stabilization of an axially moving web via regulation of axial velocity in this paper a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented the principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly the optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method the galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations odes for control design purposes these odes are rewritten into state space equations the vibration energy of the axially moving beam is represented by the quadratic form of the state variables in the optimal control problem the cost function modified from the vibration energy function is subjected to the constraints on the state variables and the axial transport velocity is considered as a control input numerical simulations are performed to confirm the effectiveness of the proposed control algorithm

supercritical stability of an axially moving beam part ii vibration and stability analyses abstract this paper focuses on the stability of axially moving beam like materials e g belts bands paper and webs which translate at speeds near to and above the so called critical speed stability limit in the companion paper a theoretical model for an axially moving beam was presented which accounted for geometrically non linear beam deflections and the initial beam curvature generated by supporting wheels and pulleys in that paper analysis of steady response revealed that the beam possesses multiple non trivial equilibrium states when translating at supercritical speeds the equations of motion are presently linearized about these equilibria and their stability is predicted from the eigenvalue problem for free response asymptotic and numerical solutions to the eigenvalue problem are presented for the respective cases of small and arbitrary equilibrium curvature the solutions illustrate that the translating beam has multiple stable equilibrium states in the supercritical speed regime the solutions confirm that the critical speed behavior for axially moving materials is extremely sensitive to system imperfections such as initial curvature

error and extrapolation of a compact lod method for parabolic differential equations this paper is concerned with a compact locally one dimensional lod finite difference method for solving two dimensional nonhomogeneous parabolic differential equations an explicit error estimate for the finite difference solution is given in the discrete infinity norm it is shown that the method has the accuracy of the second order in time and the fourth order in space with respect to the discrete infinity norm a richardson extrapolation algorithm is developed to make the final computed solution fourth order accurate in both time and space when the time step equals the spatial mesh size numerical results demonstrate the accuracy and the high efficiency of the extrapolation algorithm

on the transversal vibrations of a conveyor belt with a low and time varying velocity part ii the beam like case in this paper initial boundary value problems for a linear wave string equation are considered these problems can be used as simple models to describe the vertical vibrations of a conveyor belt for which the velocity is small with respect to the wave speed and is assumed to move with a time varying speed formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt it will also be shown that the truncation method cannot be applied to this problem in order to obtain approximations valid on long time scales

asymptotic stabilization of a nonlinear axially moving string by adaptive boundary control in this paper a robust adaptive boundary control for an axially moving string that shows nonlinear behavior resulting from spatially varying tension is investigated a hydraulic actuator equipped with a damper is used as the control actuator at the right boundary of the string the lyapunov redesign method is employed to derive a robust control algorithm employing adaptation laws that estimate three unknown system parameters mass per unit length of string lumped mass of hydraulic actuator and damping coefficient of damper and an unknown boundary disturbance the uniform asymptotic stability when the three parameters are all unknown the exponential stability when they are known and the uniform ultimate boundedness with a bounded boundary disturbance of the closed loop system are investigated the convergence of the parameter estimates to the true values is shown numerical simulations are performed to demonstrate the effectiveness of the proposed robust adaptive boundary control

using an efficient immune symbiotic evolution learning for compensatory neuro fuzzy controller this paper presents an efficient immune symbiotic evolution learning isel algorithm for the compensatory neuro fuzzy controller cnfc the proposed isel method includes three major components initial population subgroup symbiotic evolution and immune system algorithm first the self clustering algorithm that determines proper input space partitioning and finds the mean and variance of the gaussian membership functions and number of rules is applied to the initial population second the subgroup symbiotic evolution method that uses each subantibody represents a single fuzzy rule and the evolution of the rule itself third the immune system algorithm uses the clonal selection principle such that antibodies between others of high similar degree are canceled and these antibodies after processing will have higher quality accelerating the search and increasing the global search capacity finally the proposed cnfc with isel cnfc isel method is adopted to solve several nonlinear control problems the simulation results have shown that the proposed cnfc isel can outperform other methods

fourth order compact finite difference methods and monotone iterative algorithms for semilinear elliptic boundary value problems in this paper we study numerical methods for a class of two dimensional semilinear elliptic boundary value problems with variable coefficients in a union of rectangular domains a compact finite difference method with an anisotropic mesh is proposed for the problems the existence of a maximal and a minimal compact difference solution is proved by the method of upper and lower solutions and two sufficient conditions for the uniqueness of the solution are also given the optimal error estimate in the discrete l norm is obtained under certain conditions the error estimate shows the fourth order accuracy of the proposed method when two spatial mesh sizes are proportional by using an upper solution or a lower solution as the initial iteration an almost optimal picard type of monotone iterative algorithm is developed for solving the resulting nonlinear discrete system efficiently numerical results are presented to confirm our theoretical analysis

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

technical communique exponential stabilization of an axially moving string by linear boundary feedback the system modeled by an axially moving string and a mass damper spring mds controller applied at the right hand side rhs boundary of the string is considered the feature of the controller is not restricted at all and is determined by the system implicitly the mathematical model of this system is composed of an ordinary differential equation ode describing the mds and a partial differential equation pde describing the string the c 0 semigroup theory provides an elegant state space representation for the analysis of the coupled system the exponential stability is verified through the total mechanical energy dissipation and the semigroup theory the lower bound of the feedback gain is obtained

computation of optimal feedforward and feedback control by a modified reduced gradient method a computational scheme for solving problems of optimal open loop control policy and optimal state feedback control was introduced the problems were first converted into a nonlinear programming problem the conjugate reduced gradient method was then applied to find the minimum solution the sensitivity matrices of the state trajectories with respect to the coefficients of control variables could be recursively calculated so that the reduced gradients could be easily evaluated in this computational algorithm the h orthogonal property for linear optimal control problems was demonstrated such that the global minimum solution of such problems was thus achieved in finite iterations using this algorithm the computational strategy was easily and efficiently extended to determine the optimal state feedback gain matrices

graphical methods for efficient likelihood inference in gaussian covariance models in graphical modelling a bi directed graph encodes marginal independences among random variables that are identified with the vertices of the graph we show how to transform a bi directed graph into a maximal ancestral graph that i represents the same independence structure as the original bi directed graph and ii minimizes the number of arrowheads among all ancestral graphs satisfying i here the number of arrowheads of an ancestral graph is the number of directed edges plus twice the number of bi directed edges in gaussian models this construction can be used for more efficient iterative maximization of the likelihood function and to determine when maximum likelihood estimates are equal to empirical counterparts

on the dynamic properties of axially moving systems abstract the objective of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems such important mechanical systems exhibit interesting dynamic behaviors homoclinic orbits sub harmonic responses amplitude modulations and chaos these dynamics have been obtained numerically and in some cases have been experimentally observed using recent techniques of the non linear time series analysis the response of axially moving systems has been studied for a large variety of test cases the correlation dimension of the time series which is deeply related to the minimal dimension of a system able to reproduce the dynamics is estimated lyapunov exponents are evaluated in order to quantify the response regularity the present work gives a contribution towards understanding the complex dynamics observed both in conservative and dissipative systems the dynamical phenomena are analyzed within the unified framework of the non linear time series analysis in the case of experimental data the new non linear filtering techniques based on the embedding techniques have been applied to reduce high noise when classical techniques give bad results

technical communique input output pseudolinearization on controlled invariant submanifolds the original notion of input output pseudolinearization on equilibrium submanifolds is extended to general controlled invariant submanifolds for nonlinear systems input output pseudolinearizing feedback laws render the input output behavior of linearizations about nominal trajectories in the submanifold trajectory independent and equal to that of a fixed linear time invariant system thereby facilitating the subsequent construction of control laws for stabilization and tracking sufficient existence conditions are derived that are weaker than the familiar relative degree conditions for nonlinear input output decoupling that have come to be associated with exact input output linearization

a higher order compact lod method and its extrapolations for nonhomogeneous parabolic differential equations abstract a higher order compact locally one dimensional lod finite difference method for two dimensional nonhomogeneous parabolic differential equations is proposed the resulting scheme consists of two one dimensional tridiagonal systems and all computations are implemented completely in one spatial direction as for one dimensional problems the solvability and the stability of the scheme are proved almost unconditionally the error estimates are obtained in the discrete h 1 l 2 and l norms and show that the proposed compact lod method has the accuracy of the second order in time and the fourth order in space two richardson extrapolation algorithms are presented to increase the accuracy to the fourth order and the sixth order in both time and space when the time step is proportional to the spatial mesh size numerical results demonstrate the accuracy of the compact lod method and the high efficiency of its extrapolation algorithms

estimation of a covariance matrix with zeros summary we consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero we first present an algorithm which we call iterative conditional fitting for computing the maximum likelihood estimate of the constrained covariance matrix under the assumption of multivariate normality in contrast to previous approaches this algorithm has guaranteed convergence properties dropping the assumption of multivariate normality we show how to estimate the covariance matrix in an empirical likelihood approach these approaches are then compared via simulation and on an example of gene expression

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

markov equivalence for ancestral graphs ancestral graphs can encode conditional independence relations that arise in directed acyclic graph dag models with latent and selection variables however for any ancestral graph there may be several other graphs to which it is markov equivalent we state and prove conditions under which two maximal ancestral graphs are markov equivalent to each other thereby extending analogous results for dags given by other authors these conditions lead to an algorithm for determining markov equivalence that runs in time that is polynomial in the number of vertices in the graph

robust boundary control of an axially moving string by using a pr transfer function in this note a scheme for the vibration suppression of a translating string using a positive real pr transfer function is investigated the transverse vibration of the string is controlled by hydraulic touch rolls located at the right end of the string the mathematical model of the system which consists of a hyperbolic partial differential equation pde describing the dynamics of the moving string and an ordinary differential equation ode for the actuator dynamics is derived by using hamilton s principle for translating continua the transfer function of the proposed boundary controller is a nonproper but pr function the asymptotic stability of the closed loop system in the presence of output disturbance is proved

some recent developments of numerov s method abstract this paper is a survey of some recent developments of numerov s method for solving nonlinear two point boundary value problems the survey consists of three different parts the existence uniqueness of a solution computational algorithm for computing a solution and some extensions of numerov s method the sufficient conditions for the existence and uniqueness of a solution are presented some of them are best possible various iterative methods are reviewed including picard s iterative method modified newton s iterative method monotone iterative method and accelerated monotone iterative method in particular two more direct monotone iterative methods are presented to save computational work each of these iterative methods not only gives a computational algorithm for computing a solution but also leads to an existence and uniqueness theorem the estimate on the rate of convergence of the iterative sequence is given the extensions of numerov s method to a coupled problem and a general problem are addressed the numerical results are presented to validate the theoretical analysis

maximum likelihood estimation for linear gaussian covariance models summary we study parameter estimation in linear gaussian covariance models which are p dimensional gaussian models with linear constraints on the covariance matrix maximum likelihood estimation for this class of models leads to a non convex optimization problem which typically has many local maxima using recent results on the asymptotic distribution of extreme eigenvalues of the wishart distribution we provide sufficient conditions for any hill climbing method to converge to the global maximum although we are primarily interested in the case in which n p the proofs of our results utilize large sample asymptotic theory under the scheme n p 1 remarkably our numerical simulations indicate that our results remain valid for p as small as 2 an important consequence of this analysis is that for sample sizes n 14p maximum likelihood estimation for linear gaussian covariance models behaves as if it were a convex optimization problem

a new method for linearizing non linear systems the pseudolinearization consider the single input non linear system x f x u it has been shown that under mild conditions there exist transformations z t x v s x u such that in the z space the linear tangent model is independent of the operating point a constructive procedure to obtain the above transformations is described this new method is computationally attractive and effective in many practical cases

guaranteed cost control of affine nonlinear systems via partition of unity method we consider the problem of guaranteed cost control gcc of affine nonlinear systems in this paper firstly the general affine nonlinear system with the origin being its equilibrium point is represented as a linear like structure with state dependent coefficient matrices secondly partition of unity method is used to approximate the coefficient matrices as a result of which the original affine nonlinear system is equivalently converted into a linear like system with modeling error a gcc law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition the control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper bounded a suboptimal gcc law can be obtained via solving an optimization problem in terms of linear matrix inequality lmi in stead of state dependent riccati equation sdre or hamilton jacobi equations that are usually required in solving nonlinear optimal control problems finally a numerical example is provided to illustrate the validity of the proposed method

supercritical stability of an axially moving beam part i model and equilibrium analysis axially moving material problems consider the dynamic response vibration and stability of long slender members which are in a state of translation this study focuses on the response of axially moving beam like elements at translation speeds that exceed the classical critical speed stability limit a non linear model for an axially moving beam is derived that accounts for the initial beam curvature induced by supporting pulleys or wheels presently the model is used to determine steady responses at critical and supercritical translation speeds the properties of the equilibrium problem are examined using an approximate linear solution and an exact non linear solution the deficiency of the linear solution is illustrated by its inability to capture essential features of the equilibrium problem particularly near and above the critical speed in this high speed region the translating beam undergoes large overall buckling deformations leading to multiple and bifurcated equilibrium states the stability of the equilibria is assessed in part ii

complex dynamics of high speed axially moving systems in this paper the dynamic response of a simply supported travelling beam subjected to a transverse load is investigated in the super critical speed range the well known axially moving beam theory is considered and a simple viscous damping mechanism has been introduced the displacement field is expanded in a series of the buckling modes a sine series and different techniques have been used in analyzing the response of the dynamical system periodic oscillations are studied by means of continuation techniques while non stationary dynamics are investigated through direct simulations a comparison with the literature and a convergence test on the series expansion are performed a sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability and direct simulations of global postcritical dynamics a complex scenario of alternate regular and chaotic motions is found in a large range of the main parameters

stability of an accelerating beam lyapunov s method has been used to derive a sufficient condition for the transverse stability of an axially accelerating beam a multiple time scale formulation is also presented to study the stability when the beam has constant axial acceleration deceleration in such situations an accelerating beam is found to be always stable whereas a decelerating beam may undergo ephemeral instability the non linear terms do not affect the stability condition they only change the frequency of oscillation

dynamic responses of axially moving viscoelastic beam under a randomly disordered periodic excitation abstract we investigate dynamic responses of axially moving viscoelastic beam subject to a randomly disordered periodic excitation the method of multiple scales is used to derive the analytical expression of first order uniform expansion of the solution based on the largest lyapunov exponent the almost sure stability of the trivial steady state solution is examined meanwhile we obtain the first order and the second order steady state moments for the non trivial steady state solutions specially we discuss the first mode theoretically and numerically results show that under the same conditions of the parameters as the intensity of the random excitation increases non trivial steady state solution fluctuation will become strenuous which will result in the non trivial steady state solution lose stability and the trivial steady state solution can be a possible in the case of parametric principal resonance the stochastic jump is observed for the first mode which indicates that the stationary joint probability density concentrates at the non trivial solution branch when the random excitation is small but with the increase of intensity of the random excitation the probability of the trivial steady state solution will become larger this phenomenon of stochastic jump can be defined as a stochastic bifurcation

steady state response of axially moving viscoelastic beams with pulsating speed comparison of two nonlinear models abstract principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed a nonlinear partial differential equation governing the transverse vibration is derived from the dynamical constitutive and geometrical relations under certain assumption the partial differential reduces to an integro partial differential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams the method of multiple scales is applied to two equations to calculate the steady state response closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms the stability of straight equilibrium and nontrivial steady state response are analyzed by use of the lyapunov linearized stability theory numerical examples are presented to highlight the effects of speed pulsation viscoelascity and nonlinearity and to compare results obtained from two equations

accounting for covariates observed post randomization for discrete and continuous repeated measures data adjusting for covariates observed post randomization is a difficult issue in randomized clinical trials one approach is to enter these covariates as time dependent covariates in a general linear model however this approach fails to account for interactions between the primary end point and confounding variable as they evolve over time in this paper we adopt the view that since the confounder is observed following randomization it should be treated as an outcome and analysed accordingly we consider the repeated measures design where both the primary end point and the confounding measure are observed repeatedly over patient follow up a generalized estimating equation model is applied to allow each set of repeated measures to be modelled in terms of important explanatory variables seemingly unrelated regression combines the two models into an overall framework for analysis inference is then performed by imposing restrictions on the confounder regression parameters to reflect the behaviour profile of interest estimation and identification procedures are described and the methodology is illustrated with an example

incremental sliding mode control of the ball and beam we show that using a switched periodic controller we can incrementally track integral curves of certain lie brackets of the drift and controlled vector fields for the ball and beam this allows us to design a sliding mode controller which overcomes the problems associated with singular states and results in effective global tracking of large motions of the ball

nonlinear vibrations of axially moving timoshenko beams under weak and strong external excitations in this paper nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the timoshenko model the governing nonlinear partial differential equation of motion is derived from newton s second law accounting for the geometric nonlinearity caused by finite stretching of the beams the complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation the method of multiple scales is employed to investigate primary resonances nonsyntonic excitations superharmonic resonances and subharmonic resonances some numerical examples are presented to demonstrate the effects of a varying parameter such as axial speed external excitation amplitudes and nonlinearity on the response amplitudes for the first and second modes when other parameters are fixed the stability of the response amplitudes is investigated and the boundary of instability is located

divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects abstract transverse vibrations of elastically rested moving beam like nanostructures accounting for surface effect are of high concern the role of nonlocality on the free dynamic response of moving nanobeams has been revealed in recent years nevertheless the influence of the surface energy on the mechanical behavior of such elements has not been explained yet in this paper equations of motion of rested nanoscaled beams in the moving state are derived carefully via surface energetic shear deformable beam models subsequently the transverse vibrations of the nanostructure are evaluated using galerkin based assumed mode method the explicit expressions of divergence velocities are obtained analytically and these are successfully verified with the results of a numerical approach the roles of crucial parameters on the first divergence velocity are addressed in some detail additionally the stable and unstable regions are determined systematically and the influence of both surface energy and shear energy on the stability of moving nanostructure is discussed

the maximum likelihood degree maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials we study the algebraic degree of the critical equations of this optimization problem this degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces and to the euler characteristic of the complexified complement under suitable hypotheses the maximum likelihood degree equals the top chern class of a sheaf of logarithmic differential forms exact formulae in terms of degrees and newton polytopes are given for polynomials with generic coefficients

asymptotic number of roots of cauchy location likelihood equations how many elements has rn how many roots are there the standard maximum likelihood theory guarantees that one of the elements of rn the maximum likelihood estimate is close to 0 and that all other elements are bounded away in probability as n x 00 from 0 but it does not tell us how many elements there are let rn card rn be the number of roots with probability one the likelihood equation has only simple roots which are alternately local maxima and minima of the likelihood function hence rn is odd there are 2 rn 1 local maxima and 1 2 rn 1 local minima of the local maxima one is the global maximum the maximum likelihood estimate let us call the other local maxima false maxima these 1 2 rn 1 false maxima are an embarrassment for the maximum likelihood method of estimation the following theorem shows that their number is really quite small

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule this paper presents a special hierarchical fuzzy system where the outputs of the previous layer are not used in the if parts but used only in the then parts of the fuzzy rules of the current layer the proposed scheme can be shown to be a universal approximator to any continuous function on a compact set if complete fuzzy sets are used in the if parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier from the simulation of ball and beam control system it is demonstrated that the proposed scheme approximates with good accuracy the model nonlinear controller with fewer fuzzy rules than the centralized fuzzy system and its control performance is comparable to that of the nonlinear controller

an adi extrapolated crank nicolson orthogonal spline collocation method for nonlinear reaction diffusion systems an alternating direction implicit adi orthogonal spline collocation osc method is described for the approximate solution of a class of nonlinear reaction diffusion systems its efficacy is demonstrated on the solution of well known examples of such systems specifically the brusselator gray scott gierer meinhardt and schnakenberg models and comparisons are made with other numerical techniques considered in the literature the new adi method is based on an extrapolated crank nicolson osc method and is algebraically linear it is efficient requiring at each time level only o n operations where n is the number of unknowns moreover it is shown to produce approximations which are of optimal global accuracy in various norms and to possess superconvergence properties

galerkin methods for natural frequencies of high speed axially moving beams in this paper natural frequencies of planar vibration of axially moving beams are numerically investigated in the supercritical ranges in the supercritical transport speed regime the straight equilibrium configuration becomes unstable and bifurcate in multiple equilibrium positions the governing equations of coupled planar is reduced to two nonlinear models of transverse vibration for motion about each bifurcated solution those nonlinear equations are cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform the natural frequencies are investigated for the beams via the galerkin method to truncate the corresponding governing equations without nonlinear parts into an infinite set of ordinary differential equations under the simple support boundary numerical results indicate that the nonlinear coefficient has little effects on the natural frequency and the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters and the integro partial differential equation yields results quantitatively closer to those of the coupled equations

computing the dynamic response of an axially moving continuum the aim of this study was to apply an approximate galerkin finite element method to solve the initial boundary value problem of a viscously damped axially moving pre tensioned beam including arbitrary support excitations in order to validate the galerkin finite element method the results were compared with exact solutions when available and with solutions obtained using the finite difference and galerkin methods the energy dissipation of the system was considered in the form of an equivalent viscous damping model it was also shown that for certain values of the parameters especially at high velocities the galerkin method using stationary string eigenfunctions can give a poor prediction of the dynamic response

robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension in this paper a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated the lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension the axially moving string system is divided into two spans i e a controlled span and an uncontrolled span by a hydraulic touch roll actuator which is located in the middle section of the string the transverse vibration of the controlled span part of the string is controlled by the hydraulic touch roll actuator and the position of the actuator is considered as the right boundary of the controlled span part the mathematical model of the system which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics is derived by using the hamilton s principle the lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part the asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory simulation results verify the effectiveness of the robust adaptive boundary controller proposed

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

on the pseudo linearization problem for nonlinear systems abstract based on well known results for linear systems an alternate treatment of tthe pseudo linearization problem of reboulet and champetier is given sufficient conditions for pseudo linearization are obtained in the general case and these are shown to be satisfied under mild hypothesis by systems with one or two inputs advantages of the new approach include the simplicity of the derivation and a more explicit representation for a pseudo linearizing transformation

neural network enhanced output regulation in nonlinear systems a neural network based approach is developed to approximate the feedforward function needed for solving the nonlinear output regulation problem the approach eliminates the need for solving the regulator equations thus applying to complex uncertain nonlinear systems

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

multigrid method and fourth order compact scheme for 2d poisson equation with unequal mesh size discretization abstract a fourth order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two dimensional poisson equation in a rectangular domain multigrid methods using a partial semicoarsening strategy and line gauss seidel relaxation are designed to solve the resulting sparse linear systems numerical experiments are conducted to test the accuracy of the fourth order compact difference scheme and to compare it with the standard second order difference scheme convergence behavior of the partial semicoarsening and line gauss seidel relaxation multigrid methods is examined experimentally

stabilization for the kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control abstract the first objective of this paper is to make the mathematical model for vibration suppression of an axially moving heterogeneous string in order to describe the geometrical nonlinearity due to finite transverse deformation the exact expression of the strain is used the mathematical modeling is derived first by using hamilton s principle and variational lemma and the derived nonlinear pde system is the kirchhoff type equation with boundary feedback control next we show the existence and uniqueness of strong solutions of the pde system via techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of the faedo galerkin method and estimate a decay rate for the energy the theoretical results are assured by numerical results of the solution s shape and asymptotic behavior for the system

nonlinear tracking control of vibration amplitude for a parametrically excited microcantilever beam abstract in this paper a feedback control algorithm to regulate oscillation amplitude of a microelectromechanical mems cantilever beam operated at parametric resonances is developed the control objective is to drive the oscillation amplitude of the micro beam which is amplified using parametric excitation to the desired values the principle of the control algorithm is to establish an output tracking control based on the nonlinear dynamic model of the micro beam where the supply voltage is considered as a control input the tracking control algorithm is designed to solve the singularities resulting from the zero deflection state of the micro beam the galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the beam into a set of ordinary differential equations odes uniformly ultimate boundedness stability of the control system is proved using lyapunov method the effectiveness of the proposed control algorithm is illustrated via numerical simulations

computing maximum likelihood estimates in recursive linear models with correlated errors in recursive linear models the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive or acyclic system of linear structural equations these linear models have a long tradition and appear in seemingly unrelated regressions structural equation modelling and approaches to causal inference they are also related to gaussian graphical models via a classical representation known as a path diagram despite the models long history a number of problems remain open in this paper we address the problem of computing maximum likelihood estimates in the subclass of bow free recursive linear models the term bow free refers to the condition that the errors for variables i and j be uncorrelated if variable i occurs in the structural equation for variable j we introduce a new algorithm termed residual iterative conditional fitting ricf that can be implemented using only least squares computations in contrast to existing algorithms ricf has clear convergence properties and yields exact maximum likelihood estimates after the first iteration whenever the mle is available in closed form

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

stability and bifurcation of an axially moving beam tuned to three to one internal resonances abstract this study analyzed the nonlinear vibration of an axially moving beam subject to periodic lateral force excitations attention is paid to the fundamental and subharmonic resonances since the excitation frequency is close to the first two natural frequencies of the system the incremental harmonic balance ihb method was used to evaluate the nonlinear dynamic behaviour of the axially moving beam the stability and bifurcations of the periodic solutions for given parameters were determined by the multivariable floquet theory using hsu s method the solutions obtained from the ihb method agreed very well with those obtained from numerical integration furthermore numerical examples are given to illustrate the effects of the three to one internal resonance on the response of the system

a conserved quantity and the stability of axially moving nonlinear beams free nonlinear transverse vibration is investigated for an axially moving beam modeled by an integro partial differential equation based on the equation a conserved quantity is defined and confirmed for axially moving beams with pinned or clamped ends the conserved quantity is applied to demonstrate the lyapunov stability of the straight equilibrium configuration in transverse nonlinear of beam with a low axial speed

extrapolation algorithm of compact adi approximation for two dimensional parabolic equation abstract in this paper we propose a compact alternating direction implicit adi scheme for solving the two dimensional parabolic equation the maximum norm convergence is proven and the convergence rate is second order in time and fourth order in space we develop a richardson extrapolation algorithm to increase the accuracy to sixth order both in time and space numerical experiments show the effectiveness of the method

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

ancestral graph markov models this paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all dag independence models this class of graphs called maximal ancestral graphs has two attractive features there is at most one edge between each pair of vertices every missing edge corresponds to an independence relation these features lead to a simple parameterization of the corresponding set of distributions in the gaussian case

multimodality of the likelihood in the bivariate seemingly unrelated regressions model summary we analyse the simplest two equation seemingly unrelated regressions model and demonstrate that its likelihood may have up to five stationary points and thus there may be up to three local modes consequently the estimates obtained via iterative estimation methods may depend on starting values we further show that the probability of multi modality vanishes asymptotically monte carlo simulations suggest that multimodality rarely occurs if the seemingly unrelated regressions model is true but can become more frequent if the model is misspecified the existence of multimodality in the likelihood for seemingly unrelated regressions models contradicts several claims in the literature

high order compact adi methods for parabolic equations in this paper we develop a sixth order compact scheme coupled with alternating direction implicit adi methods and apply it to parabolic equations in both 2 d and 3 d unconditional stability is proved for linear diffusion problems with periodic boundary conditions numerical examples supporting our theoretical analysis are provided

multidimensional lindstedt poincare method for nonlinear vibration of axially moving beams abstract the multidimensional lindstedt poincare mdlp method is extended to the nonlinear vibration analysis of axially moving systems galerkin method is used to discretize the governing equations the forced response of an axially moving beam with internal resonance between the first two transverse modes is studied the fundamental harmonic resonance is studied the response curves exhibit the same internal resonance characteristics as that of non transferring thin plates and beams because all these systems possess cubic nonlinearity and similar frequency distribution the examples show that the results of the mdlp method agree reasonably well with that obtained by the incremental harmonic balance ihb method however the former is more straightforward and efficient for obtaining the solution

brief robust control of nonlinear systems with parametric uncertainty probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented monte carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satisfied the robust control design approach is illustrated by a simple nonlinear example a modified feedback linearization control is chosen as controller structure and the design parameters are searched by a genetic algorithm to achieve the tradeoff between stability and performance robustness

graphical gaussian models with edge and vertex symmetries summary we introduce new types of graphical gaussian models by placing symmetry restrictions on the concentration or correlation matrix the models can be represented by coloured graphs where parameters that are associated with edges or vertices of the same colour are restricted to being identical we study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates we identify conditions for restrictions on the concentration and correlation matrices being equivalent this is for example the case when symmetries are generated by permutation of variable labels for such models a particularly simple maximization of the likelihood function is available

brief paper stabilization analysis of a generalized nonlinear axially moving string by boundary velocity feedback this paper addresses vibration suppression of an axially moving nonlinear string subject to boundary control at either the downstream or the upstream end the equation of motion and the boundary conditions are derived from hamilton s principle using the exact expression of the strain to describe the geometrical nonlinearity due to the finite transverse deformation we can approximate this model by various simpler models found in the literature we show that the oscillations of the moving string can be stabilized exponentially via linear negative velocity feedback acting at one end of the string our proofs rely on lyapunov s direct method using a carefully constructed energy functional

an accurate lod scheme for two dimensional parabolic problems we propose a high order locally one dimensional scheme for solving parabolic problems the method is fourth order in space and second order in time and provides a computationally efficient implicit scheme it is shown through a discrete fourier analysis that the method is unconditionally stable numerical experiments are conducted to test its high accuracy and to compare it with other schemes

control problems in super articulated mechanical systems control of super articulated mechanical systems sams controlled mechanical system in which the dimension of the configuration space exceeds the dimension of the control input space is studied as a starting point a graphical characterization of general sams is developed in which a so called control flow diagram cfd is constructed to represent the interaction forces among the degrees of freedom of the system three types of structure namely the chain structure the tree structure and isolated points are identified degree of complexity of the system is defined based on the structure of the system a systematic backstepping type controller design is proposed for systems with a chain structure to achieve global asymptotic stability and trajectory tracking such a controller design itself illustrates the sufficient conditions for the existence of smooth feedback control such that the systems with a chain structure can be globally asymptotically stabilized the connection of the authors control algorithm with existing results is discussed

numerical analysis of coupled systems of nonlinear parabolic equations this paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method three monotone iteration processes for the finite difference system are presented and the sequences of iterations are shown to converge monotonically to a unique solution of the system including an existence uniqueness comparison theorem a theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary value problem an application to a reaction diffusion model in chemical engineering and combustion theory is given

an extension of the growth curve model summary an extension of the growth curve model of potthoff roy 1964 is presented the extension arises naturally when parallel profiles are required or profiles are concurrent at some known time point and may be of use for the analysis of longitudinal data from designed experiments linearization of a nonlinear model also results in this model under certain conditions transformation of the model leads to seemingly unrelated multivariate regressions in this case questions of identifiability and estimation are handled easily an analysis of data on the growth of lambs is presented to illustrate the approach in this paper we consider the analysis of repeated measurements on experimental units which may be grouped according to some experimental design usually successive measurements are taken over time but this need not be the case we restrict ourselves to the case where the same number of observations at identical time points are made on all the experimental units this is likely to be the case in designed experiments though not perhaps in observational studies the approach given here extends that of potthoff roy 1964 and we show below that the potential applications are quite widespread we emphasize that in this paper that we are attempting to present what we regard as a useful and practical extension to the classical growth curve model it is likely to be useful if the aim of the analysis is the estimation of an explicit model for interpretative or predictive purposes this is rather in contrast to the traditional approach to the analysis of such data where the aim is more directed towards testing for effects of treatments or covariates if testing for effects is the primary purpose of analysis then the simpler traditional methods as given initially by wishart 1938 and subsequently by many authors such as rowell walters 1976 may well suffice in this approach selected linear functions of the response over time are calculated and treatment effects are assessed using the analysis of variance since this approach concentrates on individual linear functions seriatim and generally but not always ignores correlations between such linear functions we would regard this as essentially a univariate technique however if testing is the main concern the loss of efficiency in ignoring the multivariate character of the data may not be severe our approach is more complex but the aim is more comprehensive we aim to provide an explicit model for the mean response over time if the model is then used to answer questions that could have been considered by separate tests the answers will of course usually be essentially the same as those obtained by the simpler traditional approach

model selection for gaussian concentration graphs gga multivariate gaussian graphical markov model for an undirected graph g also called a covariance selection model or concentration graph model is defined in terms of the markov properties i e conditional independences associated with g which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients by means of fisher s z transformation and sidak s correlation inequality conservative simultaneous confidence intervals for the entire set of partial correlations can be obtained leading to a simple method for model selection that controls the overall error rate for incorrect edge inclusion the simultaneous p values corresponding to the partial correlations are partitioned into three disjoint sets a significant set s an indeterminate set i and a nonsignificant set n our model selection method selects two graphs a graph g si whose edges correspond to the set s i and a more conservative graph g s whose edges correspond to s only similar considerations apply to covariance graph models which are defined in terms of marginal independence rather than conditional independence the method is applied to some well known examples and to simulated data