A Formal Resilience Framework for Cyber-Physical Embodied Systems under Device-Level Cyberattacks

In cyber-physical systems (CPSs), fault tolerance is traditionally achieved by analysing sensor and actuator outputs, detecting progressive drift or sudden failures, and initiating suitable tolerance mechanisms. Reasonable under general failure models, this approach fails to capture nuanced disruptions caused by cyberattacks, which may employ subtle strategies. This is particularly critical in embodied CPSs, where computational and physical devices not only have an active role in task completion, but also in embodiment preservation (that is, maintaining the system's physical integrity). To prevent structural physical damage, embodied CPSs require a framework that enables proactive response to cyberattacks. This paper proposes a formal dependability framework that incorporates IDS information into resilience evaluation predicates, enabling assessment of tolerance to disruption and degradation. The framework supports structured reasoning about how cyberattacks affect task execution and embodiment preservation, and whether mitigation strategies must be deployed. Analytical examples demonstrate its analytical capability and soundness, establishing a theoretical foundation for dependable and secure embodied CPSs.