In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,trunca...In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.展开更多
永磁同步直线电机(permanent magnet linear synchronous motor,PMLSM)凭借直接将电能转化为直线运动、无机械传动结构的特性,在高端装备制造中应用广泛。然而,传统矢量控制存在动态响应和稳态精度不足的问题,难以满足复杂工况下的高性...永磁同步直线电机(permanent magnet linear synchronous motor,PMLSM)凭借直接将电能转化为直线运动、无机械传动结构的特性,在高端装备制造中应用广泛。然而,传统矢量控制存在动态响应和稳态精度不足的问题,难以满足复杂工况下的高性能位置控制需求。滑模控制作为一种强鲁棒性的非线性控制方法,可有效抑制PMLSM系统中的参数摄动、摩擦扰动和负载突变等非线性因素影响。考虑PMLSM多变量、强耦合和受非线性因素影响大的特点,对PMLSM位置滑模控制策略展开综述,分析其核心原理与实现机制,探讨不同滑模控制方法的特性与进展,为提升PMLSM位置控制精度和鲁棒性提供理论参考,助推其在高端装备制造等领域的进一步应用与发展。展开更多
In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·...In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·)are allowed to contain some super-linearly growing terms.An explicit method is proposed by using the idea of truncating terms that grow too fast.Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained.The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense.Simulations are provided to demonstrate the theoretical results.展开更多
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to ...At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.展开更多
基金Supported by the National Natural Science Foundation of China(11926322)the Fundamental Research Funds for the Central Universities of South-Central MinZu University(CZY22013,3212023sycxjj001)。
文摘In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.
文摘永磁同步直线电机(permanent magnet linear synchronous motor,PMLSM)凭借直接将电能转化为直线运动、无机械传动结构的特性,在高端装备制造中应用广泛。然而,传统矢量控制存在动态响应和稳态精度不足的问题,难以满足复杂工况下的高性能位置控制需求。滑模控制作为一种强鲁棒性的非线性控制方法,可有效抑制PMLSM系统中的参数摄动、摩擦扰动和负载突变等非线性因素影响。考虑PMLSM多变量、强耦合和受非线性因素影响大的特点,对PMLSM位置滑模控制策略展开综述,分析其核心原理与实现机制,探讨不同滑模控制方法的特性与进展,为提升PMLSM位置控制精度和鲁棒性提供理论参考,助推其在高端装备制造等领域的进一步应用与发展。
基金Wei Liu would like to thank Shanghai Rising-Star Program(Grant No.22QA1406900)Science and Technology Innovation Plan of Shanghai(Grant No.20JC1414200)the National Natural Science Foundation of China(Grant Nos.11871343,11971316 and 12271368)for their financial support.
文摘In this paper,numerical methods for the time-changed stochastic differential equations of the form dY(t)=a(Y(t))dt+b(Y(t))dE(t)+s(Y(t))dB(E(t))are investigated,where all the coefficients a(·),b(·)and s(·)are allowed to contain some super-linearly growing terms.An explicit method is proposed by using the idea of truncating terms that grow too fast.Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained.The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense.Simulations are provided to demonstrate the theoretical results.
基金supported by the National Natural Science Foundation of China(No.1097123131071560)+1 种基金the NSF of Guangdong Province(No.101510225010000048151027501000053)
文摘At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
