Delta-Complete Analysis for Bounded Reachability of Hybrid Systems

TL;DR

This paper introduces delta-complete analysis for hybrid systems, enabling more tractable bounded reachability verification through delta-decision problems, with an implementation that scales to complex biomedical and robotics models.

Contribution

It proposes a novel delta-complete framework for hybrid system verification, improving mathematical tractability and robustness analysis.

Findings

The framework makes verification problems more mathematically tractable.

The open-source tool dReach scales well on complex models.

The approach accounts for robustness under numerical perturbations.

Abstract

We present the framework of delta-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. We prove that the verification problems become much more mathematically tractable in this new framework. Our implementation of the techniques, an open-source tool dReach, scales well on several highly nonlinear hybrid system models that arise in biomedical and robotics applications.