Finite-Dimensional Observation and Control of Ensembles of Linear Systems

系综控制是数学系统和控制理论的一个新兴领域，它指的是使用单个输入函数或单个反馈控制器来控制大量潜在无限数量的状态或系统的任务。系综的原型由依赖于参数的一族系统和初始状态决定，这些系统和初始状态必须由单个输入或反馈控制器控制。集成控制的应用出现在例如量子控制、系统生物学、传感器网络和机器人中，其中控制动作和测量以分布式方式执行。传统的鲁棒控制方法不足以研究系统的系综，需要一种新的理论。除了一些基本的贡献外，到目前为止还没有严格的系综控制理论。系综控制问题领域在控制理论、复变分析和逼近理论之间呈现出一种新的联系。我们建议建立线性参数系综的系统理论分析的基本概念和工具。因此，我们致力于建立一个完整的参数依赖线性系统的结构理论，解决系统的能控性和能观性、构造性集成控制和系综状态估计等基本问题。

Ensemble control is an emerging field of mathematical systems and control theory that refers to the task of controlling a large, potentially infinite, number of states, or systems, using a single input function or a single feedback controller. A prototype of an ensemble is determined by a parameter dependent family of systems and initial states which has to be controlled by a single input or feedback controller. Applications of ensemble control arise in, e.g., quantum control, systems biology, sensor networks and robotics, where control actions and measurements are performed in a distributed way. Classical methods from robust control do not suffice to study ensembles of systems and a new theory is needed. Except for few rudimentary contributions, no rigorous control theory of ensembles exists so far. The ensemble control problem area presents a new connection between control theory, complex analysis and approximation theory. We propose to establish fundamental concepts and tools for a system theoretic analysis of linear parametric ensembles. Thus we aim at a comprehensive structure theory for parameter dependent linear systems, by addressing the fundamental tasks of controllability and observability, constructive ensemble control and state estimation for ensembles.