Optimizing Attack Schedules Based on Energy Dispatch Over Two-Hop Relay Networks

In this article, the security issue of remote state estimation in cyber-physical systems (CPS) for a two-hop relay network is investigated. As the system performance depends on communication topology and communication environment over each channel, we explore the channel selection problem to maximize the attack effect, from the perspective of the jammer. Furthermore, for an energy-constrained jammer, there exists the optimal strategy to decide the attack number and the dropout rate, since the amount of attack number decreases and the dropout rate increases when the energy launched at each attack time becomes larger. For this consideration, the problem of energy dispatch, aiming to derive the optimal tradeoff between the attack number and the energy launched at each attack time, is studied along with the channel selection problem. We first formulate this problem as a mixed integer programming problem to derive the optimal attack schedule including the channel selection, the attack number, and the corresponding energy dispatch. Then, using the optimality equations based on the Markov decision process allows us to present the characteristics of the optimal energy dispatch policy for a given attack number, and further propose the dynamic energy dispatch algorithm with low complexity to approximate the optimal schedule. Besides, for the constant dispatch (CD) case, the optimum solution in an analytical form for the channel selection problem can be obtained, and we thus present a CD algorithm to acquire the optimal schedule. Last, numerical results are given to validate the theoretical findings and the effectiveness of the proposed algorithms.