主题:  随机微分方程及其应用研讨会主讲人:  Xuerong Mao、费为银、毛伟、蔡泳玫、张振中、陆见秋地点:  松江校区2号学院楼331理学院报告厅时间:  2019-08-03 09:00:00组织单位:   理学院

报告时间：2019年8月3日 9:00-10:00

报告主题：Stabilisation by Delay Feedback Control for Highly Nonlinear Hybrid Stochastic DifferentialEquations

报告学者：Xuerong Mao

学者简介：Xuerong Mao(毛学荣)，英国Strathclyde大学数学与统计系教授，苏格兰皇家学会院士，教育部海外名师，亿万先生mr01官网兼职特聘教授。

报告摘要：Given an unstable hybrid stochastic differential equation (SDE, also knownas an SDE with Markovian switching), can we design a \emph{delay} feedback control to make the controlled hybrid SDE become asymptotically stable? In 2008, Mao et al. were the first to study the stabilisation by \emph{delay} feedback controls for hybrid SDEs, though the stabilization by \emph{non-delay} feedback controls had been well studied. Acritical condition imposed there is that both drift and diffusion coefficients of the given hybrid SDE need to satisfy the linear growth condition. However, many hybrid SDE models in the real world do not fulfill this condition (namely, they are highly nonlinear) and hence there is a need to develop a new theory for these highly nonlinear SDE models. The aim of this paper is to design \emph{delay} feedback controls inorder to stabilise a class of highly nonlinear hybrid SDEs whose coefficients satisfy the polynomial growth condition.

报告时间：2019年8月3日 ‍10:15-11:15

报告主题：Stabilization of highly nonlinear continuous-time hybrid stochastic delay differential equations by discrete-time feedback control

报告学者：费为银

学者简介：费为银，博士，教授(二级)，博士生导师，安徽工程大学研究生部主任。在SIAM J.Control Optim.、Automatica、Systems andControl Letters、NonlinearAnalysis、Information Sciences、数学学报、数学年刊等国内外学术刊物上发表论文180余篇，其中SCI收录论文34篇，EI收录论文25 篇。主持了国家自然科学基金、教育部科学技术研究重点项目、安徽省自然科学基金等项目多项。

报告摘要：In this talk, we consider how to use discrete-time state feedback to stabilize hybrids to chastic differential delay equations. The coefficients of these stochastic differential delay equations do not satisfy the conventional linear growth conditions, but are highly nonlinear. Using the Lyapunov functional method, we show that a discrete feedback controller $u(x([t/\T] \T), r(t),t)$ can bedesigned to make the solutions of such controlled hybrid stochastic differential delay equations asymptotically stable and exponentially stable. The upper bound of the discrete observation interval $\T $ is also given in the article.Finally, a numerical examplesare given to illustrate our theory. This paper is a joint work with Mei C., FeiC. and Mao X.

报告时间：2019年8月3日 ‍13:30-14:15

报告主题：Almost surestability with general decay of neutral stochastic pantograph equations with Markovian switching

报告学者：毛伟

学者简介：毛伟，江苏第二师范学院副教授，主要从事随机微分方程稳定性和数值解法的研究工作。主持过国家自然科学基金，江苏省高校自然科学基金。荣获江苏省高校“青蓝工程”优秀青年骨干教师，江苏省“333高层次人才培养工程”中青年科学技术带头人。近年来在“Discrete Continuous Dynamical Systems -B”，“Journal of Computational and Applied Mathematics ”等期刊发表论文20余篇。

报告摘要：This talk focuseson the general decay stability of nonlinear neutral stochastic pantograph equations with Markovian switching (NSPEwMSs). Under the local Lipschitz condition and non-linear growth condition, the existence and almost sure stability with general decay of the solution for NSPEwMSs are investigated. By means of M-matrix theory, some sufficient conditions on the general decay stability are also established for NSPEwMSs.

报告时间：2019年8月3日 ‍14:15-15:00

报告主题：Stochastic Modelling of Nutrient Dynamics in a Sea Loch

报告学者：蔡泳玫

学者简介：蔡泳玫，博士，宁波诺丁汉大学数学科学系助理教授，主要从事生物和种群系统的随机建模。近两年在Applied Mathematical Modelling, Nonlinear Dynamics等期刊发表论文5篇。

报告摘要：This talk first constructs a stochastic differential equation (SDE) model of a fjord nutrient, based on the hydrographic and chemical data collected from the 1991 field campaign implemented in Loch Linnhe. Stochastic modelling approach is able to account for the process noise in the nutrient data. The SDE model is first extended from a deterministic nutrient model by the parameter perturbation scheme. To capture the annual variations in the sea-loch nutrient, the SDE model is refined by considering the complex physical and biological processes that make big effects on the nutrient dynamics. The model is parameterised using the least squares approach. The goodness of fit of the SDEmodel is assessed by comparing the distribution graphs and by performing statistical tests. The existence of the environmental-type process noise in the nutrient data is illustrated by a residual analysis for the data. Finally, a simulation study is carried out to identify the accuracy of the parameter estimation frameworks.

报告时间：2019年8月3日 ‍15:15-16:00

报告主题：Stability and ergodicity for non-Gaussian stable processes with Markov switching

报告学者：张振中

学者简介：张振中，亿万先生mr01官网理学院副教授、硕士生导师，中南大学博士。主要研究方向为混杂系统的随机控制及其相关问题。在相关领域已发表SCI检索论文二十多篇，部分成果发表在《Potential Analysis》、《Insurance:Mathematics and Economics》和《Stochastic Analysis and Applications》等国际重要期刊。

报告摘要：In this talk, we will focus on stability in probability and ergodicity for a class of stable processes with Markov switching. First of all, the maximum principle and the Harnack in equality for a class of stable processes with Markov switching have been established. Then some sufficient conditions for ergodicity and stability in probability of stable processes with Markov switching arepresented.

报告时间：2019年8月3日 ‍16:00-16:45

报告主题：Stabilization of nonlinear hybrid delay systems by feedback controls based on discrete-time observations

报告学者：陆见秋

学者简介：陆见秋，博士，亿万先生mr01官网统计系讲师，英国思克莱德大学（University of Strathclyde）‍统计系博士毕业。主要研究方向为随机微分方程的离散镇定控制，在SCI杂志上发表数篇论文。

报告摘要：Studying on using hybrid stochastic differential equations (with Markovian switching) to model practical systems, where the structure and parameters of these SDEs may change abruptly, has received a lot of attentions in the recent years. However, in many branches of science and industry, systems may not only depend on the current state, but also be decided by the past states. Therefore, stochasticdelay systems have also been studied intensively. One classical problem in this field is stabilization. Recently, Mao started to study on the stability problemof hybrid SDEs by discrete-time feedback control. However, as far as our knowledge, discrete-time feedback control theory has not been applied to studythe stabilization problem of hybrid delay system. Therefore, in our research,we prove the stability of hybrid SDDEs by discrete-time feedback control.

撰写：尤苏蓉