Compositional Synthesis of Symbolic Models for Infinite Networks

Abstract In this paper, we provide a compositional method for the construction of symbolic models (a.k.a. finite abstractions) for infinite networks of discrete-time control systems. The concrete infinite network and its symbolic model are related by a so-called alternating simulation function which allows one to quantify the mismatch between the output behavior of the infinite interconnection of concrete subsystems and that of their symbolic models. We show that such an alternating simulation function can be obtained compositionally by assuming some small-gain type conditions and composing so-called local alternating simulation functions constructed for subsystems. Assuming certain stability property of concrete subsystems, we also provide a technique to synthesize their symbolic models together with their corresponding local alternating simulation functions. Finally, we apply our results to a traffic network divided into infinitely many cells.