Control and averaging

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.

举办单位：数学与统计学院

发 布 人：吴双 发布时间： 2018-08-05

发 布 人：吴双 发布时间： 2018-08-05

Zuazua教授为欧洲科学院院士，从教于马德里自治大学。前任“ESIAM:COCV”主编，现任数十种国际顶尖杂志编委。Google学术引用一万余次，为科学情报研究所（ISI）“高引作者”。在欧洲数学大会（ECM）、国际数学家大会（ICM）等数十次会议上做邀请报告。多次受邀访问欧美、拉丁美洲、亚洲等各地大学与研究所，如法国Courant研究所、巴黎六大、英国剑桥牛顿研究所、美国明尼苏达大学、巴西里约热内卢联邦大学、四川大学、复旦大学等。主要研究方向为：偏微分方程、控制理论、数值分析。