In this paper, we address optimal schedule issue of a linear attacker without being detected by χ2 detector. Due to limited energy, the attacker needs to decide whether to launch attacks at each step and design optimal attack strategy over a finite-time horizon. To address it, we take average error (AE) and terminal error (TE) as indices. After analyzing AEs under three special types of schedules and studying monotonic property of TE with respect to attack time instants, the optimal attack schedules for AE and TE are respectively determined theoretically. Besides, we further investigate optimal attack schedule for multiple subsystems. The accomplished results well extend the existing work in false data attacks without optimal structure and promote the linear-attack in dynamical systems to the optimal schedule issue. Illustrative examples are also given to validate our theoretical results.

中文翻译：

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远程状态估计的最优隐形线性攻击方案


在本文中，我们解决了线性攻击者在不被 χ2 检测器检测到的情况下的最优调度问题。由于能量有限，攻击者需要在每一步决定是否发起攻击，并在有限的时间范围内设计最优的攻击策略。为了解决这个问题，我们以平均误差（AE）和终端误差（TE）作为指标。在分析了三种特殊类型调度下的AE并研究了TE相对于攻击时刻的单调性之后，从理论上分别确定了AE和TE的最佳攻击调度。此外，我们进一步研究了多个子系统的最佳攻击计划。所取得的成果很好地扩展了现有无最优结构的虚假数据攻击的工作，并将动态系统中的线性攻击推广到最优调度问题。还给出了说明性例子来验证我们的理论结果。