報(bào)告題目：Stabilisation of Hybrid Stochastic Differential Equations by Feedback Controls based on Discrete-time State Observations

主講人： 毛學(xué)榮 教授 英國(guó)思克萊德大學(xué)

課程時(shí)間：2025年7月14-16日上午8:30-11:30

課程地點(diǎn)：kaiyun開(kāi)云官方網(wǎng)站犀浦校區(qū)X30456

課程摘要：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.

報(bào)告人簡(jiǎn)介：英國(guó)思克萊德大學(xué)數(shù)學(xué)與統(tǒng)計(jì)系教授、愛(ài)丁堡皇家學(xué)會(huì)（即蘇格蘭皇家學(xué)院）院士、“英國(guó)沃弗森研究功勛獎(jiǎng)”獲得者。他是國(guó)際知名的隨機(jī)穩(wěn)定性和隨機(jī)控制領(lǐng)域的專(zhuān)家，在該領(lǐng)域做出了杰出的貢獻(xiàn)。他擅長(zhǎng)隨機(jī)分析、隨機(jī)系統(tǒng)數(shù)值計(jì)算，在隨機(jī)系統(tǒng)處理方面，提出了系列處理方法與技巧，被廣泛采用。例如，對(duì)噪聲鎮(zhèn)定給出了科學(xué)的理論，被后續(xù)跟蹤者所廣泛推崇；在隨機(jī)人口以及疾病模型理論方面做出了突出的貢獻(xiàn)；在隨機(jī)系統(tǒng)LaSalle原理方面做出了開(kāi)拓性的工作；奠定了隨機(jī)跳變系統(tǒng)理論方面的研究。