Symbolic Models for Infinite Networks of Control Systems: A Compositional Approach

TL;DR

This paper introduces a compositional method for creating symbolic models of infinite networks of control systems, ensuring guaranteed output behavior bounds and enabling decentralized safety controller synthesis.

Contribution

It develops a novel compositional framework using alternating simulation functions for infinite networks, allowing scalable symbolic model construction with guaranteed accuracy.

Findings

Successfully applied to a road traffic network with infinitely many cells.

Provides a systematic algorithm for local symbolic model construction.

Enables decentralized safety control synthesis for infinite networks.

Abstract

This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite network. The proposed approach is based on the notion of alternating simulation functions. This notion relates a concrete network to its symbolic model with guaranteed mismatch bounds between their output behaviors. We propose a compositional approach to construct a symbolic model for an infinite network, together with an alternating simulation function, by composing symbolic models and alternating simulation functions constructed for subsystems. Assuming that each subsystem is incrementally input-to-state stable and under some small-gain type conditions, we present an algorithm for orderly constructing local symbolic models with properly designed quantization parameters. In this way, the proposed compositional approach can provide us a guideline for constructing an overall symbolic model with any desired approximation accuracy. A compositional controller synthesis scheme is also provided to enforce safety properties on the infinite network in a decentralized fashion. The effectiveness of our result is illustrated through a road traffic network consisting of infinitely many road cells.