Switched Systems as Hybrid Programs

TL;DR

This paper demonstrates how to model and verify switched hybrid systems using differential dynamic logic, enabling formal safety analysis with existing tools like KeYmaera X.

Contribution

It bridges hybrid system formalisms with differential dynamic logic, allowing formal specification and verification of switched systems.

Findings

Models of switched systems in dL enable formal verification.

Completeness results improve safety verification methods.

Facilitates use of existing tools like KeYmaera X for verification.

Abstract

Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions, e.g., using impulsive differential equations and switching, to automata-theoretic and language-based approaches. This paper bridges two such formalisms by showing how various classes of switched systems can be modeled using the language of hybrid programs from differential dynamic logic (dL). The resulting models enable the formal specification and verification of switched systems using dL and its existing deductive verification tools such as KeYmaera X. Switched systems also provide a natural avenue for the generalization of dL's deductive proof theory for differential equations. The completeness results for switched system invariants proved in this paper enable effective safety verification of those systems in dL.