In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates...In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.展开更多
Unknown dynamics including mismatched mechanical dynamics(i.e.,parametric uncertainties,unmodeled friction and external disturbances)and matched actuator dynamics(i.e.,pressure and flow characteristic uncertainties)br...Unknown dynamics including mismatched mechanical dynamics(i.e.,parametric uncertainties,unmodeled friction and external disturbances)and matched actuator dynamics(i.e.,pressure and flow characteristic uncertainties)broadly exist in hydraulic actuation systems(HASs),which can hinder the achievement of high-precision motion axis control.To surmount the practical issue,an observer-based control framework with a simple structure and low computation is developed for HASs.First,a simple observer is utilized to estimate mismatched and matched unknown dynamics for feedforward compensation.Then combining the backstepping design and adaptive control,an appropriate observer-based composite controller is provided,in which nonlinear feedback terms with updated gains are adopted to further improve the tracking accuracy.Moreover,a smooth nonlinear filter is introduced to shun the“explosion of complexity”and attenuate the impact of sensor noise on control performance.As a result,this synthesized controller is more suitable for practical use.Stability analysis uncovers that the developed controller assures the asymptotic convergence of the tracking error.The merits of the proposed approach are validated via comparative experiment results applied in an HAS with an inertial load as well.展开更多
This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity~ we rewrite the two types of stochastic hype...This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity~ we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete finite element method for the regularized equation. We derive the modeling error by using “Green＇s method” and the finite element approximation error by using the error estimates of the deterministic equation. Some numerical examples are presented to verify the theoretical results.展开更多
In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY mo...In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numericalexperiments are presented to illustrate the efficiency of the proposed algorithm.展开更多
We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an i...We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the β-mixing case and the ρ-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be -consistent and fast rates of convergence have been established.展开更多
In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solv...In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method.In particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing literature.Finally,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.展开更多
In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution w...In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model areremoved, and the mild conditions are obtained to guarantee the optimal rates of the estimatorof autoregression function. In addition, the strongly consistent estimator of the variance ofwhite noise is also constructed.展开更多
In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen–Cahn equations driven by space-time white noise on T^(2). First we prove that the convergence rate for stochastic 2D he...In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen–Cahn equations driven by space-time white noise on T^(2). First we prove that the convergence rate for stochastic 2D heat equation is of order α-δ in Besov space C^(-α) for α∈(0, 1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen–Cahn equations of order α-δ in C^(-α) for α∈(0, 2/9) and δ > 0 arbitrarily small.展开更多
In this paper,we consider variational approaches to handle the multiplicative noise removal and deblurring problem.Based on rather reasonable physical blurring-noisy assumptions,we derive a new variational model for t...In this paper,we consider variational approaches to handle the multiplicative noise removal and deblurring problem.Based on rather reasonable physical blurring-noisy assumptions,we derive a new variational model for this issue.After the study of the basic properties,we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model.The relaxed model is solved by an alternating minimization approach.Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China(61873126)。
文摘In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.
基金This work was supported in part by the National Key R&D Program of China(No.2021YFB2011300)the National Natural Science Foundation of China(No.52075262,51905271,52275062)+1 种基金the Fok Ying-Tong Education Foundation of China(No.171044)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX22_0471).
文摘Unknown dynamics including mismatched mechanical dynamics(i.e.,parametric uncertainties,unmodeled friction and external disturbances)and matched actuator dynamics(i.e.,pressure and flow characteristic uncertainties)broadly exist in hydraulic actuation systems(HASs),which can hinder the achievement of high-precision motion axis control.To surmount the practical issue,an observer-based control framework with a simple structure and low computation is developed for HASs.First,a simple observer is utilized to estimate mismatched and matched unknown dynamics for feedforward compensation.Then combining the backstepping design and adaptive control,an appropriate observer-based composite controller is provided,in which nonlinear feedback terms with updated gains are adopted to further improve the tracking accuracy.Moreover,a smooth nonlinear filter is introduced to shun the“explosion of complexity”and attenuate the impact of sensor noise on control performance.As a result,this synthesized controller is more suitable for practical use.Stability analysis uncovers that the developed controller assures the asymptotic convergence of the tracking error.The merits of the proposed approach are validated via comparative experiment results applied in an HAS with an inertial load as well.
基金The authors would like to express their sincere gratitude to the anony- mous reviewers for their careful reading of the manuscript, as well as their comments that lead to a considerable improvement of the original manuscript. The first author was supported by the National Natural Science Foundation of China under grant 61271010 and by Beijing Natural Science Foundation under grant 4152029.
文摘This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity~ we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete finite element method for the regularized equation. We derive the modeling error by using “Green＇s method” and the finite element approximation error by using the error estimates of the deterministic equation. Some numerical examples are presented to verify the theoretical results.
基金Supported by the National Natural Science Foundation of China under Grants No.11671004 and 91330101Natural Science Foundation for Colleges and Universities in Jiangsu Province under Grants No.15KJB110018 and 14KJB110020
文摘In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numericalexperiments are presented to illustrate the efficiency of the proposed algorithm.
文摘We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the β-mixing case and the ρ-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be -consistent and fast rates of convergence have been established.
基金supported by the National Natural Science Foundation of China(No.12071403)the Scientific Research Foundation of Hunan Provincial Education Department of China(No.18A049).
文摘In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method.In particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing literature.Finally,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.
文摘In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model areremoved, and the mild conditions are obtained to guarantee the optimal rates of the estimatorof autoregression function. In addition, the strongly consistent estimator of the variance ofwhite noise is also constructed.
基金Research supported in part by NSFC(Nos.11671035,11922103)Financial support by the DFG through the CRC 1283“Taming uncertainty and profiting from randomness and low regularity in analysis,stochastics and their applications”is acknowledged。
文摘In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen–Cahn equations driven by space-time white noise on T^(2). First we prove that the convergence rate for stochastic 2D heat equation is of order α-δ in Besov space C^(-α) for α∈(0, 1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen–Cahn equations of order α-δ in C^(-α) for α∈(0, 2/9) and δ > 0 arbitrarily small.
基金supported in part by:Hong Kong RGC 203109,211710,RGC 211911the FRGs of Hong Kong Baptist University+2 种基金NSFC Grant No.11101195 and No.11171371Specialized Research Fund for the Doctoral Program of Higher Education of China No.20090211120011China Postdoctoral Science Foundation funded project No.2011M501488.
文摘In this paper,we consider variational approaches to handle the multiplicative noise removal and deblurring problem.Based on rather reasonable physical blurring-noisy assumptions,we derive a new variational model for this issue.After the study of the basic properties,we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model.The relaxed model is solved by an alternating minimization approach.Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.
