Characterizing simulation relations through control architectures in abstraction-based control

TL;DR

This paper develops a systematic framework for characterizing simulation relations in abstraction-based control, enabling flexible control architectures for complex cyber-physical systems.

Contribution

It introduces the concept of interfaced systems to universally enable feedback refinement relations, facilitating plug-and-play control architectures.

Findings

Existence of a simulation relation is equivalent to implementability of a specific control architecture.

The framework allows introduction of new simulation relations and comparison of their advantages.

Detailed examples illustrate the practical implications of different relations.

Abstract

Abstraction-based control design is a promising approach for ensuring safety-critical control of complex cyber-physical systems. A key aspect of this methodology is the relation between the original and abstract systems, which ensures that the abstract controller can be transformed into a valid controller for the original system through a concretization procedure. In this paper, we provide a comprehensive and systematic framework that characterizes various simulation relations, through their associated concretization procedures. We introduce the concept of interfaced system, which universally enables a feedback refinement relation with the abstract system. This interfaced system encapsulates the specific characteristics of each simulation relation within an interface, enabling a plug-and-play control architecture. Our results demonstrate that the existence of a particular simulation relation between the concrete and abstract systems is equivalent to the implementability of a specific control architecture, which depends on the considered simulation relation. This allows us to introduce new types of relations, and to establish the advantages and drawbacks of different relations, which we exhibit through detailed examples.