A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

TL;DR

This paper develops a formal logical framework and proof calculus for verifying distributed hybrid systems, addressing the complexity of dynamic, hybrid, and distributed cyber-physical systems with unbounded components.

Contribution

It introduces the first complete axiomatization of quantified differential dynamic logic tailored for distributed hybrid systems, enabling formal verification of complex dynamic behaviors.

Findings

Proves soundness and completeness of the proof calculus.

Formalizes a model combining quantified differential equations with dynamic dimensionality.

Demonstrates collision freedom in distributed car control scenarios.

Abstract

We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where neither structure nor dimension stay the same while the system follows hybrid dynamics, i.e., mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a formal model for distributed hybrid systems. It combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for this logic. This is the first formal verification approach for distributed hybrid systems. We prove that our calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when an unbounded number of new cars may appear dynamically on the road.