Approximate Bisimulation and Discretization of Hybrid CSP

TL;DR

This paper introduces an approximate bisimulation framework for HCSP, enabling the discretization of hybrid systems and facilitating the transformation of verified control models into correct program models.

Contribution

It proposes a novel approximate bisimulation concept for HCSP and an algorithm for process equivalence, along with a method to discretize HCSP processes while preserving behavior.

Findings

Algorithm to determine approximate bisimulation between HCSP processes

Method to discretize HCSP processes with specified precision

Framework for transforming control models into correct program models

Abstract

Hybrid Communicating Sequential Processes (HCSP) is a powerful formal modeling language for hybrid systems, which is an extension of CSP by introducing differential equations for modeling continuous evolution and interrupts for modeling interaction between continuous and discrete dynamics. In this paper, we investigate the semantic foundation for HCSP from an operational point of view by proposing notion of approximate bisimulation, which provides an appropriate criterion to characterize the equivalence between HCSP processes with continuous and discrete behaviour. We give an algorithm to determine whether two HCSP processes are approximately bisimilar. In addition, based on that, we propose an approach on how to discretize HCSP, i.e., given an HCSP process A, we construct another HCSP process B which does not contain any continuous dynamics such that A and B are approximately bisimilar with given precisions. This provides a rigorous way to transform a verified control model to a correct program model, which fills the gap in the design of embedded systems.