Structure theory for ensemble controllability, observability, and duality
Structure theory for ensemble controllability, observability, and duality
复制标题
系综可控性、可观测性和对偶性的结构理论
DOI：
10.1109/ita50056.2020.9244972
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Xudong Chen
中科院分区：
文献类型：
--
作者：
Xudong Chen
集成控制处理使用有限数量的控制输入同时引导大量（在极限情况下，连续体）控制系统的问题。与系综控制问题一样，系综估计处理使用有限数量的测量输出来估计系综中每个单独系统的初始状态的问题。我们在论文中介绍了一类新颖的系综系统，称为杰出系综系统，并为此类系统的可控性和可观测性建立了充分条件。每个可区分的系综系统都有两个关键组成部分，即一组可区分的控制向量场和一组可区分的观测函数。粗略地说，如果一组向量场在李括号下是闭集（达到缩放比例），则该组向量场是可区分的，并且该组中的每个向量场都可以通过同一组中的两个向量场的李括号来获得。类似地，如果函数沿给定向量场的李导数产生（按比例缩放）相同的函数集，则一组函数可与一组向量场共同区分。我们在论文中证明，杰出的系综系统的结构可以显着简化系综可控性和可观测性的分析。此外，这种结构可以作为集成系统设计的指导原则。我们在论文中进一步解决了给定流形的杰出系综系统的存在性问题。对于流形是连通半单李群的情况，我们提供了肯定的答案。具体来说，我们证明每个这样的李群都承认一组可区分的向量场，以及一组可区分的函数。该证明是建设性的，利用了半简单实李代数的结构理论和表示论。论文演示中将提供示例，说明关键定义和主要结果。
Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of control systems. Dual to the ensemble control problem, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the ensemble. We introduce in the paper a novel class of ensemble systems, termed distinguished ensemble systems, and establish sufficient conditions for controllability and observability of such systems. Every distinguished ensemble system has two key components, namely a set of distinguished control vector fields and a set of codistinguished observation functions. Roughly speaking, a set of vector fields is distinguished if it is closed (up to scaling) under Lie bracket, and moreover, every vector field in the set can be obtained by a Lie bracket of two vector fields in the same set. Similarly, a set of functions is codistinguished to a set of vector fields if the Lie derivatives of the functions along the given vector fields yield (up to scaling) the same set of functions. We demonstrate in the paper that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a guiding principle for ensemble system design. We further address in the paper the problem about existence of a distinguished ensemble system for a given manifold. We provide an affirmative answer for the case where the manifold is a connected semi-simple Lie group. Specifically, we show that every such Lie group admits a set of distinguished vector fields, together with a set of codistinguished functions. The proof is constructive, leveraging the structure theory of semi-simple real Lie algebras and representation theory. Examples will be provided along the presentation of the paper illustrating key definitions and main results.
影响因子：
6.8
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
通讯作者：
Pavon, Michele