讲座题目：Stabilization of Hybrid Stochastic Differential Equations by Delay Feedback Controls 主讲人：毛学荣 教授 主持人：李韬 教授 开始时间：2019-11-08 15:30:00 讲座地址🐌：中北校区地理馆 273教室 主办单位：数学科学学院
报告人简介： 毛学荣教授是英国斯克莱德大学数学与统计系教授、英国苏格兰皇家学院院士，英国沃弗森研究功勋奖。他是国际知名的随机稳定性和随机控制领域的专家，在本学科领域享有很高的声誉, 为现代随机稳定性领域的重要奠基人。他擅长随机分析，在对随机系统处理方面，提出了系列处理方法与技巧🤸🏽♀️，颇具特色👨🏿💻，被广泛采用，在该领域做出了巨大的贡献👶🏽。例如，对噪声镇定给出了科学的理论，被后续跟踪者所广泛推崇👊🏼；在随机系统数值计算方面做出了开创性的工作；在随机人口理论方面做出了突出的贡献；在随机系统LaSalle原理方面做出了开拓性的工作；并在随机跳变系统理论方面进行深入的研究🧝🏼♂️。毛学荣教授出版的专著和论文被该领域研究人员广发推崇、使用🧏🏽♂️、引用😗，如专著：“Stochastic Differential Equations and Their Applications (the 2nd ed.), Elsevier, 2007“已被Google Scholar检索4000多次𓀎🏑。 报告内容🏄🏼♂️🏊🏿： Given an unstable hybrid stochastic differential equation (SDE), can we design a delay feedback control to make the controlled hybrid SDE become asymptotically stable? This is possible if the drift and diffusion coefficients of the given SDE satisfy the linear growth condition. However, many hybrid SDE models in the real world do not fulfil this condition (namely, they are highly nonlinear). In order to stabilize these highly nonlinear hybrid SDEs, we will need to establish a new theory on the delay dependent stability criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) as almost all existing delay dependent stability criteria require the drift and diffusion coefficients of the SDDEs satisfy the linear growth condition. Making use of our new delay dependent stability, we willdemonstrate how to design the delay feedback controls in order to stabilize a class of highly nonlinear hybrid SDEs whose coefficients satisfy the polynomial growth condition. |
