One-shot control over an AVC-like adversarial channel

We consider a one step control problem over a malicious packet-dropping link. The link is modeled as a set of binary channels out of which a jammer strategically chooses the most damaging option based on its information set, and subject to switching costs and/or constraints. This model of an adversarial channel bears some resemblance with the framework of Arbitrarily Varying Channels (AVC) studied in Information Theory and, in the context of security of control systems, allows us to capture scenarios where the jammer is not only trying to disrupt the control task, but also to remain undetected, by “masquerading” as a legitimate non-malicious but imperfect channel. We study the resulting zero-sum game between jammer and controller, prove that it admits a value, and compute its unique saddle-point equilibrium in mixed strategies. We show that, in contrast to previous models of control over adversarial channels, the jammer does randomize in a region of the plant´s state space, thus being forced to act in a way that matches the controller´s expectations of stochastic packet drops.