a scaled difference chi square test statistic for moment structure analysis a family of scaling corrections aimed to improve the chi square approximation of goodness of fit test statistics in small samples large models and nonnormal data was proposed in satorra and bentler 1994 for structural equations models satorra bentler s sb scaling corrections are available in standard computer software often however the interest is not on the overall fit of a model but on a test of the restrictions that a null model saym0 implies on a less restricted onem1 ift0 andt1 denote the goodness of fit test statistics associated tom0 andm1 respectively then typically the differencetd t0 t1 is used as a chi square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the modelsm0 andm1 as in the case of the goodness of fit test it is of interest to scale the statistictd in order to improve its chi square approximation in realistic that is nonasymptotic and nonormal applications in a recent paper satorra 2000 shows that the difference between two sb scaled test statistics for overall model fit does not yield the correct sb scaled difference test statistic satorra developed an expression that permits scaling the difference test statistic but his formula has some practical limitations since it requires heavy computations that are not available in standard computer software the purpose of the present paper is to provide an easy way to compute the scaled difference chi square statistic from the scaled goodness of fit test statistics of modelsm0 andm1 a monte carlo study is provided to illustrate the performance of the competing statistics

on the multivariate asymptotic distribution of sequential chi square statistics the multivariate asymptotic distribution of sequential chi square test statistics is investigated it is shown that a when sequential chi square statistics are calculated for nested models on the same data the statistics have an asymptotic intercorrelation which may be expressed in closed form and which is in many cases quite high and b sequential chi squaredifference tests are asymptotically independent some monte carlo evidence on the applicability of the theory is provided

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

the asymptotic covariance matrix of sample correlation coefficients under general conditions abstract a general matrix expression for the asymptotic covariance matrix of correlation coefficients is derived it is applicable when the data are drawn from any distribution with finite fourth order moments the result is specialized to the cases where the data have a distribution from the elliptical class and where the sample covariance matrix has a noncentral wishart distribution

adjustments for kurtosis in factor analysis with elliptically distributed errors on donne des corrections simples aux tests d ajustement de la theorie normale pour le modele d analyse factorielle dans le cas ou les facteurs communs ont des distributions arbitraires et ou les erreurs ont une distribution de la classe elliptique

goodness of fit test for copulas copulas are often used in finance to characterize the dependence between assets however a choice of the functional form for the copula is an open question in the literature this paper develops a goodness of fit test for copulas based on positive definite bilinear forms the suggested test avoids the use of plug in estimators that is the common practice in the literature the test statistics can be consistently computed on the basis of v estimators even in the case of large dimensions the test is applied to a dataset of us large cap stocks to assess the performance of the gaussian copula for the portfolios of assets of various dimension the gaussian copula appears to be inadequate to characterize the dependence between assets

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

containment control of leader following multi agent systems with markovian switching network topologies and measurement noises this paper investigates the distributed containment tracking control problem for first order agents with multiple dynamic leaders under directed markovian switching network topologies the control input of each agent can only use its local state and the states of its neighbors corrupted by white noises firstly when the dynamic leaders velocities have some special forms which include the stationary leaders as a special case some necessary and sufficient conditions are presented for the containment tracking in the asymptotic unbiased mean square sense secondly for more general leaders velocities necessary and sufficient conditions are provided for the containment tracking with bounded errors in the mean square sense finally a simulation example is given to illustrate the performance of the proposed control scheme

equivariant symplectic difference schemes and generating functions abstract we show that all the known results on the preservation of first integrals by a symplectic difference scheme can be unified under the equivalence theorem of feng ge in particular when the equivalence theorem is applied to the first type of generating function on a lie group we obtain the lie poisson integrator

numerical integrators that preserve symmetries and reversing symmetries we consider properties of flows the relationships between them and whether numerical integrators can be made to preserve these properties this is done in the context of automorphisms and antiautomorphisms of a certain group generated by maps associated to vector fields this new framework unifies several known constructions we also use the concept of covariance of a numerical method with respect to a group of coordinate transformations the main application is to explore the relationship between spatial symmetries reversing symmetries and time symmetry of flows and numerical integrators

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

accurate and efficient simulation of rigid body rotations abstract this paper introduces efficient and accurate algorithms for simulating the rotation of a three dimensional rigid object and compares them to several prior methods first we introduce a second order accurate method that incorporates a third order correction then we introduce a third order accurate method and finally we give a fourth order accurate method these methods are single step and the update operation is only a single rotation the algorithms are derived in a general lie group setting second we introduce a near optimal energy correction method which allows exact conservation of energy this algorithm is faster and easier to implement than implicit methods for exact energy conservation our third order method with energy conservation is experimentally seen to act better than a fourth order accurate method these new methods are superior to naive runge kutta or predictor corrector methods which are only second order accurate for sphere valued functions the second order symplectic mclachlan reich methods are observed to be excellent at approximate energy conservation but are not as good at long term accuracy as our best methods finally we present comparisons with fourth order accurate symplectic methods which have good accuracy but higher computational cost

least squares theory based on general distributional assumptions with an application to the incomplete observations problem the linear regression modely x e is reanalyzed taking the modest position that x is an approximation of the best predictor ofy we derive the asymptotic distribution ofb andr 2 under mild assumptions the method of derivation yields an easy answer to the estimation of from a data set which contains incomplete observations where the incompleteness is random

adaptive multi agent containment control with multiple parametric uncertain leaders in this paper an adaptive containment control is considered for a class of multi agent systems with multiple leaders containing parametric uncertainties the agents are heterogeneous though their dynamics have the same relative degree and are minimum phase while the interconnection topology is described by a general directed graph a distributed containment control is proposed for the agents to enter the moving convex set spanned by the leaders based on an adaptive internal model and a recursive stabilization control law

a note for lie poisson hamilton jacobi equation and lie poisson integrator abstract in this paper a clear lie poisson hamilton jacobi theory is presented how to construct a lie poisson integrator by generating function methods is also given which is different from the ge marsden methods 1 an example on a rigid body has been given to illustrate this point

copula structure analysis in this paper we extend the standard approach of correlation structure analysis for dimension reduction of highdimensional statistical data the classical assump tion of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula for elliptical copulae a correlation like structure remains but different margins and non existence of moments are possible after introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators the theoretical asymptotic behavior of the statistics can be observed even for small sample sizes finally we show our method at work for a financial data set and explain differences between our copula based approach and the classical approach our new method yields a considerable dimension reduction also in non linear models

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

containment control of multi agent systems in a noisy communication environment the containment problem of first order and second order integral multi agent systems with communication noises is investigated in this paper motivated by the previous work a time varying gain a t is introduced to attenuate the noise effect it is proved that the proposed protocol can solve the mean square containment problem if the following conditions hold 1 the communication topology graph has a spanning forest whose roots are leaders of the multi agent system 2 0 a t dt 3 lim t a t 0 moreover if a t is uniformly continuous these conditions are necessary for ensuring the mean square containment in addition the proposed protocol is also extended to allow the case where each agent has its own gain a i t it is proved that the mean square containment problem can still be solved if all agent dependent gains are infinitesimals of the same order as time goes to infinity finally two simulation examples are provided to demonstrate the effectiveness of the proposed protocols

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

momentum conserving symplectic integrators abstract in this paper we show that symplectic partitioned runge kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of hamiltonian differential equations by extended point transformation we also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of lie poisson systems on certain submanifolds of the general matrix group gl n

dynamic leaders containment control of high order multi agent systems with state time delay an lmi approach abstractthis paper addresses the containment control of a multi agent system with dynamic leaders while considering the state time delay and time varying input disturbances the agents dynamics are assumed to be high order integrals and an unkown state time delay with a known upper bound is considered in order to deal with dynamic leaders and time varying input disturbances an appropriate distributed pip type based control protocol is proposed in this study thereafter utilising the lyapunov krasovskii stability theorem and based on lmi linear matrix inequality approach two theorems are proved which guarantee asymptotically stability of the multi agent system with fixed and switching networks in addition to stability assurance the gains of the proposed protocol are achieved through solving the lmi finally some numerical examples are given to demonstrate the validity of the theoretical results