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Control Theory of Ensembles of Dynamical Systems

动力系统系综控制理论

基本信息

批准号：
295903128
负责人：
Professor Dr.-Ing. Frank Allgöwer
金额：
--
依托单位：
Harvard School of Engineering and Applied Sciences
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/295903128?language=en
关键词：
Control Theory Ensembles Dynamical Systems

项目摘要

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.

系综是几乎相同的动力系统的种群，只能作为一个整体来控制和观察。一个典型的例子，说明需要考虑这样的系统类是由异质细胞群体，其中群体中的异质单细胞不能单独影响，但只有通过共同的刺激，这是相同的群体中的所有细胞的应用。同样地，为了观察细胞内的动态过程，典型的测量设备（例如流式细胞仪）仅提供关于整个群体的数据。除了这个细胞生物学的例子，在量子物理、过程工程和机器人等领域，也出现了许多与系综相关的问题。这些看似不同的问题的共同主题是考虑一个系统的副本的总体，以及仅在总体水平上相互作用的前提，这也是近年来开始引起控制界的大量关注。然而，尽管对这些新问题的兴趣越来越大，我们对控制理论中的基本方面的理解仍然非常有限。该项目的目的是通过为以系综类为中心的问题提供系统和控制理论基础，启动对系综控制理论基本原理的研究。为此，该项目将重点研究由概率分布描述的集合的可控性和可观测性的基本概念，并开发新的集合框架所需的新方法和概念。