On Separating Points for Ensemble Controllability
On Separating Points for Ensemble Controllability
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DOI：
10.1137/19m1278648
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
Jr-Shin Li;Wei Zhang;Lin Tie
中科院分区：
文献类型：
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作者：
Jr-Shin Li;Wei Zhang;Lin Tie
近年来，系统科学中出现了一股研究人口系统的热潮。这一转变背后的驱动力是由生命和物理科学和工程领域的许多新兴和不断变化的技术所驱动的，从神经科学，生物学和量子物理学到机器人技术，其中许多控制应用涉及操纵大量结构相同的动态单元或代理。分析系综控制系统的基本性质反过来又起着基础性和关键性的作用，使这些应用程序，并进一步推进，分析在很大程度上超出了经典控制技术的能力。在本文中，我们考虑一个系综的时不变的线性系统发展的无限维空间的连续函数。我们利用分离点和多项式逼近技术的概念，发展必要和充分的系综可控性条件。特别是，我们引入了一个扩展的概念的可控性矩阵，称为EnclusionControllability Gramian。该方法通过评价系综中每个单独系统的可控性来表征系综可控性。其结果是，工作提供了一个统一的框架与系统的程序分析控制系统定义在一个无限维空间的有限维的方法。
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 Ensemble Controllability Gramian. This means 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.