brief paper the strong stabilization of a one dimensional wave equation by non collocated dynamic boundary feedback control the stabilization of a one dimensional wave equation with non collocated observation at its unstable free end and control at another end is considered the controller comprises a state estimator which is designed in the case where the velocity is not available the method of backstepping is adopted in our design of the feedback law we use the theory of c 0 semigroups and lyapunov functionals to prove the strong stability of the resulting closed loop system

testing and modeling multivariate threshold models abstract threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years in this article i use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model the thresholds and the model are selected jointly based on the akaike information criterion the finite sample performance of the proposed test is studied by simulation the modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost of carrying the contracts in this particular application thresholds are determined in part by the transaction costs i also apply the proposed procedure to u s monthly interest rates and two river flow series of iceland

closed loop non linear control of an initially imperfect beam with non collocated input abstract a closed loop non linear control strategy to reduce the flexural vibrations of a hinged hinged initially imperfect beam is investigated the beam is subjected to a harmonic transverse excitation involved in a primary resonance of the first antisymmetric mode a closed loop symmetric control action bending moments imparted by two piezoceramic actuators although non collocated is designed to be non orthogonal in a non linear sense to the excited mode and be capable of exerting resonant beneficial damping effects onto it the approximate responses of the controlled and uncontrolled beam are constructed by applying the method of multiple scales directly to the integral partial differential equations of motion and boundary conditions the frequency response curve governing the primary resonance of the uncontrolled system is compared with that obtained when the controller is in action it is shown that by exerting feasible control efforts the response of the beam may be reduced by an order of magnitude and is stable in the overall frequency range in contrast with the uncontrolled large amplitude responses which undergo jumps at the saddle node bifurcations

strong stability of an unstable wave equation by boundary feedback with only displacement observation the stabilization of a 1 d wave equation that contains instability at its free end and control at the other end is considered the controller is designed through the estimated state that is designed in the case that only displacement is available the method of backstepping is adopted in investigation the c0 semigroup theory and lyapunov method are used to show that the closed loop system is asymptotically stable

exponential stability of variable coefficients rayleigh beams under boundary feedback controls a riesz basis approach in this paper we study the boundary stabilizing feedback control problem of rayleigh beams that have non homogeneous spatial parameters we show that no matter how non homogeneous the rayleigh beam is as long as it has positive mass density stiffness and mass moment of inertia it can always be exponentially stabilized when the control parameters are properly chosen the main steps are a detail asymptotic analysis of the spectrum of the system and the proving of that the generalized eigenfunctions of the feedback control system form a riesz basis in the state hilbert space as a by product a conjecture in guo j optim theory appl 112 3 2002 529 is answered

self weighted lad based inference for heavy tailed threshold autoregressive models abstract the least squares estimator of the threshold autoregressive tar model may not be consistent when its tail is less than or equal to 2 neither theory nor methodology can be applied to model fitting in this case this paper is to develop a systematic procedure of statistical inference for the heavy tailed tar model we first investigate the self weighted least absolute deviation estimation for the model it is shown that the estimated slope parameters are n consistent and asymptotically normal and the estimated thresholds are n consistent each of which converges weakly to the smallest minimizer of a compound poisson process based on this theory the wald test statistic is considered for testing the linear restriction of slope parameters and a procedure is given for inference of threshold parameters we finally construct a sign based portmanteau test for model checking simulations are carried out to assess the performance of our procedure and a real example is given

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

finite element approximations of compensator design for analytic generators with fully unbounded controls observations an approximation theory leading to a design of a finite dimensional compensator for control systems generated by analytic semigroups is presented the novelty of this paper with respect to other results available in the literature is threefold i it treats fully unbounded control observation operators ii it does not require compactness property of the underlined generator an assumption that is often violated in practice and iii the design of a finite dimensional compensator is based on finite element approximation of the original model rather than on modal eigenfunctions approximations which in turn require the a priori knowledge of the eigenvalues for the system applications of the theory to heat equations and plate equations are provided

the expansion of a semigroup and a riesz basis criterion problems on the expansion of a semigroup and a criterion for being a riesz basis are discussed in the present paper suppose that a is the generator of a c0 semigroup on a hilbert space and a 1 a 2 a with 2 a is consisted of isolated eigenvalues distributed in a vertical strip it is proved that if 2 a is separated and for each 2 a the dimension of its root subspace is uniformly bounded then the generalized eigenvectors associated with 2 a form an l basis under different conditions on the riesz projection the expansion of a semigroup is studied in particular a simple criterion for the generalized eigenvectors forming a riesz basis is given as an application a heat exchanger problem with boundary feedback is investigated it is proved that the heat exchanger system is a riesz system in a suitable state hilbert space

dynamic stabilization of an euler bernoulli beam under boundary control and non collocated observation abstract we study the dynamic stabilization of an euler bernoulli beam system using boundary force control at the free end and bending strain observation at the clamped end we construct an infinite dimensional observer to track the state exponentially a proportional output feedback control based on the estimated state is designed the closed loop system is shown to be non dissipative but admits a set of generalized eigenfunctions which forms a riesz basis for the state space as consequences both the spectrum determined growth condition and exponential stability are concluded

sampled data observers for 1 d parabolic pdes with non local outputs abstract the present work provides a systematic approach for the design of sampled data observers to a wide class of 1 d parabolic pdes with non local outputs the studied class of parabolic pdes allows the presence of globally lipschitz nonlinear and non local terms in the pde two different sampled data observers are presented one with an inter sample predictor for the unavailable continuous measurement signal and one without an inter sample predictor explicit conditions on the upper diameter of the uncertain sampling schedule for both designs are derived for exponential convergence of the observer error to zero in the absence of measurement noise and modeling errors moreover explicit estimates of the convergence rate can be deduced based on the knowledge of the upper diameter of the sampling schedule when measurement noise and or modeling errors are present input to output stability ios estimates of the observer error hold for both designs with respect to noise and modeling errors the main results are illustrated by two examples which show how the proposed methodology can be extended to other cases e g boundary point measurements

control of friction driven oscillation by time delayed state feedback an experimental set up is designed and fabricated to yield a single degree of freedom friction driven oscillator self excited limit cycles obtained experimentally are used to determine the numerical values of the parameters that appear in the mathematical model under pure slip condition then the control of the limit cycle using a time delayed displacement feedback is investigated the same system under harmonic excitation is also considered a pd control system with identical time delay in the displacement and velocity feedback is analysed only the primary harmonic entrainment region is investigated both the best and worst time delays are determined stability and bifurcation conditions are discussed numerical results are used to verify the analytical results obtained by using the method of multiple time scales and a parametric investigation is included the proper choice of time delay which depends on the model parameters is crucial it is shown that with appropriate choices of time delay and gain factors both the limit cycle and the steady state forced amplitude can be controlled no time delay or inappropriate time delay can enhance the vibration level

asymptotic inference in multiple threshold double autoregressive models abstract this paper investigates a class of multiple threshold models called multiple threshold double ar mtdar models a sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first order mtdar model we study the quasi maximum likelihood estimator qmle of the mtdar model the estimated thresholds are shown to be n consistent asymptotically independent and to converge weakly to the smallest minimizer of a two sided compound poisson process the remaining parameters are n consistent and asymptotically multivariate normal in particular these results apply to the multiple threshold arch model with or without ar part and to the multiple threshold ar models with arch errors a score based test is also presented to determine the number of thresholds in mtdar models the limiting distribution is shown to be distribution free and is easy to implement in practice simulation studies are conducted to assess the performance of the qmle and our score based test in finite samples the results are illustrated with an application to the quarterly us real gnp data over the period 1947 2013

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

output feedback exponential stabilization for a one dimensional wave equation with control matched nonlinear disturbance in this paper we study the output feedback exponential stabilization of a one dimensional wave equation with control matched nonlinear disturbance the well posedness of the open loop system which is essentially important for the designs of observer and controller is verified by designing an infinite dimensional unknown input state observer in place of the conventional extended state observer we estimate the total disturbance in real time moreover we prove the convergence of the disturbance estimator based on the disturbance estimator we design a state observer by compensating the total disturbance and an estimated state feedback controller to exponentially stabilize the original system by means of the riesz basis approach some numerical simulations are presented

the regularity of the wave equation with partial dirichlet control and colocated observation in this paper we analyze a multidimensional controlled wave equation on a bounded domain subject to partial dirichlet control and colocated observation by means of a partial fourier transform it is shown that the system is well posed and regular in the sense of d salamon and g weiss the corresponding feedthrough operator is found to be the identity operator on the input space

limiting properties of the least squares estimator of a continuous threshold autoregressive model the continuous threshold autoregressive model is a sub class of the threshold autoregressive model subject to the requirement that the piece wise linear autoregressive function be continuous everywhere in contrast with the discontinuous case it is shown that under suitable regularity conditions the conditional least squares estimator of the parameters including the threshold parameter is root n consistent and asymptotically normally distributed the theory is illustrated by a simulation study and is applied to the quarterly u s unemployment rates

output feedback stabilization of a one dimensional schrodinger equation by boundary observation with time delay in this article we are concerned with the stabilization of a 1 d schrodinger equation with boundary control and observation the boundary observation is suffered from an arbitrary given time delay we first show that the proportional output feedback control that stabilizes exponentially the time delay free system can not stabilize the corresponding time delay system anymore we then use the observer and predictor to solve the stabilization problem of time delay system the state is estimated in the time span where the observation is available and the state is predicted in the time interval when the observation is not available it is shown that the estimated state feedback stabilizes exponentially the time delay system the numerical simulation is presented to illustrate the effect of the stabilizing controller

the state feedback regulator problem for regular linear systems this paper is about the state feedback regulator problem for infinite dimensional linear systems the plant assumed to be an exponentially stable regular linear system is driven by a linear possibly infinite dimensional exosystem via a disturbance signal the exosystem has its spectrum in the closed right half plane and also generates the reference signal for the plant output the regulator problem is to design a controller that while guaranteeing the stability of the closed loop system without the exosystem drives the tracking error to zero a particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller under suitable assumptions we show that the latter problem is solvable if and only if a pair of algebraic equations called the regulator equations is solvable we derive conditions in terms of the transfer function of the plant and eigenvalues of the exosystem for the solvability of the regulator equations three examples illustrating the theory are presented

threshold autoregressive models for interval valued time series data abstract modeling and forecasting symbolic data especially interval valued time series its data has received considerable attention in statistics and related fields the core of available methods on its analysis is based on various applications of conventional linear modeling however few works have considered possible nonlinearities in its data in this paper we propose a new class of threshold autoregressive interval tari models for its data by matching the interval model with interval observations we develop a minimum distance estimation method for tari models and establish the asymptotic theory for the proposed estimators we show that the threshold parameter estimator is t consistent and follows an asymptotic compound poisson process as the sample size t and the estimators for other tari model parameters are root t consistent and asymptotically normal simulation studies show that the proposed tari model provides more accurate out of sample forecasts than the existing center radius self exciting threshold cr setar model for its data in the literature empirical applications to the s p 500 price index document significant asymmetric reactions of the stock markets in japan u k and france to shocks from the u s stock market and that incorporating this asymmetric effect yield better out of sample forecasts than a variety of popular models available in the literature

asymptotic error distributions for the euler method for stochastic differential equations we are interested in the rate of convergence of the euler scheme approximation of the solution to a stochastic differential equation driven by a general possibly discontinuous semimartingale and by the asymptotic behavior of the associated normalized error it is well known that for ito s equations the rate is 1 sqrt n we provide a necessary and sufficient condition for this rate to be 1 sqrt n when the driving semimartingale is a continuous martingale or a continuous semimartingale under a mild additional assumption we also prove that in these cases the normalized error processes converge in law the rate can also differ from 1 sqrt n this is the case for instance if the driving process is deterministic or if it is a levy process without a brownian component it is again 1 sqrt n when the driving process is levy with a nonvanishing brownian component but then the normalized error processes converge in law in the finite dimensional sense only while the discretized normalized error processes converge in law in the skorohod sense and the limit is given an explicit form

controlling friction induced instability by recursive time delayed acceleration feedback a novel time delayed acceleration feedback method of controlling friction induced instability is proposed a single degree of freedom mechanical oscillator on a moving belt represents the basic friction driven system the control force is synthesized based on an infinite weighted sum of the acceleration of the vibrating mass measured at regular intervals in the past such a control force can be effectively produced by the recursive summation of the time delayed acceleration and the time delayed control signal and hence the technique is termed as the recursive time delayed acceleration feedback control the local stability analysis of the equilibrium reveals nontrivial and beneficial influences of the recursive gain on the system performance robustness of the control is shown to improve with the increasing value of the recursive gain a multiple time scale based analysis of the system elucidates the role of the recursive gain in enhancing the amount of dissipation produced by the control action the influences of the time delay and the control gain on the optimized performance of the system are also discussed numerical simulations of the system equations corroborate the analytical results the present method is believed to be applicable to any self excited system having a large degree of instability that is not removable by an ordinary time delayed feedback

nonlinear analysis of a maglev system with time delayed feedback control abstract this paper undertakes a nonlinear analysis of a model for a maglev system with time delayed feedback using linear analysis we determine constraints on the feedback control gains and the time delay which ensure stability of the maglev system we then show that a hopf bifurcation occurs at the linear stability boundary to gain insight into the periodic motion which arises from the hopf bifurcation we use the method of multiple scales on the nonlinear model this analysis shows that for practical operating ranges the maglev system undergoes both subcritical and supercritical bifurcations which give rise to unstable and stable limit cycles respectively numerical simulations confirm the theoretical results and indicate that unstable limit cycles may coexist with the stable equilibrium state this means that large enough perturbations may cause instability in the system even if the feedback gains are such that the linear theory predicts that the equilibrium state is stable

on the least squares estimation of multiple regime threshold autoregressive models abstract this paper studies the least squares estimator lse of the multiple regime threshold autoregressive tar model and establishes its asymptotic theory it is shown that the lse is strongly consistent when the autoregressive function is discontinuous over each threshold the estimated thresholds are n consistent and asymptotically independent each of which converges weakly to the smallest minimizer of a one dimensional two sided compound poisson process the remaining parameters are n consistent and asymptotically normal the theory of chan 1993 is revisited and a numerical approach is proposed to simulate the limiting distribution of the estimated threshold via simulating a related compound poisson process based on the numerical result one can construct a confidence interval for the unknown threshold this issue is not straightforward and has remained as an open problem since the publication of chan 1993 this paper provides not only a solution to this long standing open problem but also provides methodological contributions to threshold models simulation studies are conducted to assess the performance of the lse in finite samples the results are illustrated with an application to the quarterly u s real gnp data over the period 1947 2009

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

a general necessary condition for exact observability suppose a generates an exponentially stable strongly continuous semigroup on the hilbert space x y is another hilbert space and c d a rightarrow y is an admissible observation operator for this semigroup this means that to any initial state in x we can associate an output function in l 2 0 infty y this paper gives a necessary condition for the exact observability of the system defined by a and c this condition called bf e is related to the hautus lemma from finite dimensional systems theory it is an estimate in terms of the operators a and c alone in particular it makes no reference to the semigroup this paper shows that bf e implies approximate observability and if a is bounded it implies exact observability this paper conjectures that bf e is in fact equivalent to exact observability the paper also shows that for diagonal semigroups bf e takes on a very simple form and applies the results to sequences of complex exponential functions

adaptive estimation of the threshold point in threshold regression this paper studies semiparametric efficient estimation of the threshold point in threshold regression the classical literature of semiparametric efficient estimation rests on the fact that the maximum likelihood estimator is efficient in any parametric submodel for a large class of loss functions however in threshold regression the maximum likelihood estimator is not efficient while the bayes estimators are efficient and different loss functions induce different efficient estimators for an additively separable loss function that separates the efficiency problem of the threshold point from that of other parameters we show that the semiparametric and parametric efficiency risk bounds coincide then we design a semiparametric empirical bayes estimator to achieve this bound in consequence the threshold point can be adaptively estimated even under conditional moment restrictions we also provide a valid confidence interval called the nonparametric posterior interval for the threshold point simulation studies show that the semiparametric empirical bayes approach is substantially better than existing methods to illustrate our procedure in practice we apply it to an economic growth model for detecting different growth patterns

adaptive observer design with heat pde sensor the problem of state and parameter estimation is addressed for systems with cascade structure including finite dimensional dynamics followed in series with infinite dimensional dynamics the formers are captured through an ode that is state and parameter affine the latter referred to as sensor dynamics are represented by a diffusion parabolic pde both equations are subject to parameter uncertainty furthermore the connection point between the ode and the pde blocs is not accessible to measurements the aim is to get online estimates of all inaccessible states and unknown parameters of both the ode and the pde subsystems this observation problem is dealt with by combining the backstepping design method and the extended kalman observer approach the obtained adaptive observer is shown to be exponentially convergent under an ad hoc persistent excitation condition

relations between the s selfdecomposable and selfdecomposable measures the classes of the s selfdecomposable and decomposable probability measures are related to the limit distributions of sequences of random variables deformed by some nonlinear or linear transformations respectively both are characterized in many different ways among others as distributions of some random integrals in particular we get that each selfdecomposable probability measure is s selfdecomposable this and other relations between these two classes seem to be rather unexpected

consistency and limiting distribution of the least squares estimator of a threshold autoregressive model it is shown that under some regularity conditions the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent the limiting distribution of the least squares estimator is derived it is shown that the estimator of the threshold parameter is n consistent and its limiting distribution is related to a compound poisson process

stabilization of bernoulli euler beams by means of a pointwise feedback force we study the energy decay of a bernoulli euler beam which is subject to a pointwise feedback force we show that both uniform and nonuniform energy decay may occur the uniform or nonuniform decay depends on the boundary conditions in the case of nonuniform decay in the energy space we give explicit polynomial decay estimates valid for regular initial data our method consists of deducing the decay estimates from observability inequalities for the associated undamped problem via sharp trace regularity results

vibration control by recursive time delayed acceleration feedback this paper presents a theoretical basis of time delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators the control signal is synthesized by an infinite weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past the proposed method is shown to have controlled linear resonant vibrations low frequency non resonant vibrations primary and 1 3 subharmonic resonances of a forced duffing oscillator the concept of an equivalent damping and natural frequency of the system is also introduced it is shown that a large amount of damping can be produced by appropriately selecting the control parameters for some combinations of the control parameters the effective damping factor of the system is shown to be inversely related to the time delay in the small delay limit selection of the optimum control parameters for controlling the forced and free vibrations is discussed it is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time delay parameter however the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain the delay values for the optimal forced response may be different from that required for the optimum transient response when both are important a suboptimal choice of the delay parameters with unity recursive gain is recommended

brief paper dynamic stabilization of an euler bernoulli beam equation with time delay in boundary observation an euler bernoulli beam equation under boundary control and delayed observation is considered an observer predictor based scheme is developed to stabilize the equation on a time interval where the observation is available the state is tracked by the observer when the observation is not available due to the delay the state is estimated by the predictor the estimation is then used in proportional feedback it is shown that the state of closed loop system decays exponentially for smooth initial values

observers for compressible navier stokes equation we consider a multidimensional model of a compressible fluid in a bounded domain we want to estimate the density and velocity of the fluid based on the observations for only velocity we build an

vibration amplitude control for a van der pol duffing oscillator with time delay abstract periodic solutions for the fundamental resonance response of a van der pol duffing system under time delayed position and velocity feedbacks are investigated using the asymptotic perturbation method two slow flow equations for the amplitude and phase of the fundamental resonance response are derived their fixed points correspond to limit cycles phase locked periodic solutions for the original system in the uncontrolled system periodic solutions exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude in many cases the amplitudes of periodic solutions do not correspond to the technical requirements it is demonstrated that if the vibration control terms are added stable periodic solutions with arbitrarily chosen amplitude can be accomplished therefore the results obtained show that an effective vibration amplitude control is possible if appropriate time delay and feedback gains are chosen

testing and modeling threshold autoregressive processes abstract the threshold autoregressive model is one of the nonlinear time series models available in the literature it was first proposed by tong 1978 and discussed in detail by tong and lim 1980 and tong 1983 the major features of this class of models are limit cycles amplitude dependent frequencies and jump phenomena much of the original motivation of the model is concerned with limit cycles of a cyclical time series and indeed the model is capable of producing asymmetric limit cycles the threshold autoregressive model however has not received much attention in application this is due to a the lack of a suitable modeling procedure and b the inability to identify the threshold variable and estimate the threshold values the primary goal of this article therefore is to suggest a simple yet widely applicable model building procedure for threshold autoregressive models based on some predictive residuals a simple statistic is proposed to test for threshold nonlinearity and specify the

symmetry based observers for some water tank problems in this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured the fluid motion is described by shallow water equations in two horizontal dimensions we build a simple nonlinear observer which takes advantage of the symmetries of fluid dynamics laws as a result its structure is based on convolutions with smooth isotropic kernels and the observer is remarkably robust to noise we prove the convergence of the observer around a steady state in numerical applications local exponential convergence is expected the observer is also applied to the problem of predicting the ocean circulation realistic simulations illustrate the relevance of the approach compared with some standard oceanography techniques

a sampled data singularly perturbed boundary control for a heat conduction system with noncollocated observation this note presents a sampled data strategy for a boundary control problem of a heat conduction system modeled by a parabolic partial differential equation pde using the zero order hold the control law becomes a piecewise constant signal in which a step change of value occurs at each sampling instant through the dasialiftingpsila technique the pde is converted into a sequence of constant input problems to be solved individually for a sampled data formulation the eigenspectrum of the parabolic system can be partitioned into two groups a finite number of slow modes and an infinite number of fast modes which is studied via the theory of singular perturbations controllability and observability of the sampled data system are preserved irrelevant to the sampling period a noncollocated output feedback design based upon the state observer is employed for set point regulation the state observer serves as an output feedback compensator with no static feedback directly from the output satisfying the so called dasialow pass propertypsila the feedback controller is thus robust against the observation error due to the neglected fast modes

estimation and model selection based inference in single and multiple threshold models this paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models we initially proceed under the assumption that the number of regimes is known a priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly theoretical properties of the resulting estimators are derived and their finite sample properties investigated

a smoothed least squares estimator for threshold regression models abstract we propose a smoothed least squares estimator of the parameters of a threshold regression model our model generalizes that considered in hansen 2000 sample splitting and threshold estimation econometrica 68 575 603 to allow the thresholding to depend on a linear index of observed regressors thus allowing discrete variables to enter we also do not assume that the threshold effect is vanishingly small our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the slope and threshold parameters

parameter estimation and stabilisation for a one dimensional wave equation with boundary output constant disturbance and non collocated control we are concerned with the parameter estimation and stabilisation of a one dimensional wave equation with an unknown constant disturbance suffered by boundary observation at one end and the non collocated control at another end an adaptive observer is designed in terms of measured velocity with unknown constant disturbance the backstepping method for infinite dimensional system is adopted in the design of the feedback law it is shown that the resulting closed loop system is asymptotically stable meanwhile the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity

output feedback stabilisation of a tree shaped network of vibrating strings with non collocated observation in this article the authors consider the simple tree shaped network of strings with non collocated observation suppose that the network consists of three strings and the displacements of these strings are continuous at the common vertex the sensors and actuators are required to be set at different vertices we propose an observer based output feedback controller to stabilise this network the exponential stability of the closed loop network is obtained based on the riesz basis approach together with estimates of the spectral distribution finally a numerical simulation is given to support these results

stabilization of an abstract second order system with application to wave equations under non collocated control and observations abstract the objective of this paper is to deal with the stabilization of multi dimensional wave equations under non collocated control and observation with the following cases a locally internal distributed control and observation b internal distributed control and boundary observation c boundary control and internal distributed observation d locally internal distributed control and boundary observation we first discuss the stability of an abstract second order infinite dimensional system under the estimated state feedback control the well posedness in the sense of d salamon is specially emphasized the result is then applied to the multi dimensional wave equations with the aforementioned three different non collocated control and observations a c finally we prove the stabilizability of a wave equation with non collocated control and observation d by using the same idea although it cannot be cast into the abstract setting

estimation of multiple regime threshold autoregressive models with structural breaks the threshold autoregressive tar model is a class of nonlinear time series models that have been widely used in many areas due to its nonlinear nature one major difficulty in fitting a tar model is the estimation of the thresholds as a first contribution this article develops an automatic procedure to estimate the number and values of the thresholds as well as the corresponding ar order and parameter values in each regime these parameter estimates are defined as the minimizers of an objective function derived from the minimum description length mdl principle a genetic algorithm ga is constructed to efficiently solve the associated minimization problem the second contribution of this article is the extension of this framework to piecewise tar modeling that is the time series is partitioned into different segments for which each segment can be adequately modeled by a tar model while models from adjacent segments are different for such piecewise tar modeling a procedure is developed to est

fitting an error distribution in some heteroscedastic time series models this paper addresses the problem of fltting a known distribution to the innovation distribution in a class of stationary and ergodic time series models the asymptotic null distribution of the usual kolmogorov smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution to overcome the dependence on the underlying model parameters we propose that tests be based on a vector of certain weighted residual empirical processes under the null hypothesis and under minimal moment conditions this vector of processes is shown to converge weakly to a vector of independent copies of a gaussian process whose covariance function depends only on the fltted distribution and not on the model under certain local alternatives the proposed test is shown to have nontrivial asymptotic power the monte carlo critical values of this test are tabulated when fltting standard normal and double exponential distributions the results obtained are shown to be applicable to garch and arma garch models the often used models in econometrics and flnance a simulation study shows that the test has satisfactory size and power for flnite samples at these models the paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions a result of independent interest

anti collocated observer based output feedback control of wave equation with cubic velocity nonlinear boundary and dirichlet control this study focuses on the observer and observer based output feedback control design for a one dimensional wave equation with van der pol type nonlinear boundary condition and dirichlet boundary co

pointwise exponential stabilization of a linear parabolic pde system using non collocated pointwise observation this paper deals with the problem of exponential stabilization for a linear distributed parameter system dps using pointwise control and non collocated pointwise observation where the system is modeled by a parabolic partial differential equation pde the main objective of this paper is to construct an output feedback controller for pointwise exponential stabilization of the linear parabolic pde system using the non collocated pointwise observation the observer based output feedback control technique is utilized to overcome the design difficulty caused by the non collocation pointwise observation we construct a luenberger type pde state observer to exponentially track the state of the pde system a collocated pointwise feedback controller is proposed based on the estimated state a variation of poincare wirtinger inequality is derived and the spatial domain is decomposed into multiple sub domains according to the number of the actuators and sensors by using lyapunov s direct method integration by parts and the variation of poincare wirtinger inequality at each sub domain sufficient conditions for the existence of the observer based out feedback controller are developed such that the resulting closed loop system is exponentially stable and presented in terms of standard linear matrix inequalities lmis furthermore the closed loop well posedness analysis is also provided by the semigroup approach extensive numerical simulation results are presented to show the performance of the proposed output feedback controller

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

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

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

admissibility and exact observability of observation operators for micro beam model time and frequency domain approaches this study focuses on the exact observability of a non classical euler bernoulli micro beam equation this non classical model was derived based on the strain gradient elasticity theory which is intended to explain the phenomenon of size effect at the micron scale spectral properties of the corresponding state operator are studied an asymptotic expression for eigenvalues is calculated and eigenfunctions are analyzed in order to check the necessary conditions for the exact observability of the system by examining the eigenfunctions it is shown that among non collocated boundary outputs only measurement of the non classical moment at the root of the beam yields an admissible observation operator and also defines an exactly observable system an alternative proof based on the multiplier method which is commonly employed in the literature on the observability and controllability of infinite dimensional dynamical systems is presented to provide a comparison between the time and frequency domain approaches

panel threshold regressions with latent group structures abstract in this paper we consider the least squares estimation of a panel structure threshold regression pstr model where both the slope coefficients and threshold parameters may exhibit latent group structures we study the asymptotic properties of the estimators of the latent group structure and the slope and threshold coefficients we show that we can estimate the latent group structure correctly with probability approaching 1 and the estimators of the slope and threshold coefficients are asymptotically equivalent to the infeasible estimators that are obtained as if the true group structures were known we study likelihood ratio based inferences on the group specific threshold parameters under the shrinking threshold effect framework we also propose two specification tests one tests whether the threshold parameters are homogeneous across groups and the other tests whether the threshold effects are present when the number of latent groups is unknown we propose a bic type information criterion to determine the number of groups in the data simulations demonstrate that our estimators and tests perform reasonably well in finite samples we apply our model to revisit the relationship between capital market imperfection and the investment behavior of firms and to examine the impact of bank deregulation on income inequality we document a large degree of heterogeneous effects in both applications that cannot be captured by conventional panel threshold regressions

the stabilization of a one dimensional wave equation by boundary feedback with noncollocated observation this note addresses the stabilization of a one dimensional wave equation with control at one end and noncollocated observation at another end a simple exponentially convergent observer is constructed the dynamical stabilizing boundary output feedback is designed via the observed state while the closed loop system is nondissipative we show its exponential stability using riesz basis approach

exponential stability of uniform euler bernoulli beams with non collocated boundary controllers a b s t r a c t we study the stability of a robot system composed of two euler bernoulli beams with noncollocated controllers by the detailed spectral analysis we prove that the asymptotical spectra of the system are distributed in the complex left half plane and there is a sequence of the generalized eigenfunctions that forms a riesz basis in the energy space since there exist at most finitely many spectral points of the system in the right half plane to obtain the exponential stability we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half plane hence the riesz basis property ensures that the system is exponentially stable finally we give some simulation for spectra of the system

on asymptotic errors in discretization of processes we study the rate at which the difference xnt xt x nt n between a process x and its time discretization converges when x is a continuous semimartingale it is known that under appropriate assumptions the rate is n so we focus here on the discontinuous case then nxn explodes for any sequence n going to infinity so we consider integrated errors of the form ynt t0xnsds or zn pt t0 xns pds for p 0 we essentially prove that the variables sups t nyns and sups tnzn ps are tight for any finite t when x is an arbitrary semimartingale provided either p 2 or break p 0 2 and x has no continuous martingale part and the sum s t xs p converges a s for all t and in addition x is the sum of its jumps when p 1 under suitable additional assumptions we even prove that the discretized processes nyn nt n and nzn p nt n vadjust vspace 1pt converge in law to nontrivial processes which are explicitly given as a by product we also obtain a generalization of ito s formula for functions that are not twice continuously differentiable and which may be of interest by itself

riesz basis property and exponential stability of controlled euler bernoulli beam equations with variable coefficients this paper studies the basis property and the stability of a distributed system described by a nonuniform euler bernoulli beam equation under linear boundary feedback control it is shown that there is a sequence of generalized eigenfunctions of the system which forms a riesz basis for the state hilbert space the asymptotic distribution of eigenvalues the spectrum determined growth condition and the exponential stability are concluded the results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam

vibration control for the primary resonance of a cantilever beam by a time delay state feedback abstract the primary resonance of a cantilever beam under state feedback control with a time delay is investigated by means of the asymptotic perturbation method two slow flow equations on the amplitude and phase of the oscillator are obtained and external excitation response and frequency response curves are shown vibration control and high amplitude response suppression can be performed with appropriate time delay and feedback gains moreover energy considerations are used in order to investigate existence and characteristics of quasiperiodic modulated motion for the cantilever beam it can be demonstrated that appropriate choices for the feedback gains and the time delay can exclude the possibility of modulated motion and reduce the amplitude peak of the primary resonance analytical results are verified with numerical simulations

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

backstepping observers for a class of parabolic pdes in this paper we design exponentially convergent observers for a class of parabolic partial integro differential equations p i des with only boundary sensing available the problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system observer gain output injection function is shown to satisfy a well posed hyperbolic pde that is closely related to the hyperbolic pde governing backstepping control gain for the state feedback problem for several physically relevant problems the observer gains are obtained in closed form the observer gains are then used for an output feedback design in both collocated and anti collocated setting of sensor and actuator the order of the resulting compensator can be substantially lowered without affecting stability explicit solutions of a closed loop system are found in particular cases

subsampling inference in threshold autoregressive models this paper discusses inference in self exciting threshold autoregressive setar models of main interest is inference for the threshold parameter it is well known that the asymptotics of the corresponding estimator depend upon whether the setar model is continuous or not in the continuous case the limiting distribution is normal and standard inference is possible in the discontinuous case the limiting distribution is non normal and it is not known how to estimate it consistently we show that valid inference can be drawn by the use of the subsampling method moreover the method can even be extended to situations where the dis continuity of the model is unknown in this case the inference for the regression parameters of the model also becomes difficult and subsampling can be used again in addition we consider an hypothesis test for the continuity of a setar model a simulation study examines small sample performance and an application illustrates how the proposed methodology works in practice

brief paper arbitrary decay rate for two connected strings with joint anti damping by boundary output feedback in this paper we are concerned with the boundary stabilization of two connected strings with middle joint anti damping for which all eigenvalues of the control free system are located on the right complex plane we first design an explicit state feedback controller to achieve exponential stability for the closed loop system consequently we design the output feedback by using infinite dimensional observer the backstepping approach is adopted in investigation it is shown that by using one boundary stabilizer only the output feedback can make the closed loop system exponentially stable with arbitrary decay rate

a new approach of stabilization of nondissipative distributed systems in this paper we propose a new approach to prove the nonlinear internal or boundary stabilization of certain nondissipative distributed systems the usual energy is not decreasing this approach leads to decay estimates known in the dissipative case when the integral inequalities method due to komornik exact controllability and stabilization the multiplier method masson paris john wiley chichester uk 1994 cannot be applied due to the lack of dissipativity first we study the stability of a semilinear wave equation with a nonlinear damping based on the equation u delta u h nabla u f u g u 0 we consider the general case with a function h satisfying a smallness condition and we obtain uniform decay of strong and weak solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related with the above equation in the second part we consider the case h nabla u nabla phi cdot nabla u with phi in w 1 infty omega we prove some precise decay estimates exponential or polynomial of equivalent energy without any restriction on phi the same results will be proved in the case of boundary feedback finally we comment on some applications of our approach to certain nondissipative distributed systems some results of this paper were announced without proof in a guesmia c r acad sci paris ser i math 332 2001 pp 633 636

hysteretic autoregressive time series models this paper extends the classical two regime threshold autoregressive model by introducing hysteresis to its regime switching structure which leads to a new model the hysteretic autoregressive model the proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism a sufficient condition is given for geometric ergodicity conditional least squares estimation is discussed and the asymptotic distributions of its estimators and information criteria for model selection are derived simulation results and an example support the model