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

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