Strategic Control Against an Intruder for Timely and Accurate Updates to a Reactive Receiver

Remote sensing is a key component of control for cyber-physical systems, and is susceptible to the injection of false data by adversaries. We consider a transmitter sending status updates about a physical process to a receiver, incurring a cost for each transmission. We use a two-state Markov chain to represent whether the receiver has correct information about the process or not. In normal conditions, transitions to the wrong state happen because the physical process drifted away from the last reported value and the transmitter did not update the receiver yet. However, an adversary can also inject false data to increase the rate of such a transition. The receiver cannot tell the malicious updates apart from the legitimate ones, but, upon detecting a higher arrival rate of data, can counteract it by requesting additional legitimate updates from the transmitter. The ensuing interaction can be examined using game theory, treating both the receiver and the adversary as strategic players. Specifically, they act as a minimizer and a maximizer, respectively, of the age of incorrect information at the receiver's side, while also minimizing their activity costs. We analyze the equilibria of the game and evaluate the impact of strategic decision-making on the system performance.