# Modeling and Verifying Cyber-Physical Systems with Hybrid Active Objects

## TL;DR

This paper introduces Hybrid Active Objects (HAO), an extension of the ABS language, enabling intuitive modeling and automated verification of cyber-physical systems through differential dynamic logic and theorem proving.

## Contribution

It presents a novel hybrid active object framework that combines high-level modeling with formal verification for cyber-physical systems.

## Key findings

- Effective modeling of CPS with HAO demonstrated in case studies
- Automated translation to differential dynamic logic enabled verification
- Approach improves usability and validation of CPS models

## Abstract

Formal modeling of cyber-physical systems (CPS) is hard, because they pose the double challenge of combined discrete-continuous dynamics and concurrent behavior. Existing formal specification and verification languages for CPS are designed on top of their underlying proof search technology. They lack high-level structuring elements. In addition, they are not efficiently executable. This makes formal CPS models hard to understand and to validate, hence impairs their usability. Instead, we suggest to model CPS in an Active Objects (AO) language designed for concise, intuitive modeling of concurrent systems. To this end, we extend the AO language ABS and its runtime environment with Hybrid Active Objects (HAO). CPS models and requirements formalized in HAO must follow certain communication patterns that permit automatic translation into differential dynamic logic, a sequential hybrid program logic. Verification is achieved by discharging the resulting formulas with the theorem prover KeYmaera X. We demonstrate the practicality of our approach with case studies.