论文标题
线性系统的定量弹性
Quantitative Resilience of Linear Systems
论文作者
论文摘要
执行器故障可能对无法减轻它们的系统产生灾难性的后果。我们专注于对执行者失去控制权的损失，在这些执行器中，某些执行器不受控制，但仍然有能力。为了抵消这些故障执行器的不良输出，我们使用实时测量和冗余执行器。在这种情况下，仍然可以达到目标的系统被认为是弹性的。为了量化系统的弹性，我们比较了未损坏的系统到达目标最短的时间最短的时间，最短的时间为故障系统达到相同目标的最短时间，即当故障使该时间最长时。与先前在无线线性系统上进行的工作相反，一般线性系统的时间优势对照的分析表达缺乏，可以防止定量弹性的精确计算。取而代之的是，依靠Lyapunov理论，我们在标称和故障到达时间的分析范围中得出了分析界限，以结合定量弹性。我们说明了我们在温度控制系统上的工作。
Actuator malfunctions may have disastrous consequences for systems not designed to mitigate them. We focus on the loss of control authority over actuators, where some actuators are uncontrolled but remain fully capable. To counteract the undesirable outputs of these malfunctioning actuators, we use real-time measurements and redundant actuators. In this setting, a system that can still reach its target is deemed resilient. To quantify the resilience of a system, we compare the shortest time for the undamaged system to reach the target with the worst-case shortest time for the malfunctioning system to reach the same target, i.e., when the malfunction makes that time the longest. Contrary to prior work on driftless linear systems, the absence of analytical expression for time-optimal controls of general linear systems prevents an exact calculation of quantitative resilience. Instead, relying on Lyapunov theory we derive analytical bounds on the nominal and malfunctioning reach times in order to bound quantitative resilience. We illustrate our work on a temperature control system.
