Optimal DoS Attacks on Remote State Estimation with a Router

In this paper, we consider Denial-of-service attacks against remote state estimation with a router. A sensor measures the state of a discrete-time linear process, and sends the preprocessed data to a remote estimator via a router. A malicious attacker can generate noises to degenerate the performance of this two-hop network. Due to the capability limitation, the attacker can only deliver attacks on one transmission link at each time step. The aim of the attacker is to jeopardize the estimation quality of the remote estimator. We first formulate the problem as a Markov decision process (MDP), and then prove the existence of the optimal stationary and deterministic policy of the attacker. It is shown that the optimal policy has a switching-curve structure, which is beneficial for offline computation and online implementation. Simulation examples are provided to illustrate the results.