A Scalable Design Approach to Resilient Architectures for Interconnected Cyber-Physical Systems: Safety Guarantees under Multiple Attacks

Complex, interconnected cyber-physical systems (CPS) are increasingly prevalent in domains such as power systems. Cyber-resilient architectures have been proposed to recover compromised cyber components of CPS. Recent works have studied tuning the recovery times of such architectures to guarantee safety in single-system settings. Extending these designs to interconnected CPS is more challenging, since solutions must account for attacks on multiple subsystems that can occur in any order and potentially infinite possible temporal overlap. This paper aims to address the aforementioned challenge by developing a scalable framework to assign resilient architectures and to inform the tuning of their recovery times. Our approach introduces a scalar index that quantifies the impact of each subsystem on safety under compromised input. These indices aggregate linearly across subsystems, enabling scalable analysis under arbitrary attack orderings and temporal overlaps. We establish a linear inequality relating each subsystem's index and recovery time that guarantees safety and guides resilient architecture assignment. We also propose a segmentation-based approach to strengthen the previously derived conditions. We then present algorithms to compute the proposed indices and to find a cost-optimal architecture assignment with a safety guarantee. We validate the framework through a case study on temperature regulation in interconnected rooms under different attack scenarios.