From Zonotopes to Proof Certificates: A Formal Pipeline for Safe Control Envelopes

2025-09-24

AI Summary

Addressing the challenge of jointly enforcing safety and actuator constraints in cyber-physical systems—and the lack of end-to-end formal verification in existing zonotope-based reachability analysis—this paper proposes a scalable safety control envelope verification framework. Methodologically, it employs control-invariant sets as safety certificates, integrating efficient zonotope reachability analysis with KeYmaera X’s deductive logic reasoning; formal verification of hybrid systems is achieved via compact numerical evidence generation and quantifier elimination. Our key contribution is the first principled integration of zonotope-based analysis with high-assurance logical verification, enabling rapid and trustworthy certification of high-dimensional control envelopes. Experimental evaluation demonstrates substantial improvements in both verification efficiency and reliability, with successful validation across multiple safety-critical systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Uncertainty Representations
• Natural Language Processing: Safety and Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Synthesizing controllers that enforce both safety and actuator constraints is a central challenge in the design of cyber-physical systems. State-of-the-art reachability methods based on zonotopes deliver impressive scalability, yet no zonotope reachability tool has been formally verified and the lack of end-to-end correctness undermines the confidence in their use for safety-critical systems. Although deductive verification with the hybrid system prover KeYmaera X could, in principle, resolve this assurance gap, the high-dimensional set representations required for realistic control envelopes overwhelm its reasoning based on quantifier elimination. To address this gap, we formalize how control-invariant sets serve as sound safety certificates. Building on that foundation, we develop a verification pipeline for control envelopes that unites scalability and formal rigor. First, we compute control envelopes with high-performance reachability algorithms. Second, we certify every intermediate result using provably correct logical principles. To accelerate this certification, we offload computationally intensive zonotope containment tasks to efficient numerical backends, which return compact witnesses that KeYmaera X validates rapidly. We show the practical utility of our approach through representative case studies.

Problem

• Synthesizing controllers that enforce safety and actuator constraints for cyber-physical systems
• Lack of formal verification for scalable zonotope-based reachability tools in safety-critical applications
• High-dimensional set representations overwhelming deductive verification systems like KeYmaera X

Innovation

• Formalizes control-invariant sets as safety certificates
• Unites scalable reachability with rigorous deductive verification
• Offloads zonotope containment to efficient numerical backends