Previous approaches to constructing abstractions for control systems rely on geometric conditions or, in the case of an interconnected control system, a condition on the interconnection topology. Since these conditions are not always satisfiable, we relax the restrictions on the choice of abstractions, instead opting to select ones which nearly satisfy such conditions via optimization-based approaches. To quantify the resulting effect on the error between the abstraction and concrete control system, we introduce the notions of practical simulation functions and practical storage functions. We show that our approach facilitates the procedure of aggregation, where one creates an abstraction by partitioning agents into aggregate areas. We demonstrate the results on an application where we regulate the temperature in three separate zones of a building.

构造控制系统抽象的先前方法依赖于几何条件，或者在互连控制系统的情况下，取决于互连拓扑上的条件。由于这些条件并不总是可以满足的，因此我们放宽了对抽象选择的限制，而选择通过基于优化的方法选择几乎满足这些条件的抽象。为了量化对抽象和具体控制系统之间的错误产生的影响，我们介绍了实用的仿真功能和实用的存储功能的概念。我们证明了我们的方法促进了聚合过程，在该过程中，通过将代理划分为聚合区域来创建抽象。我们在一个应用中演示了结果，该应用可调节建筑物三个独立区域中的温度。