Control Theory of Ensembles of Dynamical Systems

点击翻译按钮获取中文摘要

Ensembles are populations of nearly identical dynamical systems that can only be controlled and observed as a whole. A typical example that illustrates the need for considering such system classes is given by heterogeneous cell populations in which the heterogeneous single cells in the population cannot be influenced individually but only through the application of a common stimulus that is the same for all cells in the population. Likewise, for the observation of dynamical processes within cells, typical measurement devices such as flow cytometers only provide data about the whole population. Besides this example from cell biology, many problems related to ensembles have been emerging in fields ranging from quantum physics, process engineering and robotics. The common theme of the seemingly different problems is the consideration of populations of copies of one system, as well as the premise of interaction on the population-level only, which is also starting to attracted a lot of attention within the control community in recent years. Yet, despite the increasing interest for these novel problems, our understanding of the basic aspects in the control theory of ensembles is still very limited. The aim of this project is to initiate the study of the basic principles in the control theory of ensembles, by providing a systems and control theoretic foundation for problems centered around the class of ensembles. To this end, the project will focus on the study of the fundamental concepts of controllability and observability of ensembles which are described by probability distributions, and develops new methods and concepts which are needed for the novel framework of ensembles.