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Complex, interconnected Cyber-physical Systems (CPS) are increasingly commonin applications including smart grids and transportation. Ensuring safety ofinterconnected systems whose dynamics are coupled is challenging because theeffects of faults and attacks in one sub-system can propagate to othersub-systems and lead to safety violations. In this paper, we study the problemof safety-critical control for CPS with coupled dynamics when some sub-systemsare subject to failure or attack. We first propose resilient-safety indices(RSIs) for the faulty or compromised sub-systems that bound the worst-caseimpacts of faulty or compromised sub-systems on a set of specified safetyconstraints. By incorporating the RSIs, we provide a sufficient condition forthe synthesis of control policies in each failure- and attack- freesub-systems. The synthesized control policies compensate for the impacts of thefaulty or compromised sub-systems to guarantee safety. We formulatesum-of-square optimization programs to compute the RSIs and the safety-ensuringcontrol policies. We present a case study that applies our proposed approach onthe temperature regulation of three coupled rooms. The case study demonstratesthat control policies obtained using our algorithm guarantee system's safetyconstraints.

A Compositional Approach to Safety-Critical Resilient Control for Systems with Coupled Dynamics