a computationally efficient quadrature procedure for the one factor multinomial probit model a problem of estimation that has long confronted many economists is the difficulty of estimating the parameters of equations with limited dependent variables on cross section time series i e panel data while there are widely available packaged computer programs for estimating either a cross section probit and tobit models or b simple permanent transitory random effects panel models with continuous dependent variables there are no available computationally feasible methods of combining these two models this is because the likelihood function that arises in such a combined model contains multivariate normal integrals whose evaluation is quite difficult if not impossible with conventional approximation methods there is a widespread feeling among those working in the area that one possible method of evaluation the use of quadrature techniques is in principle possible but is in practice computationally too burdensome to consider e g albright et al 2 p 13 hausman and wise 6 p 12 in this note we point out that this is true only of standard quadrature techniques such as trapezoidal integration or its improved variants gaussian quadrature on the other hand is extremely efficient and is well within the bounds of computational feasibility on modern computers in what follows we state the nature of the integrals that need to be evaluated provide a brief exposition of gaussian quadrature and provide a numerical illustration of its use in

convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment a new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed it is suggested to collocate the equations not only at the inner grid points but also at the boundary points and use the boundary conditions as penalty terms in the pseudo spectral legrendre method with the new boundary treatment a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

simulation based inference a survey with special reference to panel data models abstract in this article we study the recent developments of inference methods based on simulations in particular we discuss the simulated generalized method of moments the simulated maximum likelihood method and the simulated pseudo maximum likelihood methods the asymptotic properties of the estimators are described when the number of observations n goes to infinity and we distinguish the case where the number h of simulations per observation is fixed from the case where this number also goes to infinity in the former case the possible asymptotic bias is evaluated and in the latter case we carefully examine the consequences of the assumptions on the relative divergence rates of n and h we also show how these methods apply to various contexts in particular to the case of panel data models

chebyshev legendre super spectral viscosity method for nonlinear conservation laws in this paper a super spectral viscosity method using the chebyshev differential operator of high order d s sqrt 1 x 2 opx s is developed for nonlinear conservation laws the boundary conditions are treated by a penalty method compared with the second order spectral viscosity method the super one is much weaker while still guaranteeing the convergence of the bounded solution of the chebyshev galerkin chebyshev collocation or legendre galerkin approximations to nonlinear conservation laws which is proved by compensated compactness arguments

integration preconditioning matrix for ultraspherical pseudospectral operators in this paper we give an integration rectangular preconditioner for ultraspherical pseudospectral operators we present an explicit solution of matrix equations with the structure provided by the pseudospectral discretization of the nth order differential operator subject to various types of boundary conditions this occurs in two steps in the first step we introduce an integration rectangular preconditioner in the second step we use a new strategy to impose the boundary conditions on the condition that the coefficients matrix has a known inverse computational examples are given

on the stability and convergence of a galerkin reduced order model rom of compressible flow with solid wall and far field boundary treatment a reduced order model rom based on the proper orthogonal decomposition pod galerkin projection method is proposed as an alternative discretization of the linearized compressible euler equations it is shown that the numerical stability of the rom is intimately tied to the choice of inner product used to define the galerkin projection for the linearized compressible euler equations a symmetry transformation motivates the construction of a weighted l 2 inner product that guarantees certain stability bounds satisfied by the rom sufficient conditions for well posedness and stability of the present galerkin projection method applied to a general linear hyperbolic initial boundary value problem ibvp are stated and proven well posed and stable far field and solid wall boundary conditions are formulated for the linearized compressible euler rom using these more general results a convergence analysis employing a stable penalty like formulation of the boundary conditions reveals that the rom solution converges to the exact solution with refinement of both the numerical solution used to generate the rom and of the pod basis an a priori error estimate for the computed rom solution is derived and examined using a numerical test case published in 2010 by john wiley sons ltd

vibration control of an euler bernoulli beam under unknown spatiotemporally varying disturbance in this article the vibration suppression of an euler bernoulli beam system is considered by using the adaptive boundary control technique the dynamics of the beam are represented by a partial differential equation and four ordinary differential equations involving functions of both space and time by using lyapunov synthesis the robust boundary control with a disturbance observer is first proposed to suppress the vibration and attenuate the effect of the external disturbances to compensate for both the system parametric uncertainties and the disturbances uncertainties the adaptive boundary control is developed with the proposed boundary control the state of the beam system is proven to be uniformly ultimately bounded and converge to a small neighbourhood of zero by appropriately choosing the design parameters the effectiveness of the proposed control is successfully verified by numerical simulations

brief paper boundary control with integral action for hyperbolic systems of conservation laws stability and experiments a strict lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with riemann invariants is presented the time derivative of this lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains previous stability results are extended to guarantee the local convergence of the state towards a desired set point furthermore the control can be implemented as a feedback of the state measured only at the boundaries the control design method is illustrated with a hydraulic application namely the level and flow regulation in a reach of the sambre river and in the micro channel of valence respectively through simulations and experimentations

the active disturbance rejection control to stabilization for multi dimensional wave equation with boundary control matched disturbance in this paper we consider boundary stabilization for a multi dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables the active disturbance rejection control adrc approach is adopted in investigation an extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi dimensional system by infinitely many test functions the disturbance is canceled in the feedback loop together with a collocated stabilizing controller all subsystems in the closed loop are shown to be asymptotically stable in particular the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature the overall picture of the adrc in dealing with the disturbance for multi dimensional partial differential equation is presented through this system the numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction

convergence of spectral methods of hyperbolic initial boundary value systems we present here a convergence proof for spectral approximations for hyperbolic systems with initial and boundary conditions we treat in detail chebyshev collocation but the final result is readily applicable to other spectral methods such as legendre collocation or tau methods

fault tolerant control for a class of switched linear hyperbolic systems this paper considers the fault tolerant control ftc problem for switched systems described by linear hyperbolic partial differential equations with the process and boundary faults the effect of

stabilization of ode with hyperbolic equation actuator subject to boundary control matched disturbance in this paper we consider stabilisation for a cascade of ode and first order hyperbolic equation with external disturbance flowing to the control end the active disturbance rejection control adr

misspecified heteroskedasticity in the panel probit model a small sample comparison of gmm and sml estimators abstract this paper compares generalized method of moments gmm and simulated maximum likelihood sml approaches to the estimation of the panel probit model both techniques circumvent multiple integration of joint density functions without the need to restrict the error term variance covariance matrix of the latent normal regression model particular attention is paid to a three stage gmm estimator based on nonparametric estimation of the optimal instruments for given conditional moment functions monte carlo experiments are carried out which focus on the small sample consequences of misspecification of the error term variance covariance matrix the correctly specified experiment reveals the asymptotic efficiency advantages of sml the gmm estimators outperform sml in the presence of misspecification in terms of multiplicative heteroskedasticity this holds in particular for the three stage gmm estimator allowing for heteroskedasticity over time increases the robustness with respect to misspecification in terms of multiplicative heteroskedasticity an application to the product innovation activities of german manufacturing firms is presented

smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models abstract we apply a new simulation method that solves the multidimensional probability integrals that arise in maximum likelihood estimation of a broad class of limited dependent variable models the simulation method has four key features the simulated choice probabilities are unbiased they are a continuous and differentiable function of the parameters of the model they are bounded between 0 and 1 and their computation takes an effort that is nearly linear in the dimension of the probability integral independent of the magnitudes of the true probabilities we also show that the new simulation method produces probability estimates with substantially smaller variance than those generated by acceptance rejection methods or by stern s 1992 method the simulated probabilities can therefore be used to revive the lerman and manski 1981 procedure of approximating the likelihood function using simulated choice probabilities by overcoming its computational disadvantages

tracking control of the uncertain heat and wave equation via power fractional and sliding mode techniques in the present paper preliminary results towards the generalization to the infinite dimensional setting of some well known robust finite dimensional control algorithms are illustrated more specifically we deal with the tracking problem for some classes of linear uncertain infinite dimensional systems evolving in hilbert spaces we design distributed variable structure stabilizers that are shown to be effective in the presence of external disturbances the main focus of the present paper is on the rejection of nonvanishing external disturbances the generalization to the infinite dimensional setting of the well known finite dimensional controllers namely the power fractional controller s p bhat and d s bernstein siam j control optim 38 2000 pp 751 766 and two second order sliding mode control algorithms the twisting and supertwisting algorithms l fridman and a levant higher order sliding modes as a natural phenomenon in control theory in robust control via variable structure and lyapunov techniques springer verlag berlin 1996 pp 107 133 a levant internat j control 58 1993 pp 1247 1263 is the main contribution of the present investigation first the distributed twisting control algorithm is developed to address the asymptotic state tracking of the perturbed wave equation next the finite time state tracking of the unperturbed heat equation is provided by means of a distributed power fractional controller finally the distributed supertwisting controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances constructive proofs of stability are developed via the lyapunov functional technique which leads to simple tuning rules for the controller parameters simulation results are discussed to verify the effectiveness of the proposed schemes

an error minimized pseudospectral penalty direct poisson solver this paper presents a direct poisson solver based on an error minimized chebyshev pseudospectral penalty formulation for problems defined on rectangular domains in this study the penalty parameters are determined analytically such that the discrete l 2 error is minimized numerical experiments are conducted and the results show that the penalty scheme computes numerical solutions with better accuracy compared to the traditional approach with boundary conditions enforced strongly

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

the active disturbance rejection control approach to stabilisation of coupled heat and ode system subject to boundary control matched disturbance we consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation subject to boundary control matched disturbance the active disturbance rejection control approach is applied to estimate in real time the disturbance with both constant high gain and time varying high gain the disturbance is cancelled in the feedback loop the closed loop systems with constant high gain and time varying high gain are shown respectively to be practically stable and asymptotically stable

sliding mode control to stabilization of cascaded heat pde ode systems subject to boundary control matched disturbance in this paper we are concerned with the boundary feedback stabilization of a cascade of heat pde ode system with dirichlet neumann interconnection and with the external disturbance flowing the control end in order to deal with the disturbance the sliding model control smc is integrated with the backstepping approach where the disturbance is supposed to be bounded only the existence and uniqueness of the solution for the closed loop system are proved and the monotonicity of the reaching condition is presented without differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system finally the numerical simulations validate the effectiveness of this method for the system with periodic and normal random disturbances respectively

a multidomain spectral method for supersonic reactive flows this paper has a dual purpose it presents a multidomain chebyshev method for the solution of the two dimensional reactive compressible navier stokes equations and it reports the results of the application of this code to the numerical simulations of high mach number reactive flows in recessed cavity the computational method utilizes a newly derived interface boundary conditions as well as an adaptive filtering technique to stabilize the computations the results of the simulations are relevant to recessed cavity flame holders

stability analysis of spectral methods for hyperbolic initial boundary value systems we treat a constant coefficient hyperbolic system in one space variable with zero initial data dissipative boundary conditions are imposed at the two points x pm 1 this problem is discretized either by a spectral or pseudospectral approximation in space we demonstrate sufficient conditions under which the spectral numerical solution is stable moreover these conditions have to be checked only for scalar equations the stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data the dependence of these bounds on n the number of points in the domain or equivalently the degree of the polynomials involved is investigated for a class of standard spectral methods including chebyshev and legendre collocations

parameter estimation and non collocated adaptive stabilization for a wave equation subject to general boundary harmonic disturbance this paper is concerned with the parameter estimation and asymptotic stabilization of a 1 d wave equation that is subject to general harmonic disturbances at the controlled end and suffers from instability at the other end first we design an adaptive observer in terms of measured position and velocity we then adopt the backstepping method for infinite dimensional systems to design an observer based output feedback law the resulting closed loop system is shown to be asymptotically stable and the estimates of the parameters converge to the unknown parameters

a new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations a new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested this method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions stability and convergence results are proven for the chebyshev approximation of linear scalar hyperbolic equations the eigenvalues of this method applied to parabolic equations are shown to be real and negative

brief paper sliding mode boundary control of a parabolic pde system with parameter variations and boundary uncertainties this paper considers the stabilization problem of a one dimensional unstable heat conduction system rod modeled by a parabolic partial differential equation pde powered with a dirichlet type actuator from one of the boundaries by applying the volterra integral transformation a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties the associated lyapunov function is used for designing an infinite dimensional sliding manifold on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances it is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero a continuous control law satisfying the reaching condition is obtained by passing a discontinuous signum signal through an integrator

active disturbance rejection control for rejecting boundary disturbance from multidimensional kirchhoff plate via boundary control in this paper an algorithm is developed to reject time and spatially varying boundary disturbances from a multidimensional kirchhoff plate via boundary control the disturbance and control input are assumed to be matched the active disturbance rejection control approach is adopted for developing the algorithm a state feedback scheme is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multidimensional system using infinitely many time dependent test functions the proposed control law cancels the disturbance using its estimated value all subsystems in the closed loop are shown to be asymptotically stable simulation results are presented to validate the theoretical conclusions and to exhibit the reduction in the peaking phenomenon due to the use of time varying gains instead of constant high gains

the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli beam equation with boundary input disturbance in this paper we are concerned with the boundary feedback stabilization of a one dimensional euler bernoulli beam equation with the external disturbance flowing to the control end the active disturbance rejection control adrc and sliding mode control smc are adopted in investigation by the adrc approach the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed loop it is shown that the external disturbance can be attenuated in the sense that the resulting closed loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity in the second part we use the smc to reject the disturbance by removing the condition in adrc that the derivative of the disturbance is supposed to be bounded the existence and uniqueness of the solution for the closed loop via smc are proved and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system the numerical simulations validate the effectiveness of both methods

high order implicit time marching methods based on generalized summation by parts operators this article extends the theory of classical finite difference summation by parts fd sbp time marching methods to the generalized summation by parts gsbp framework dual consistent gsbp time marching methods are shown to retain a and l stability as well as superconvergence of integral functionals when integrated with the quadrature associated with the discretization this also implies that the solution approximated at the end of each time step is superconvergent in addition gsbp time marching methods constructed with a diagonal norm are bn stable this article also formalizes the connection between fd sbp gsbp time marching methods and implicit runge kutta methods through this connection the minimum accuracy of the solution approximated at the end of a time step is extended for nonlinear problems it is also exploited to derive conditions under which nonlinearly stable gsbp time marching methods can be constructed the gsbp approach to time marching can simplify the construction of high order f

on the convergence of an extended state observer for nonlinear systems with uncertainty abstract the extended state observer first proposed by jingqing han in j q han a class of extended state observers for uncertain systems control decis 10 1 1995 85 88 in chinese is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering unfortunately there is no rigorous proof of convergence to date in this paper we attempt to tackle this long unsolved extraordinary problem the main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance for which the effect of total disturbance error is eliminated by the high gain

a stable penalty method for the compressible navier stokes equations i open boundary conditions the purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible navier stokes equations in three spatial dimensions the treatment uses the conservation form of the navier stokes equations and utilizes linearization and localization at the boundaries based on these variables the proposed boundary conditions are applied through a penalty procedure thus ensuring correct behavior of the scheme as the reynolds number tends to infinity the versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder

solution of time dependent diffusion equations with variable coefficients using multiwavelets a new numerical algorithm is developed for the solution of time dependent differential equations of diffusion type it allows for an accurate and efficient treatment of multidimensional problems with variable coefficients nonlinearities and general boundary conditions for space discretization we use the multiwavelet bases introduced by alpert 1993 siam j math anal 24 246 262 and then applied to the representation of differential operators and functions of operators presented by alpert beylkin and vozovoi representation of operators in the multiwavelet basis in preparation an important advantage of multiwavelet basis functions is the fact that they are supported only on non overlapping subdomains thus multiwavelet bases are attractive for solving problems in finite non periodic domains boundary conditions are imposed with a penalty technique of hesthaven and gottlieb 1996 siam j sci comput 579 612 which can be used to impose rather general boundary conditions the penalty approach was extended to a procedure for ensuring the continuity of the solution and its first derivative across interior boundaries between neighboring subdomains while time stepping the solution of a time dependent problem this penalty procedure on the interfaces allows for a simplification and sparsification of the representation of differential operators by discarding the elements responsible for interactions between neighboring subdomains consequently the matrices representing the differential operators on the finest scale have block diagonal structure for a fixed order of multiwavelets i e a fixed number of vanishing moments the computational complexity of the present algorithm is proportional to the number of subdomains the time discretization method of beylkin keiser and vozovoi 1998 pam report 347 is used in view of its favorable stability properties numerical results are presented for evolution equations with variable coefficients in one and two dimensions

construction of energy stable projection based reduced order models an approach for building energy stable galerkin reduced order models roms for linear hyperbolic or incompletely parabolic systems of partial differential equations pdes using continuous projection is developed this method is an extension of earlier work by the authors specific to the equations of linearized compressible inviscid flow the key idea is to apply to the pdes a transformation induced by the lyapunov function for the system and to build the rom in the transformed variables for linear problems the desired transformation is induced by a special inner product termed the symmetry inner product which is derived herein for several systems of physical interest connections are established between the proposed approach and other stability preserving model reduction methods giving the paper a review flavor more specifically it is shown that a discrete counterpart of this inner product is a weighted l 2 inner product obtained by solving a lyapunov equation first proposed by rowley et al and termed herein the lyapunov inner product comparisons between the symmetry inner product and the lyapunov inner product are made and the performance of roms constructed using these inner products is evaluated on several benchmark test cases

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results abstract an extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral p b a b n v dv e v 1 v b where v is a m dimensional normal vector with mean covariance matrix and density n v and 1 v b is an indicator for the event b v a a leading case of such an integral is the negative orthant probability where b v v the problem is computationally difficult except in very special cases the multinomial probit mnp model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities with and depending on unknown parameters and in general on covariates estimation of this model requires for each trial parameter vector and each observation in a sample evaluation of p b and of its derivatives with respect to and this paper surveys monte carlo techniques that have been developed for approximations of p b and its linear and logarithmic derivatives that limit computation while possessing properties that facilitate their use in iterative calculations for statistical inference the crude frequency simulator cfs normal importance sampling nis a kernel smoothed frequency simulator kfs stern s decomposition simulator sds the geweke hajivassiliou keane simulator ghk a parabolic cylinder function simulator pcf deak s chi squared simulator dcs an acceptance rejection simulator ars the gibbs sampler simulator gss a sequentially unbiased simulator sus and an approximately unbiased simulator aus we also discuss gauss and fortran implementations of these algorithms and present our computational experience with them we find that ghk is overall the most reliable method

spectral methods for hyperbolic problems we review the current state of fourier and chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations throughout the discussion we emphasize recent developments in the area such as spectral penalty methods the use of filters the resolution of the gibbs phenomenon and issues related to the solution of nonlinear conservations laws such as conservation and convergence we also include a brief discussion on the formulation of multi domain methods for hyperbolic problems and conclude with a few examples of the application of pseudospectral collocation methods for solving nontrivial systems of conservation laws

a stable penalty method for the compressible navier stokes equations iii multidimensional domain decomposition schemes this paper concluding the trilogy develops schemes for the stable solution of wave dominated unsteady problems in general three dimensional domains the schemes utilize a spectral approximation in each subdomain and asymptotic stability of the semidiscrete schemes is established the complex computational domains are constructed by using nonoverlapping quadrilaterals in the two dimensional case and hexahedrals in the three dimensional space to illustrate the ideas underlying the multidomain method a stable scheme for the solution of the three dimensional linear advection diffusion equation in general curvilinear coordinates is developed the analysis suggests a novel yet simple stable treatment of geometric singularities like edges and vertices the theoretical results are supported by a two dimensional implementation of the scheme the main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible navier stokes equations on conservation form and a unified approach for dealing with the open boundaries and subdomain boundaries is presented well posedness and asymptotic stability of the semidiscrete scheme is established in a general curvilinear volume with special attention given to a hexahedral domain the treatment includes a stable procedure for dealing with boundary conditions at a solid wall the efficacy of the scheme for the compressible navier stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions the results are found to agree with the solution of the compressible boundary layer equations

spectral methods in the presence of discontinuities abstract spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds for smooth problems truncation error for spectral methods vanishes exponentially in the infinity norm and l 2 norm however for non smooth problems convergence is significantly worse the l 2 norm of the error for a discontinuous problem will converge at a sub linear rate and the infinity norm will not converge at all we explore and improve upon a post processing technique optimally convergent mollifiers to recover exponential convergence from a poorly converging spectral reconstruction of non smooth data this is an important first step towards using these techniques for simulations of realistic systems