error linearization problem state equivalence to a triangular nonlinear observer canonical form with index d and the restricted dynamic observer error linearization problem are defined in this paper the necessary and sufficient conditions for the above two problems are given since our proofs are constructive a desired state transformation can also be found in the theorem

upper bounds for ergodic sums of infinite measure preserving transformations for certain conservative infinite measure preserving transformations t we identify increasing functions a for which lim sup n 1 a n k 1 n f o t k x fd a e holds for any nonnegative integrable function f in particular the results apply to some markov shifts and number theoretic transformations and include the other law of the iterated logarithm

regression splines for threshold selection in survival data analysis the cox proportional hazards model restricts the hazard ratio to be linear in the covariates a survival model based on data from a clinical trial is developed using spline functions with variable knots to estimate the log hazard function moreover the main point of the method is that a knot seen as free parameters for a piecewise linear spline represents a break point in the log hazard function which may be interpreted as a threshold value the likelihood ratio test is used to select the final model and to determine the threshold number for a covariate confidence intervals for these threshold values are computed by bootstrapping the data two examples illustrate the method

an invariance principle for the local time of a recurrent random walk let s j be a lattice random walk i e s j x 1 x j where x 1 x 2 are independent random variables with values in the integer lattice and common distribution f and let l n omega k sum limits j 0 n 1 chi k s j omega the local time of the random walk at k before time n suppose ex 1 0 and f is in the domain of attraction of a stable law g of index 1 i e there exists a sequence a n necessarily of the form n 1 l n where l is slowly varying such that s n a n g define g n omega u frac c n n l n omega uc n where c n a n log log n and x greatest integer x then we identify the limit set of g n n 1 almost surely with a nonrandom set in terms of the i functional of donsker and varadhan the limit set is the one that donsker and varadhan obtain for the corresponding problem for a stable process several corollaries are then derived from this invariance principle which describe the asymptotic behavior of l n as n

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

algebraic conditions for state equivalence to a discrete time nonlinear observer canonical form abstract algebraic necessary and sufficient conditions for a single output discrete time system to be state equivalent to a generalized nonlinear observer canonical form with or without output transformation are derived our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry in addition our proofs are constructive and contain the state and output transformations for generalized nonlinear observer canonical forms

linearization of discrete time systems abstract we characterize the equivalence of single input single output discrete time nonlinear systems to linear ones via a state coordinate change and with or without feedback four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not the interdependence of these problems is analyzed an important feature that distinguishes these discrete time problems from the corresponding problem in continuous time is that the state coordinate transformation is here directly computable as a higher composition of the system and output maps finally certain connections are made with the continuous time case

sampled data observer error linearization the effects of time sampling on the solvability conditions for the observer linearization design methodology are investigated it is shown that the class of systems for which this design method can be applied for an open set of sampling times is quite small in particular when the dimension of the state space is two it consists only of those systems that are state equivalent to a linear system the practical implication is that digital implementations of this methodology will have to be approximate

discrete time observer error linearizability via restricted dynamic systems in this technical note we define the observer error linearization problem of a discrete time autonomous nonlinear system via a restricted dynamic system this is the dual to restricted dynamic feedback linearization in a loose sense necessary and sufficient conditions for this problem are obtained in terms of the index

necessary and sufficient conditions for state equivalence to a nonlinear discrete time observer canonical form in this technical note we obtain necessary and sufficient conditions for a multi input multi output discrete time nonlinear system to be state equivalent to a nonlinear observer form and for an uncontrolled multi output system to be state equivalent to a linear observer form we adopt a geometric approach and the proofs are constructive with respect to the required coordinate change

segmented regression with errors in predictors semi parametric and parametric methods we consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors with a focus on linear and logistic regression in epidemiologic studies segmented regression models often occur as threshold models where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold furthermore in occupational and environmental studies the exposure typically cannot be measured exactly ignoring this measurement error leads to asymptotically biased estimators of the threshold it is shown that this asymptotic bias is different from that observed for estimating standard generalized linear model parameters in the presence of measurement error being both larger and in different directions than expected in most cases considered the threshold is asymptotically underestimated two standard general methods for correcting for this bias are considered regression calibration and simulation extrapolation simex in ordinary logistic and linear regression these procedures behave similarly but in the threshold segmented regression model they operate quite differently the regression calibration estimator usually has more bias but less variance than the simex estimator regression calibration and simex are typically thought of as functional methods also known as semi parametric methods because they make no assumptions about the distribution of the unobservable covariate x the contrasting structural parametric maximum likelihood estimate assumes a parametric distributional form for x in ordinary linear regression there is typically little difference between structural and functional methods one of the major surprising findings of our study is that in threshold regression the functional and structural methods differ substantially in their performance in one of our simulations approximately consistent functional estimates can be as much as 25 times more variable than the maximum likelihood estimate for a properly specified parametric model structural parametric modelling ought not be a neglected tool in measurement error models an example involving dust concentration and bronchitis in a mechanical engineering plant in munich is used to illustrate the results 1997 by john wiley sons ltd

non linear observer design by observer canonical forms this paper studies the non linear observer design problem by observer canonical forms we present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non linear state coordinate change under which a time variable system is transformed into an observer canonical form these conditions give the multiple versions of li and tao 1986 for the single output case then a comparison is made with the lie algebraic conditions obtained by krener and respondek 1985 and modified by the authors in a recent paper xia and gao 1987

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

observability and controllability for smooth nonlinear systems the definition of a smooth nonlinear system as proposed recently by willems is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input output system mini

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

bayesian analysis of logistic regression with an unknown change point and covariate measurement error we discuss bayesian estimation of a logistic regression model with an unknown threshold limiting value tlv in these models it is assumed that there is no effect of a covariate on the response under a certain unknown tlv the estimation of these models in a bayesian context by markov chain monte carlo mcmc methods is considered with focus on the tlv we extend the model by accounting for measurement error in the covariate the bayesian solution is compared with the likelihood solution proposed by kuchenhoff and carroll using a data set concerning the relationship between dust concentration in the working place and the occurrence of chronic bronchitis

erratum nonlinear observer design in the siegel domain there is an error in the proof of the main result of our paper siam j control optim 41 2002 pp 932 953 an additional assumption is needed for the main result to hold in this erratum we supply a corrected version of the main result

discrete time nonlinear observer design using functional equations abstract the present research work proposes a new approach to the discrete time nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer the proposed approach develops a nonlinear analogue the formulation of the discrete time nonlinear observer design problem is realized via a system of first order linear nonhomogeneous functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

verifiable conditions for multioutput observer error linearizability the verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades in this technical note we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature using these conditions a verifiable sufficient condition also necessary with additional restriction on the problem is derived since our proofs are constructive a desired state transformation can also be found in the theorem also our algorithmic conditions can be easily implemented by a matlab programming

on the observer design in discrete time abstract the paper deals with the equivalence under coordinates change and output transformation of a discrete time nonlinear system to observer canonical forms necessary and sufficient conditions for local equivalence to these forms are given

threshold dose response models in toxicology summary after a brief discussion of the threshold concept in toxicology we consider models for the estimation of thresholds in the case where the observed response is binary or quantal a generalization of the four parameter tukey lambda family of distributions is proposed as a useful class of models for threshold estimation properties of these models are discussed and the process of model fitting and evaluation is illustrated using a number of data sets the discussion includes consideration of background or spontaneous response and comparison with other models one of these is the linearplateau or hockey stick model which has been used in a number of toxicological studies

estimating regression models with unknown break points this paper deals with fitting piecewise terms in regression models where one or more break points are true parameters of the model for estimation a simple linearization technique is called for taking advantage of the linear formulation of the problem as a result the method is suitable for any regression model with linear predictor and so current software can be used threshold modelling as function of explanatory variables is also allowed differences between the other procedures available are shown and relative merits discussed simulations and two examples are presented to illustrate the method

a statistical method for assessing a threshold in epidemiological studies i describe a method for estimating and testing a threshold value in epidemiological studies a threshold effect indicates an association between a risk factor and a defined outcome above the threshold value but none below it an important field of application is occupational medicine where for a lot of chemical compounds and other agents which are non carcinogenic health hazards so called threshold limit values or tlvs are specified the method is presented within the framework of the logistic regression model which is widely used in the analysis of the relationship between some explanatory variables and a dependent dichotomous outcome in most available programs for this and also for other models the concept of a threshold is disregarded the method for assessing a threshold consists of an estimation procedure using the maximum likelihood technique and a test procedure based on the likelihood ratio statistic r following under the null hypothesis no threshold a quasi one sided chi 2 distribution with one degree of freedom this use of this distribution is supported by a simulation study the method is applied to data from an epidemiological study of the relationship between occupational dust exposure and chronic bronchitic reactions the results are confirmed by bootstrap resampling

nonlinear observer design in the siegel domain we extend the method of kazantzis and kravaris systems control lett 34 1998 pp 241 247 for the design of an observer to a larger class of nonlinear systems the extended method is applicable to any real analytic observable nonlinear system it is based on the solution of a first order singular nonlinear pde this solution yields a change of state coordinates which linearizes the error dynamics under very general conditions the existence and uniqueness of the solution is proved lyapunov s auxiliary theorem and siegel s theorem are obtained as corollaries the technique is constructive and yields a method for constructing approximate solutions