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Coupling cyber and physical systems gives rise to numerous engineeringchallenges and opportunities. An important challenge is the contagion offailure from one system to another, which can lead to large-scale cascadingfailures. However, the self-healing ability emerges as a valuable opportunitywhere the overlaying cyber network can cure failures in the underlying physicalnetwork. To capture both self-healing and contagion, this paper considers agraphical model representation of an interdependent cyber-physical system, inwhich nodes represent various cyber or physical functionalities, and edgescapture the interactions between the nodes. A message-passing algorithm isproposed for this representation to study the dynamics of failure propagationand healing. By conducting a density evolution analysis for this algorithm,network reaction to initial disruptions is investigated. It is proved that asthe number of message-passing iterations increases, the network reaches asteady-state condition that would be either a complete healing or a completecollapse. Then, a sufficient condition is derived to select the networkparameters to guarantee the complete healing of the system. The result of thedensity evolution analysis is further employed to jointly optimize the designof cyber and physical networks for maximum resiliency. This analyticalframework is then extended to the cases where propagation of failures in thephysical network is faster than the healing responses of the cyber network.Such scenarios are of interest in many real-life applications such as smartgrid. Finally, extensive numerical results are presented to verify the analysisand investigate the impact of the network parameters on the resiliency of thenetwork.

Error Correction Coding Meets Cyber-Physical Systems: Message-Passing Analysis of Self-Healing Interdependent Networks