Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using c...Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using complex network theory,this study proposes a hierarchy for TSN and introduces the concept of bounded time error.A coupling model between traffic scheduling and time synchronization is established,deriving functional relationships among end-to-end delay,delay jitter,gate window,and time error.These relationships illustrate that time errors can trigger jumps in delay and delay jitter.To evaluate different time errors impact on traffic scheduling performance,an end-to-end transmission experiment scheme is designed,along with the construction of a TSN test platform implementing two representative cases.Case A is a closed TSN domain scenario with pure TSN switches emulating closed factory floor network.Case B depicts remote factory interconnection where TSN domains link via non-TSN domains composed of OpenFlow switches.Results from Case A show that delay and delay jitter on a single node are most significantly affected by time errors,up to one gating cycle.End-to-end delay jitter tends to increase with the number of hops.When the ratio of time error bound to window exceeds 10%,the number of schedulable traffic flows decreases rapidly.Case B reveals that when time error is below 1μs,the number of schedulable traffic flows begins to increase significantly,approaching full schedulability at errors below 0.6μs.展开更多
The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower b...The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.展开更多
In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.T...In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.展开更多
Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and unif...Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.展开更多
We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap function...We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.展开更多
Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive an...Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.展开更多
The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction pr...The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.展开更多
Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time interva...Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time intervals,Gawronski and Juang’s time-limited model reduction schemes produce an unstable reduced-order model for the 2-D and 1-D models.Researchers revealed some stability preservation solutions to address this key flaw which ensure the stability of 1-D reduced-order systems;nevertheless,these strategies result in large approximation errors.However,to the best of the authors’knowledge,there is no literature available for the stability preserving time-limited-interval Gramian-based model reduction framework for the 2-D discrete-time systems.In this article,2-D models are decomposed into two separate sub-models(i.e.,two cascaded 1-D models)using the condition of minimal rank-decomposition.Model reduction procedures are conducted on these obtained two 1-D sub-models using limited-time Gramian.The suggested methodology works for both 2-D and 1-D models.Moreover,the suggested methodology gives the stability of the reduced model as well as a priori error-bound expressions for the 2-D and 1-D models.Numerical results and comparisons between existing and suggested methodologies are provided to demonstrate the effectiveness of the suggested methodology.展开更多
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
We consider the abstract linear inequality system （A, C, b） and give a sufficient condition for the system （A, C, b） to have an error bound, which extends the previous result.
In this paper,we consider the global error bound for the generalized complementarity problem(GCP)with analytic functions.Based on the new technique,we establish computable global error bound under milder conditions,wh...In this paper,we consider the global error bound for the generalized complementarity problem(GCP)with analytic functions.Based on the new technique,we establish computable global error bound under milder conditions,which refines the previously known results.展开更多
In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper ...In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).展开更多
Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and ...Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.展开更多
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-v...Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-varying,nonlinear,and strongly coupled characteristics of parallel machining modules.In addition,the time delay in the system reduces the timeliness of the feedback data,thereby making online contour error calculations and compensation particularly difficult.To solve this problem,the generation mechanism of the time delay of the feedback data and contour error is revealed,and a systematic method for the identification of the time-delay parameter based on Beckhoff’s tracking error calculation mechanism is proposed.The temporal alignment between the position commands and feedback data enables the online calculation of the contour error.On this basis,the tracking error of the drive axes(an important factor resulting in end-effector contour errors)is used for the contour error calculation.Considering the ambiguous parameter-setting logic of the servo drive,the servo parameter is calculated in reverse using the steady-state error to obtain the tracking error model of the drive axes.Furthermore,combined with the system time-delay model,an online correction method for the tracking error estimation model is established.To achieve an accurate mapping of the drive-axis tracking error and end-effector contour error,a bounded iterative search method for the nearest contour point and online calculation model for the contour error are respectively established.Finally,an online compensation controller for contour error is designed.Its effectiveness is verified by a machining experiment on a frame workpiece.The machining results show that the contour error reduces from 68μm to 45μm,and the finish machining accuracy increases by 34%.This study provides a feasible method for online compensation of contour error in a system with time delay.展开更多
Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
基金supported in part by the Science and Technology Research and Development Foundation of China Academy of Railway Sciences Corporation Limited(Grant No.2023YJ364)in part by National Key R&D Program of China(Grant No.2022YFC3803700)in part by the project of Beijing Laboratory of Advanced Information Networks.
文摘Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using complex network theory,this study proposes a hierarchy for TSN and introduces the concept of bounded time error.A coupling model between traffic scheduling and time synchronization is established,deriving functional relationships among end-to-end delay,delay jitter,gate window,and time error.These relationships illustrate that time errors can trigger jumps in delay and delay jitter.To evaluate different time errors impact on traffic scheduling performance,an end-to-end transmission experiment scheme is designed,along with the construction of a TSN test platform implementing two representative cases.Case A is a closed TSN domain scenario with pure TSN switches emulating closed factory floor network.Case B depicts remote factory interconnection where TSN domains link via non-TSN domains composed of OpenFlow switches.Results from Case A show that delay and delay jitter on a single node are most significantly affected by time errors,up to one gating cycle.End-to-end delay jitter tends to increase with the number of hops.When the ratio of time error bound to window exceeds 10%,the number of schedulable traffic flows decreases rapidly.Case B reveals that when time error is below 1μs,the number of schedulable traffic flows begins to increase significantly,approaching full schedulability at errors below 0.6μs.
文摘The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.
基金This work is supported by the National Natural Science Foundation of China(11661058,11761053)the Natural Science Foundation of Inner Mongolia(2017MS0107)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07).
文摘In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.
基金Project supported by Scientific Research Common Program of Beijing Municipal Commission of Education of China (No.KM200310015060)
文摘Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
基金supported by the National Natural Science Foundation of China (No. 10671050)the Natural Science Foundation of Heilongjiang Province of China (No. A200607)
文摘We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.
基金Project supported by the Major State Basic Research Development Program of China(Grant No.2012CB215202)the National Natural Science Foundation of China(Grant Nos.61104080 and 61134001)the Fundamental Research Funds for the Central Universities(Grant No.CDJZR13 175501)
文摘Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.
文摘The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.
文摘Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time intervals,Gawronski and Juang’s time-limited model reduction schemes produce an unstable reduced-order model for the 2-D and 1-D models.Researchers revealed some stability preservation solutions to address this key flaw which ensure the stability of 1-D reduced-order systems;nevertheless,these strategies result in large approximation errors.However,to the best of the authors’knowledge,there is no literature available for the stability preserving time-limited-interval Gramian-based model reduction framework for the 2-D discrete-time systems.In this article,2-D models are decomposed into two separate sub-models(i.e.,two cascaded 1-D models)using the condition of minimal rank-decomposition.Model reduction procedures are conducted on these obtained two 1-D sub-models using limited-time Gramian.The suggested methodology works for both 2-D and 1-D models.Moreover,the suggested methodology gives the stability of the reduced model as well as a priori error-bound expressions for the 2-D and 1-D models.Numerical results and comparisons between existing and suggested methodologies are provided to demonstrate the effectiveness of the suggested methodology.
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
基金Supported by the National Science Foundation of China（10361008） Supported by the Natural Science Foundation of Yunnan Province（2003A0002M）
文摘We consider the abstract linear inequality system （A, C, b） and give a sufficient condition for the system （A, C, b） to have an error bound, which extends the previous result.
基金supported by National Natural Science Foundation of China(Nos.11171180 and 11101303)Specialized Research Fund for the Doctoral Program of Chinese Higher Education(No.20113705110002)Shandong Provincial Natural Science Foundation(Nos.ZR2010AL005 and ZR2011FL017)
文摘In this paper,we consider the global error bound for the generalized complementarity problem(GCP)with analytic functions.Based on the new technique,we establish computable global error bound under milder conditions,which refines the previously known results.
文摘In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).
基金Supported by the Natural Science Foundation of Zhejiang Province（Y6090361）
文摘Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.
文摘In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
基金Supported by National Natural Science Foundation of China(Grant Nos.52375018,92148301).
文摘Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-varying,nonlinear,and strongly coupled characteristics of parallel machining modules.In addition,the time delay in the system reduces the timeliness of the feedback data,thereby making online contour error calculations and compensation particularly difficult.To solve this problem,the generation mechanism of the time delay of the feedback data and contour error is revealed,and a systematic method for the identification of the time-delay parameter based on Beckhoff’s tracking error calculation mechanism is proposed.The temporal alignment between the position commands and feedback data enables the online calculation of the contour error.On this basis,the tracking error of the drive axes(an important factor resulting in end-effector contour errors)is used for the contour error calculation.Considering the ambiguous parameter-setting logic of the servo drive,the servo parameter is calculated in reverse using the steady-state error to obtain the tracking error model of the drive axes.Furthermore,combined with the system time-delay model,an online correction method for the tracking error estimation model is established.To achieve an accurate mapping of the drive-axis tracking error and end-effector contour error,a bounded iterative search method for the nearest contour point and online calculation model for the contour error are respectively established.Finally,an online compensation controller for contour error is designed.Its effectiveness is verified by a machining experiment on a frame workpiece.The machining results show that the contour error reduces from 68μm to 45μm,and the finish machining accuracy increases by 34%.This study provides a feasible method for online compensation of contour error in a system with time delay.
文摘Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
