Control and averaging
报 告 人:: Enrique Zuazua
报告地点:: 综合教学楼106室
报告时间:: 2018年08月10日星期五10:00-11:00

This lecture is devoted to discussing various manners on which averaging methods may interact with control problems.First, we address the problem of controlling uncertain systems submitted to parametrized perturbations. We introduce the notion of averaged control according to which one aims to control the average of the states with respect to the parameters. We observe that this property is equivalent to a suitable averaged observability one. We discuss both finite-dimensional systems and Partial Differential Equations. As we shall observe, the averaged dynamics may have a rather different behaviour than the original one, but, despite of this, averaged controllability still holds in a number of relevant situations. We shall also describe how this averaged controllability property can be seen as an weaker version of the classical notion of simultaneous controllability.We shall also present the role that averaging can play in a different context of optimal location of actuators and sensors. As we shall show averaging with respect to some randomisation parameter may led to a diagonalization of the criteria under consideration to make the problem become spectrally diagonal and easier to treat.We will also present some open problems and perspectives of future developments. This work has been developed in collaboration with J. Lohéac, M. Lazar, Q. Lü, Y. Privat and E. Trélat.


发 布 人:吴双 发布时间: 2018-08-05