SIAM Journal on Control and Optimization, Volume 58, Issue 5, Page 2740-2764, January 2020.
Recent years have witnessed a wave of research activities in systems science toward the study of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies in life and physical sciences and engineering, from neuroscience, biology, and quantum physics to robotics, where many control-enabled applications involve manipulating a large ensemble of structurally identical dynamic units, or agents. Analyzing fundamental properties of ensemble control systems in turn plays a foundational and critical role in enabling and, further, advancing these applications, and the analysis is largely beyond the capability of classical control techniques. In this paper, we consider an ensemble of time-invariant linear systems evolving on an infinite-dimensional space of continuous functions. We exploit the notion of separating points and techniques of polynomial approximation to develop necessary and sufficient ensemble controllability conditions. In particular, we introduce an extended notion of controllability matrix, called the ensemble controllability matrix. This enables the characterization of ensemble controllability through evaluating controllability of each individual system in the ensemble. As a result, the work provides a unified framework with a systematic procedure for analyzing control systems defined on an infinite-dimensional space by a finite-dimensional approach.

中文翻译：

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关于集合可控性的分离点

SIAM控制与优化杂志，第58卷，第5期，第2740-2764页，2020年1月。
近年来，目睹了针对人口系统研究的系统科学研究热潮。从神经科学，生物学，量子物理学到机器人技术，生命和物理科学与工程学中众多新兴和日新月异的技术为这种转变提供了动力，其中许多控制使能的应用程序涉及操纵结构相同的大型整体动力学。单位或代理商。反过来，对集成控制系统的基本属性进行分析在实现并进一步促进这些应用方面起着基础性和关键性的作用，而这种分析在很大程度上超出了传统控制技术的能力。在本文中，我们考虑在连续函数的无穷维空间上演化的时不变线性系统的集合。我们利用分离点的概念和多项式逼近的技术来开发必要和足够的整体可控性条件。特别是，我们引入了可控性矩阵的扩展概念，称为整体可控性矩阵。通过评估集成中每个单独系统的可控制性，这可以表征集成可控制性。结果，该工作提供了具有系统过程的统一框架，该系统过程用于通过有限维方法分析在无限维空间上定义的控制系统。通过评估集成中每个单独系统的可控制性，这可以表征集成可控制性。结果，该工作提供了具有系统过程的统一框架，该系统过程用于通过有限维方法分析在无限维空间上定义的控制系统。通过评估集成中每个单独系统的可控制性，这可以表征集成可控制性。结果，该工作提供了具有系统过程的统一框架，该系统过程用于通过有限维方法分析在无限维空间上定义的控制系统。