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

Abstract

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.

A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

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Formal verification of distributed aircraft controllers

“…QHPs [16,17] are defined by the following grammar (α, β are QHPs, θ terms, i a variable of sort C, f a function symbol, s a term with sort compatible to f , and H is a formula of first-order logic):…”

“…The formulas of QdL [16,17] are defined as in first-order dynamic logic plus many-sorted first-order logic by the following grammar (φ, ψ are formulas, θ 1 , θ 2 are terms of the same sort, i is a variable of sort C, and α is a QHP):…”

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Certifying the safe design of a virtual fixture control algorithm for a surgical robot

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