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.

中文翻译：

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基于能量调度的两跳中继网络攻击调度优化

在本文中，研究了两跳中继网络的网络物理系统 (CPS) 中远程状态估计的安全问题。由于系统性能取决于每个信道上的通信拓扑和通信环境，我们从干扰者的角度探索信道选择问题以最大化攻击效果。此外，对于能量受限的干扰机，由于每次攻击时发射的能量越大，攻击次数越少，丢包率越高，所以存在决定攻击次数和丢包率的最优策略。为此，与信道选择问题一起研究了能量调度问题，旨在推导出攻击次数和每次攻击时发射的能量之间的最佳权衡。我们首先将这个问题表述为一个混合整数规划问题，以推导出最优攻击计划，包括信道选择、攻击次数和相应的能量调度。然后，利用基于马尔可夫决策过程的最优性方程，我们可以展示给定攻击次数的最优能量调度策略的特征，并进一步提出低复杂度的动态能量调度算法来逼近最优调度。此外，对于恒定调度（CD）情况，可以获得信道选择问题的解析形式的最优解，因此我们提出了一种获得最优调度的CD算法。最后，给出了数值结果来验证理论结果和所提出算法的有效性。