Symbolic Models for a Class of Impulsive Systems

TL;DR

This paper develops a method to construct symbolic models for impulsive systems with stability properties, enabling approximate behavioral equivalence and safe control design, filling a gap in existing hybrid systems literature.

Contribution

It introduces a novel approach for symbolic modeling of impulsive systems using alternating simulation functions, extending control design tools to this class.

Findings

Successfully constructed symbolic models for impulsive systems.

Demonstrated approximate behavioral equivalence between models.

Applied method to a storage-delivery process for safety control.

Abstract

Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating simulation function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a model of storage-delivery process by constructing its symbolic model and designing controllers enforcing some safety specifications.