Complete Robust Hybrid Systems Reachability

2026-02-26

AI Summary

This work addresses the challenge of verifying reachability in hybrid systems under infinitesimal perturbations by introducing robust differential dynamic logic (rDDL). By imposing syntactic constraints that guarantee all expressible properties correspond to topologically open sets, rDDL inherently ensures robustness against arbitrarily small disturbances without explicitly incorporating error margins. This approach establishes, for the first time, an absolutely complete formal verification framework for reachability in hybrid systems with precise semantics. The key contribution lies in enabling the automatic provability of robustly correct reachability specifications and in constructing the first absolutely complete logical system tailored specifically for hybrid systems.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. Practically meaningful syntactic restrictions naturally ensure that definable properties are topologically open and thus by construction robust with respect to infinitesimal perturbations, without explicit quantitative margins of error in the syntax or in proofs. The main result is a proof of absolute completeness of robust differential dynamic logic for reachability properties of general hybrid systems. This is the first absolute completeness proof for hybrid systems with exact semantics. The proof is constructive, self-contained, and demonstrates how robustly correct hybrid systems reachability specifications can be automatically verified through proof.

Problem

• robust hybrid systems
• reachability
• differential dynamic logic
• absolute completeness
• formal verification

Innovation

• robust differential dynamic logic
• hybrid systems
• reachability
• absolute completeness
• topological robustness