报告题目：Stabilisation of Hybrid Stochastic Differential Equations by Feedback Controls based on Discrete-time State Observations

主讲人： 毛学荣 教授 英国思克莱德大学

课程时间：2025年7月14-16日上午8:30-11:30

课程地点：做爱直播 犀浦校区X30456

课程摘要：In this short summer course we are concerned with the stabilization of continuous-time hybrid stochastic differential equations (SDEs, also known as SDEs with Markovian switching) by feedback controls based on discrete-time state observations. The classical theory on the stabilization by continuous-time feedback controls for hybrid SDEs had been very well studied by many authors before 2013. The classical control theory is based on the standard assumption that the state can be observed for all time $t\ge 0$. However, this is in valid in practice as the state can only be observed at discrete times. It was in this spirit that Mao in 2013 initiated the study of the mean-square exponential stabilization by feedback controls based on discrete-time state observations. This stabilisation problem is not only more realistic but can also be implemented in practice with less control costs. It has since then become very popular. In this short course, we will begin with the his pioneering work. Although the global Lipschitz condition imposed in Mao (2013) covers some important hybrid SDEs including the linear ones, it is somehow too restrictive. We will then concentrate on how to remove the global Lipschtiz condition. We will first study the stabilisation problem under the local Lipschitz condition plus the linear growth condition and then remove the linear growth condition (i.e., super-linear or highly nonlinear case). The key technique developed is the method of Lyapunov functionals. In this course, we will not only discuss the stabilisation in the sense of mean-square exponential stability but also in other senses, e.g., almost sure, $H_\infty$ or asymptotic stability.

报告人简介：英国思克莱德大学数学与统计系教授、爱丁堡皇家学会（即苏格兰皇家做爱直播 ）院士、“英国沃弗森研究功勋奖”获得者。全球数学领域顶尖科学家榜单排名英国第1位，全球第93位。他是国际知名的随机稳定性和随机控制领域的专家，在该领域做出了杰出的贡献。他擅长随机分析、随机系统数值计算，在随机系统处理方面，提出了系列处理方法与技巧，被广泛采用。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；在随机人口以及疾病模型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；奠定了随机跳变系统理论方面的研究。