Control over adversarial packet-dropping communication networks revisited

We revisit a one-step control problem over an adversarial packet-dropping link. The link is modeled as a set of binary channels controlled by a strategic jammer whose intention is to wage a `denial of service' attack on the plant by choosing a most damaging channel-switching strategy. The paper introduces a class of zero-sum games between the jammer and controller as a scenario for such attack, and derives necessary and sufficient conditions for these games to have a nontrivial saddle-point equilibrium. At this equilibrium, the jammer's optimal policy is to randomize in a region of the plant's state space, thus requiring the controller to undertake a nontrivial response which is different from what one would expect in a standard stochastic control problem over a packet dropping channel.