Automata Theory Meets Barrier Certificates: Temporal Logic Verification of Nonlinear Systems

TL;DR

This paper introduces a novel method combining automata-based verification and barrier certificates for the temporal logic verification of nonlinear dynamical systems, enabling efficient and conservative analysis without explicit system abstractions.

Contribution

It presents an integrated approach that leverages automata and barrier certificates to verify temporal properties of nonlinear systems more efficiently.

Findings

Enables verification without explicit system abstraction.

Uses optimization to construct barrier certificates.

Successfully verifies nonlinear systems against temporal logic.

Abstract

We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based verification allows the decomposition the verification task into a finite collection of simpler constraints over the continuous state space. The satisfaction of these constraints in turn can be (potentially conservatively) proved by appropriately constructed barrier certificates. As a result, our approach, together with optimization-based search for barrier certificates, allows computational verification of dynamical systems against temporal logic properties while avoiding explicit abstractions of the dynamics as commonly done in literature.