讲座主题：Generalized solution and ISS stability of PDE-ODE system with discontinuous control

专家姓名：王军民

工作单位：北京理工大学

讲座时间：2021年10月15日 19:00-20:00

讲座地点：腾讯会议，会议ID：953 199 320，会议密码：666666

主办单位：9728太阳集团数学院

内容摘要：

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.

主讲人介绍：

王军民，北京理工大学教授、博导。研究领域：控制理论与应用。2004年在香港大学获博士学位，2009年为北京理工大学教授。主持国家自然科学基金5项，自然科学重点基金子课题1项，发表学术期刊论文100多篇，撰写专著2部。2007年入选教育部新世纪优秀人才、2012年获北京市科学技术二等奖、2019年获教育部自然科学二等奖、《Control Theory and Technology》期刊副主编。