the importance of assessing measurement reliability in multivariate regression abstract in many contexts involving multivariate linear regression models some or all of the independent predictor variables are measured with error it is argued that if the goal is to assess the relationship of the dependent variables to the true predictor variables then it is important to determine the reliability matrix of the measurement x of the vector of true predictors if is singular then the slope matrix b is not identifiable if is nearly singular then b cannot be accurately estimated a two step estimation procedure is proposed in which is estimated from data on the measured predictors x and on prior information from reliability studies on these predictors and the parameters of the latent linear relationship are estimated by classical linear regression methods this approach not only allows the use of available software but also lends itself to traditional diagnostic methods large sample properties of the estimators resulting from this approach are derived it is shown how a c

maximum likelihood estimators and likelihood ratio criteria in multivariate components of variance on obtient des estimateurs sous la condition que la matrice de covariance des effets est semidefinie positive avec un rang maximum le rang de l estimateur etant aleatoire

global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

feedback control of affine nonlinear singular control systems this paper discusses feedback control problems for affine nonlinear singular systems namely the problems of regularization regular singular systems have for a particular initial state and input a unique solution non interaction and exact linearization first an algorithm providing necessary and sufficient conditions for the regularizability of the affine nonlinear singular systems is introduced this algorithm resembles the well known constrained dynamics algorithm for affine nonlinear systems for regularizable affine nonlinear singular systems necessary and sufficient conditions for the solvability of the non interacting control problem are derived they are based on another algorithm producing a sequence of integers the generalization of the well known notion of relative degree for usual affine nonlinear systems finally the problem of feedback exact linearization of the dynamic part of singular systems is briefly addressed an example is provided to illustrate the main results

solution of output regulation of singular nonlinear systems by normal output feedback the output regulation problem of singular nonlinear systems via the normal output feedback control has been a challenging problem existing approaches for solving this problem employed techniques similar to those used for linear singular systems results from these approaches either rely on a normalizability assumption or are limited to systems with special structures this paper gives a complete solution for this problem by employing a novel approach that is also interesting for linear systems

asymptotic properties of an estimator in nonlinear functional errors in variables models with dependent error terms nonlinear functional errors in variables models with error terms satisfying mixing conditions are studied it is pointed out that under certain conditions the least squares estimator of regression parameters is not consistent an alternative estimator for regression parameters is proposed the consistency of the alternative estimator is established

inverse nodal problems it is shown that nodal sequences determine the underlying manifold up to scaling within classes of rectangles with dirichlet boundary conditions separable two dimensional tori two dimensional flat klein bottles and flat tori in two and three dimensions

nonlinear output regulation with adaptive conditional servocompensator an output feedback controller with adaptive conditional servocompensator is developed for robust output regulation of a class of nonlinear minimum phase systems it is shown that the controller achieves asymptotic regulation and can be tuned to recover the transient performance of a state feedback sliding mode controller

stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count the nodal domains of eigenvectors of the discrete schr dinger operator on simple finite and connected graphs are considered courant s well known nodal domain theorem applies in the present case and sets an upper bound to the number of nodal domains of eigenvectors arranging the spectrum as a non decreasing sequence and denoting by n the number of nodal domains of the nth eigenvector courant s theorem guarantees that the nodal deficiency n n is non negative the above applies for generic eigenvectors special care should be exercised for eigenvectors with vanishing components the main result of this work is that the nodal deficiency for generic eigenvectors is equal to a morse index of an energy functional whose value at its relevant critical points coincides with the eigenvalue the association of the nodal deficiency to the stability of an energy functional at its critical points was recently discussed in the context of quantum graphs band et al 2011 commun math phys at press doi 10 1007 s00220 011 1384 9 and dirichlet laplacian in bounded domains in berkolaiko et al 2011 arxiv 1107 3489 this work adapts this result to the discrete case the definition of the energy functional in the discrete case requires a special setting substantially different from the one used in band et al and berkolaiko et al and it is presented here in detail

adaptive consensus of multi agents in networks with jointly connected topologies in this paper the consensus problem of multi agent following a leader is studied an adaptive design method is presented for multi agent systems with non identical unknown nonlinear dynamics and for a leader to be followed that is also nonlinear and unknown by parameterizations of unknown nonlinear dynamics of all agents a decentralized adaptive consensus algorithm is proposed in networks with jointly connected topologies by incorporating local consensus errors in addition to relative position feedback analysis of stability and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and lyapunov theory finally examples are provided to validate the theoretical results

a note on maximizing a special concave function subject to simultaneous loewner order constraints maximization of functions with multivariate arguments can be computationally difficult we show that for a special function which is proportional to the density of a wishart distribution reparametrization can lead to maximization of a concave function we use this fact to produce an algorithm which maximizes the function over a restricted parameter space of the form 0 l u where l u means that u l is a nonnegative definite matrix and l u means that u l is positive definite this restriction is often referred to as the loewner ordering

isospectral graphs with identical nodal counts according to a recent conjecture isospectral objects have different nodal count sequences gnutzmann et al 2005 j phys a math gen 38 8921 33 we study generalized laplacians on discrete graphs and use them to construct the first non trivial counterexamples to this conjecture in addition these examples demonstrate a surprising connection between isospectral discrete and quantum graphs

cooperative global robust output regulation for a class of nonlinear multi agent systems with switching network this technical note studies the cooperative global robust output regulation problem for a class of nonlinear multi agent systems with switching network by a distributed output feedback control law we first convert the problem via the internal model approach to a global robust stabilization problem of an augmented system then using average dwell time method we present a set of solvability conditions for the latter problem by a distributed switched output feedback control law thus leading to the solution of the original problem our approach is illustrated by a family of lorenz systems subject to a harmonic exosystem

efficient estimation in the errors in variables model we consider efficient estimation of the slope in the errors in variables model with normal error when either the ratio of error variances is known and the distribution of the independent is arbitrary and unknown or the distribution of the independent variable is not gaussian or degenerate we calculate information bounds and exhibit estimates achieving these bounds using an initial minimum distance estimate and suitable estimates of the efficient score function

the limiting distribution of least squares in an errors in variables regression model abstract there is a substantial literature concerning linear regression when some of the predictors independent variables are measured with error such models are of importance in econometrics instrumental variables models psychometrics correction for attenuation models of change and in instrumental calibration studies in medicine and industry recent theoretical work concerning maximum likelihood estimation in such models appears in healy 1980 fuller 1980 and anderson 1984 while reilly and patino leal 1981 take a bayesian approach in an applied context an investigator may either overlook the measurement errors in the predictors or choose the classical ordinary least squares ols estimator of the parameters because of its familiarity and ease of use certainly the methodology of classical least squares theory confidence intervals multiple comparisons tests of hypotheses residual analysis is considerably more developed than the corresponding errors in variables methodology particularly in samples of moderate size in this paper it is shown that under reasonable regularity conditions such linear combinations are jointly asymptotically normally distributed

adaptive robust output regulation of uncertain linear periodic systems this paper considers the robust output regulation problem for parameterized families of periodic systems to extend the solution of the output regulation problem to the periodic or time varying setup a classification of the immersion mappings based on various non equivalent observability properties is derived the connections between different canonical realizations of internal models that fully exploit such properties for robust and adaptive output regulation design in periodic systems are investigated it is shown how non minimal realizations of suitable periodic internal models are instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models an important feature of the proposed solution is the fact that a persistence of excitation condition for the exogenous signals is not required for asymptotic regulation

asymptotic output tracking of nonlinear differential algebraic control systems abstract the problem of asymptotic output tracking is considered for control systems described by a class of nonlinear differential algebraic equations assumptions are introduced and an algorithm is developed based on the algorithm a nonlinear feedback control law is then constructed which ensures under appropriate conditions that the closed loop system has a unique bounded differentiable solution and the tracking error in the closed loop system approaches zero when time goes to infinity

stability of a class of linear switching systems with applications to two consensus problems in this paper we first establish a stability result for a class of linear switched systems involving kronecker product the problem is interesting in that the system matrix does not have to be hurwitz at any time instant this class of linear switched systems arises in the control of multi agent systems under switching network topology as applications of this stability result we give the solvability conditions for both the leaderless consensus problem and the leader following consensus problem for general marginally stable linear multi agent systems under switching network topology in contrast with some existing results our results only assume that the dynamic graph is uniformly connected

impluse free output regulation of singular nonlinear systems this paper addresses the output regulation problem for the class of singular nonlinear systems a generalized version of the centre manifold theorem that applies to singular nonlinear systems is established first then necessary and sufficient conditions are given for the solvability of the output regulation problem the work extends the existing results of output regulation problem for singular linear systems or normal nonlinear systems to the singular nonlinear systems

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

the number of nodal domains on quantum graphs as a stability index of graph partitions the courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of laplacian type operators in particular it holds for generic eigenfunctions of a quantum graph the theorem stipulates that after ordering the eigenvalues as a non decreasing sequence the number of nodal domains n of the n th eigenfunction satisfies n n here we provide a new interpretation for the courant nodal deficiency d n n n in the case of quantum graphs it equals the morse index at a critical point of an energy functional on a suitably defined space of graph partitions thus the nodal deficiency assumes a previously unknown and profound meaning it is the number of unstable directions in the vicinity of the critical point corresponding to the n th eigenfunction to demonstrate this connection the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail

solutions to the output regulation problem of linear singular systems in this paper we revisit the output regulation problem for linear singular systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated we derive a necessary and sufficient condition for the regulation problem to be solvable via either full information feedback or error feedback then we show how full information feedback and error feedback controllers can be constructed explicitly

robust output regulation of singular nonlinear systems via a nonlinear internal model the robust output regulation problem for singular nonlinear systems has been studied recently under a restrictive assumption that the solution of the regulator equations is polynomial this assumption essentially limits the nonlinear systems to contain only polynomial nonlinearities in this note we will further show that the polynomial assumption can be replaced by a much milder condition the new condition applies to a larger class of nonpolynomial nonlinear systems thus significantly improving the existing result

distributed coordination for second order multi agent systems with nonlinear dynamics using only relative position measurements in this paper we study the distributed coordination for second order multi agent systems with intrinsic nonlinear dynamics under an undirected graph that characterizes the interaction among the agents or followers both the leaderless consensus problem and the coordinated tracking problem with a dynamic leader are considered by introducing a distributed filter for each agent or follower the proposed control algorithms use only relative position measurements in the absence of communication in the special case without the intrinsic nonlinear dynamics i e for multi agent systems with double integrator dynamics we further derive a necessary and sufficient condition for the leaderless consensus problem under a general directed graph finally simulation examples are provided to show the effectiveness of the proposed control algorithms

reml estimation of covariance matrices with restricted parameter spaces abstract restricted parameter spaces for covariance matrices such as 2 i or i j are often used to simplify estimation in addition fixed upper and or lower bounds may be needed to ensure that estimates satisfy a priori hypotheses with multivariate variance components models several covariance matrices need to be simultaneously estimated and even with a reduced parameter space estimation can be difficult in earlier work we have discussed estimation for a widely used class of models where the variance components matrices need only be nonnegative definite in this article we extend these results to handle a wide class of restricted parameter spaces we state the conditions required for a parameterization to be a member of the class discuss the implementation of the results for several different members of the class and discuss estimation with both balanced and unbalanced data we give several examples to demonstrate the results

a bayesian study of the error in variables model this article presents the results of a study of the functional case of the problem of parameter estimation when there is error in all the variables there is consequently no distinction between independent and dependent variables posterior probability density functions are developed for the parameters with both linear and nonlinear and possibly multiple relations among the true values of the variables there is no distinction between models that are linear or nonlinear in the parameters the results are equivalent to generalizations of the work of some previous authors but lead to new and efficient algorithms for finding point estimates and their precisions for most of the results the error covariance matrix is assumed known though a case is treated where it is known except for a scalar multiplier the results are also shown to be valid if the covariance matrix is singular geometric interpretations are described

maximum likelihood estimation under order restrictions by the prior feedback method abstract algorithms for deriving isotonic regression estimators in order restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered we propose here an optimization method based on a sequence of formal bayes estimates whose variances converge to zero this method akin to simulated annealing can be applied universally that is as long as these bayes estimators can be derived by exact computation or markov chain monte carlo sampling approximation we then give an illustration of our method for two real life examples

semiglobal stabilization and output regulation of singular linear systems with input saturation the semi global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed a reduced order normal system is obtained by a standard coordinate transformation it is further shown that the controller that solves the stabilization output regulation problem of the reduced order normal systems also solves the stabilization output regulation problem of the original singular systems

the nonexistence of 100 1 alpha confidence sets of finite expected diameter in errors in variables and related models on montre que pour certains modeles il est impossible de construire des intervalles de confiance pour les parametres cles qui aient a la fois une confiance positive et une longueur esperee finie

nodal domains statistics a criterion for quantum chaos we consider the distribution of the properly normalized numbers of nodal domains of wave functions in 2d quantum billiards we show that these distributions distinguish clearly between systems with integrable separable or chaotic underlying classical dynamics and for each case the limiting distribution is universal system independent thus a new criterion for quantum chaos is provided by the statistics of the wave functions which complements the well established criterion based on spectral statistics

improved nonnegative estimation of multivariate components of variance in this paper we consider a multivariate one way random effect model with equal replications we propose nonnegative definite estimators for between and within components of variance under the stein loss function it is shown that the proposed estimators of the within component dominate the best unbiased estimator restricted maximum likelihood truncated and order preserving minimax estimators are also proposed a monte carlo simulation is carried out to choose among these estimators for estimating the between component we consider the stein loss function for jointly estimating the two positive definite matrices within and within plus between and obtain estimators for the between component dominating the best unbiased estimator other estimators as considered for within are also proposed a monte carlo simulation is carried out to choose among these estimators

distributed output regulation of nonlinear multi agent systems via host internal model this note presents a host internal model h im approach to distributed output regulation of reaching nonlinear leader following consensus focusing on a basic nonlinear scenario of identical or homogeneous agents of a normal form it is shown that the problem is solvable as long as its interaction digraph contains a certain directed spanning tree a constructive lyapunov protocol is proposed by incorporating a single h im the result is also demonstrated by fitzhugh nagumo fhn and lorenz type nonlinear dynamic networks

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

least squares estimation of covariance matrices in balanced multivariate variance components models abstract the problem of estimating covariance matrices in balanced multivariate variance components models is discussed as with univariate models it is possible for the traditional estimators based on differences of the mean square matrices to produce estimates that are outside the parameter space in fact in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite nnd in this article we develop an iterative estimation procedure satisfying a least squares criterion that is guaranteed to produce nnd estimates of the covariance matrices discuss the speed of convergence and provide an example to show how the estimates change

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

consensus in multi agent systems with coupling delays and switching topology the robustness of consensus in single integrator multi agent systems mas to coupling delays and switching topologies is investigated it is shown that consensus is reached for arbitrarily large constant time varying or distributed delays if consensus is reached without delays this delay robustness holds under the weakest possible connectivity assumptions on the underlying graph i e as long as the graph is uniformly quasi strongly connected and switches with a dwell time the proof is based on a contraction argument and allows to remove technical assumptions that were used in previous publications moreover the result also applies to non scalar single integrators an important extension toward consensus and rendezvous in higher dimensions

robust multivariate regression we introduce a robust method for multivariate regression based on robust estimation of the joint location and scatter matrix of the explanatory and response variables as a robust estimator of location and scatter we use the minimum covariance determinant mcd estimator of rousseeuw based on simulations we investigate the finite sample performance and robustness of the estimator to increase the efficiency we propose a reweighted estimator selected from several possible reweighting schemes the resulting multivariate regression does not need much computation time and is applied to real datasets we show that the multivariate regression estimator has the appropriate equivariance properties has a bounded influence function and inherits the breakdown value of the mcd estimator these theoretical robustness properties confirm the good finite sample results obtained from the simulations

technical communique asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems this paper deals with global disturbance rejection of nonlinear systems the disturbance is assumed to be sinusoidal with completely unknown phases amplitude and frequencies but the number of distinct frequencies or the order of the corresponding unknown linear exosystem is known different from the common structural assumptions of nonlinear systems needed in literature for disturbance rejection of nonlinear systems the proposed method only requires the information of control design with a known lyapunov function when the system is disturbance free and a mild assumption needed for internal model design the proposed disturbance rejection algorithm extends complete global rejection of unknown sinusoidal disturbances for nonlinear dynamic systems beyond the common nonlinear models such as the strict feedback forms and the output feedback forms

h filter design for a class of nonlinear discrete time singular systems this paper deals with the h filter design problem for a class of discrete time lipschitz nonlinear singular systems the approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given the method also unifies the design for the full order reduced order minimal order filters for discrete time systems the presented results are less conservative than those existing in the literature this is due to the introduction of new slack variables application to systems with unknown input is presented via a numerical example

nonlinear internal models for output regulation in this note we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems this result provides a significant enhancement of the nonequilibrium theory for output regulation which we have presented in a recent paper

consensus for multi agent systems with inherent nonlinear dynamics under directed topologies abstract this paper considers the consensus problem for multi agent systems with inherent nonlinear dynamics under directed topologies a variable transformation method is used to convert the consensus problem to a partial stability problem both first order and second order systems are investigated under fixed and switching topologies respectively it is assumed that the inherent nonlinear terms satisfy the lipshitz condition sufficient conditions on the feedback gains are given based on a lyapunov function method for first order systems under a fixed topology the consensus is achieved if the feedback gain related to the agents positions is large enough for first order systems under switching topologies the effect of the minimum dwell time for the switching signal on the consensus achievement is considered for second order systems under a fixed topology the consensus is achieved if the feedback gains related to the agents positions and velocities respectively are both large enough for second order systems under switching topologies a switching variable transformation is given then the consensus problem is investigated when all the digraphs are strongly connected and weighted balanced with a common weighted vector finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

the leader following consensus for multiple uncertain euler lagrange systems with an adaptive distributed observer in this note we first propose an adaptive distributed observer for a linear leader system this observer only assumes those followers who are the children of the leader know the system matrix of the leader system then we further develop a distributed adaptive controller utilizing this adaptive distributed observer to solve the leader following consensus problem for multiple uncertain euler lagrange systems without assuming that all the followers need to know the system matrix of the leader system

adaptive leader following consensus for a class of higher order nonlinear multi agent systems with directed switching networks abstract in this paper we study the leader following consensus problem for a class of uncertain nonlinear multi agent systems under jointly connected directed switching networks the uncertainty includes constant unbounded parameters and external disturbances we first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence then by integrating the conventional adaptive control technique with the adaptive distributed observer we present our solution by a distributed adaptive state feedback control law our result is illustrated by the leader following consensus problem for a group of van der pol oscillators

comparison of least squares and errors in variables regression with special reference to randomized analysis of covariance abstract in an errors in variables regression model the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter we explore the conjecture that when the least squares estimate is consistent for a linear combination of the regression parameter it will be preferred to an errors in variables estimate at least asymptotically the conjecture is false in general but it is true for some important classes of problems one such problem is a randomized two group analysis of covariance upon which we focus

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

local disturbance decoupling of nonlinear singular systems the problem of local disturbance decoupling is considered for a class of non linear singular control systems assumptions are introduced and an algorithm is developed such that the control system can be expressed in a simple form a nonlinear feedback control law is then constructed which ensures the closed loop system has a unique solution without impulses and its output is unaffected by disturbances sufficient and necessary conditions for the existence of such a feedback are derived an example is provided to illustrate the results of the paper

semi global robust output regulation for a class of singular nonlinear systems via nonlinear internal model abstractmost of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions in this paper the semi global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi global robust stabilisation solution leads to the solution of the semi global robust output regulation problem of the original singular nonlinear system the solvability conditions of the semi global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system finally a numerical simulation example is used to illustrate the design of the semi global regulator for the singular nonlinear systems

resolving isospectral drums by counting nodal domains several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different one important class consists of laplace beltrami operators for pairs of flat tori in r n with n 4 we propose that the spectral ambiguity can be resolved by comparing the nodal sequences the numbers of nodal domains of eigenfunctions arranged by increasing eigenvalues in the case of isospectral flat tori in four dimensions where a four parameter family of isospectral pairs is known we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count thus one can count the shape of a drum if it is designed as a flat torus in four dimensions less

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

on the nodal count for flat tori we give an explicit formula for the number of nodal domains of certain eigenfunctions on a flat torus we apply this to an isospectral but not isometric family of pairs of flat four dimensional tori constructed by conway and sloane and we show that corresponding eigenfunctions have the same number of nodal domains this disproves a conjecture by bruning gnutzmann and smilansky

duality of i projections and maximum likelihood estimation for log linear models under cone constraints abstract important order restrictions and general log linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone here we exhibit a duality relationship by way of a fenchel duality theorem between these types of problems and projections in i divergence geometry we show that many cone constrained maximum likelihood estimation problems are exactly equivalent to an i projection onto a translation of the negative polar cone this duality relationship permits the concise characterization of cone restricted maximum likelihood estimates and the use of iterative algorithms proposed by csiszar 1975 and dykstra 1985b which are analogous to the iterative proportional fitting procedure computational aspects of maximum likelihood estimates are discussed and a relationship with least squares projections onto isotonic cones is presented we discuss examples in detail to exhibit the usefulness and power

on the nodal count statistics for separable systems in any dimension we consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in an arbitrary dimension we give an explicit expression for the limiting distribution of normalized nodal counts and analyse some of its universal properties our results are illustrated by the detailed discussion of simple examples and numerical nodal count distributions

asymptotic minimax estimation in semiparametric models we give several conditions on the estimator of efficient score function for estimating the parametric component of semiparametric models a semiparametric version of the one step mle using an estimator of efficient score function which fulfills the conditions is shown to converge to the normal distribution with minimum variance locally uniformly over a fairly large neighborhood around the assumed semiparametric model consequently it is shown to be asymptotically minimax with bounded subconvex loss functions a few examples are also considered

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

reml estimation in unbalanced multivariate variance components models using an em algorithm estimation of covariance matrices when data are missing is a difficult problem in the multivariate mixed model setting problems can arise either because the data are unbalanced or because the response vectors are incomplete jennrich and schluchter 1986 biometrics 42 805 820 and laird lange and stram 1987 journal of the american statistical association 82 97 105 have proposed em algorithms for estimating the parameters associated with longitudinal data models in this paper a new em algorithm is proposed for the general multivariate mixed model the algorithm is derivativefree and based on an algorithm for balanced data proposed by calvin and dykstra 1991 annals qf statistics 19 850 869 once the algorithm is described it is used to produce estimates of the variance components matrices associated with a completely random two factor nested model for a bivariate response vector the data for this example come from calvin and sedransk 1991 journal of the american statistical association 86 36 48 who analyze a study of the quality of care received by cancer patients receiving radiation therapy

bayesian and frequentist predictive inference for the patterns of care studies abstract the patterns of care studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy in this article we propose and evaluate models which if acceptable permit bayesian and frequentist model based predictive inference for the desired finite population parameters using both hierarchical bayesian and frequentist mixed linear models we describe methodology for making the desired inferences emphasizing the use of transformed random variables finally we compare the frequentist bayes and empirical bayes approaches using data from one of the surveys all three methods produce essentially the same value for the finite population mean the standard empirical bayes and frequentist measures of variability are very much smaller than those derived from the bayesian approach the latter reflecting uncertainty about the values of the scale parameters in the model

cooperative global robust output regulation for nonlinear output feedback multiagent systems under directed switching networks in this paper we study the cooperative global robust output regulation problem for nonlinear multiagent systems in output feedback form with any relative degree subject to directed switching networks through the augmentation by a distributed internal model and a distributed observer of the given system we first convert the original problem into the global robust stabilization problem of the so called extended augmented system which is a multi input coupled switched system then we establish a few technical lemmas to lay the foundation for constructing a switching control law and the corresponding multiple lyapunov functions for the switched system then we present the solvability conditions of our problem via the multiple lyapunov functions and average dwell time method the main result will be applied to the leader following synchronization problem for a group of hyperchaotic lorenz multiagent systems with a directed switching network

the invariance of some score tests in the linear model with classical measurement error the linear model with classical measurement error is an alternative to the standard regression model in which it is assumed that the independent variables are subject to error this assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model however in some cases inferences remain unchanged even though the independent variables are assumed to be subject to error this article investigates the invariance property of score tests for assessing heteroscedasticity first order autoregressive disturbance and the need for a box cox power transformation under specific constraints we show that the score tests for measurement error models are identical to the corresponding well established tests derived from standard regression models hence practitioners can assess assumptions of constant variance and independent errors as well as the need for a box cox transformation irrespective of whether or not the variables are measu

output stabilization via nonlinear luenberger observers the present paper addresses the problem of the existence of an output feedback law that asymptotically steers to zero prescribed outputs while keeping all state variables bounded for any initial conditions in a given compact set the problem can be viewed as an extension of the classical problem of semiglobally stabilizing the trajectories of a controlled system to a compact set the problem also encompasses a version of the classical problem of output regulation under only a weak minimum phase assumption it is shown that there exists a controller solving the problem at hand the paper is deliberately focused on theoretical results regarding the existence of such a controller practical aspects involving the design and the implementation of the controller are left to a forthcoming work

estimation of censored linear errors in variables models this paper deals with a linear errors in variables model where the dependent variable is censored a two step procedure is proposed to estimate the model and the corresponding asymptotic covariance matrices are derived the framework covers the usual error free tobit model as a special case it is shown that under normality and a certain identifying condition this model can be uniquely reduced to an error free censored regression model and hence the existing estimators for the tobit model can be used to obtain estimators for this model in particular the maximum likelihood estimator is derived in this way the small sample behavior of the two estimators and their sensitivities to misspecified identifying information are studied through monte carlo simulations

nodal domains of a non separable problem the right angled isosceles triangle we study the nodal set of eigenfunctions of the laplace operator on the right angled isosceles triangle a local analysis of the nodal pattern provides an algorithm for computing the number n of nodal domains for any eigenfunction in addition an exact recursive formula for the number of nodal domains is found to reproduce all existing data eventually we use the recursion formula to analyse a large sequence of nodal counts statistically our analysis shows that the distribution of nodal counts for this triangular shape has a much richer structure than the known cases of regular separable shapes or completely irregular shapes furthermore we demonstrate that the nodal count sequence contains information about the periodic orbits of the corresponding classical ray dynamics

on the duality between locally optimal tests and optimal experimental designs abstract locally unbiased tests with maximal power curvature are determined as the solutions of an optimization problem which turns out to be of dual type as compared to the optimal design problem in both cases the proper optimization problem is concerned with matrices only and the transition from the matrix problem to the original variables is a separate second step this approach provides a novel statistical interpretation of the dual problem that arises with the optimal design problem

tracking in nonlinear differential algebraic control systems with applications to constrained robot systems we consider the design of a feedback control law for control systems described by a class of nonlinear differential algebraic equations so that certain desired outputs track given reference inputs the nonlinear differential algebraic control system being considered is not in state variable form assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential algebraic equations is expressed in a familiar normal form a nonlinear feedback control law is then proposed which ensures under appropriate assumptions that the tracking error in the closed loop differential algebraic system approaches zero exponentially applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints constrained robot systems with joint flexibility and constrained robot systems with significant actuator dynamics are discussed

brief paper distributed adaptive control for synchronization of unknown nonlinear networked systems this paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics a design method is presented for adaptive synchronization controllers for distributed systems having non identical unknown nonlinear dynamics and for a target dynamics to be tracked that is also nonlinear and unknown the development is for strongly connected digraph communication structures a lyapunov technique is presented for designing a robust adaptive synchronization control protocol the proper selection of the lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the frobenius norm the resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node singular value analysis is used it is shown that the singular values of certain key matrices are intimately related to structural properties of the graph

comment on resolving isospectral drums by counting nodal domains in gnutzmann et al 2005 j phys a math gen 38 8921 33 the authors studied the 4 parameter family of isospectral flat 4 tori t a b c d discovered by conway and sloane with a particular method of counting nodal domains they were able to distinguish these tori numerically by computing the corresponding nodal sequences relative to a few explicit tuples a b c d in this note we confirm the expectation expressed in gnutzmann et al 2005 j phys a math gen 38 8921 33 by proving analytically that their nodal count distinguishes any 4 tuple of distinct positive real numbers