Optimal DoS Attack Policy Against Periodically Switched System With Two-Hop Relay Networks

Periodically switched systems (PSS) are an important class of hybrid dynamic systems. This paper studies the security of PSS with two-hop relay networks, from which the results can be extended to multiple hops. From the perspective of an attacker with limited energy, our objective is to find the optimal trade-off between energy allocation and channel coverage. If the attacker allocates more energy each time, the packet loss rate of the channel increases, leading to a decrease in system performance. Our contributions are threefold. First, the stability conditions of PSS are provided based on the initial values of prior estimation errors in both specific and general cases. Second, we give system stability conditions in the presence of an external attacker, for the case that the relay node adopts the Direct Forwarding Strategy (DFS). Finally, the attack strategy optimization is cast as a Markov decision process (MDP) problem. A Q-learning algorithm is designed to find the optimal attack policy to reduce the estimation performance of the estimator. The effectiveness of the designed algorithm is demonstrated by a simulation study involving an undamped oscillator model.