Strategic Interaction Over Age of Incorrect Information for False Data Injection in Cyber-Physical Systems

Ambient monitoring through remote sensing is the first required step of many control operations in cyber-physical systems to enable accurate decision-making by network intelligence. We consider a controller that sends status updates about a process to a receiver, incurring a cost when doing so. The process is dynamical, implying that the information the receiver has may become outdated due to a natural drift of the process. To determine the correctness of the information at the receiver, we model this interaction using a Markov Chain with two states, namely right (R) and Wrong (W). The controller can restore the receiver status to R by performing a new transmission, which comes at a cost. The staleness of information, when the system state is erroneous, is quantified through the average value of the age of incorrect information metric. Moreover, an adversary may inject false data at a price to make the information available at the receiver less fresh, which can only be contrasted by ad...