Abstraction of Elementary Hybrid Systems by Variable Transformation

TL;DR

This paper introduces a symbolic abstraction method that transforms elementary hybrid systems with elementary functions into polynomial hybrid systems by variable substitution, facilitating their safety verification with existing tools.

Contribution

It proposes a novel abstraction technique that converts EHSs into PHSs, overcoming limitations of previous methods and enabling effective safety verification.

Findings

Successfully applied to real-world examples.

Enables use of existing PHS verification tools.

Reduces verification complexity for EHSs.

Abstract

Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions which lead to undecidable arithmetic, verification of EHSs is very hard. Existing approaches based on partition of state space or over-approximation of reachable sets suffer from state explosion or inflation of numerical errors. In this paper, we propose a symbolic abstraction approach that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all non-polynomial terms with newly introduced variables. Thus the verification of EHSs is reduced to the one of PHSs, enabling us to apply all the well-established verification techniques and tools for PHSs to EHSs. In this way, it is possible to avoid the limitations of many existing methods. We illustrate the abstraction approach and its application in safety verification of EHSs by several real world examples.