講座主題：Generalized solution and ISS stability of PDE-ODE system with discontinuous control
專家姓名：王軍民
工作單位：北京理工大學
講座時間：2021年10月15日 19:00-20:00
講座地點：騰訊會議，會議ID：953 199 320，會議密碼：666666
主辦單位：煙臺大學數學院
內容摘要：
It is known that an ODE equation has a unique local solution if the right side function has the Lipschitz continuity. However, for a control system, the control input is usually discontinuous. The new concept of Filippov solution is introduced to overcome the mathematical obstructions of the discontinuous ODE in 1990's, and a generalized solution is developed by Levaggi in 2002 to treat for a PDE system with discontinuous input.
In this talk, we discuss the generalized solution and ISS stability for a PDE-ODE cascaded system with disturbances appearing in all channels subject to discontinuous boundary controller. Firstly, we extend the definition of Filippov solution of ODE with discontinuous right hand to PDE subject to discontinuous boundary controller. Secondly, we take an ODE cascaded with a reaction- diffusion equation as an example to illustrate the solution of PDE-ODE cascaded system with discontinuous boundary controller. Finally, based on the Lyapunov method, the input-to-state stability of an ODE cascaded with a reaction-diffusion equation subject to discontinuous boundary controller is achieved.
主講人介紹：
王軍民，北京理工大學教授、博導。研究領域：控制理論與應用。2004年在香港大學獲博士學位，2009年為北京理工大學教授。主持國家自然科學基金5項，自然科學重點基金子課題1項，發表學術期刊論文100多篇，撰寫專著2部。2007年入選教育部新世紀優秀人才、2012年獲北京市科學技術二等獎、2019年獲教育部自然科學二等獎、《Control Theory and Technology》期刊副主編。
