Quantitative Resilience of Linear Driftless Systems
Quantitative Resilience of Linear Driftless Systems
复制标题
线性无漂移系统的定量弹性
DOI：
10.1137/1.9781611976847.5
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Melkior Ornik
中科院分区：
文献类型：
--
作者：
Jean;Kathleen Xu;Melkior Ornik
本文介绍了控制系统定量弹性的概念。在之前的工作之后，我们研究了对其某些执行器失去控制权限的线性无漂移系统。这样的故障导致执行器产生可能不希望的输入，控制器有实时读数，但没有控制。根据定义，如果系统在部分失去控制权限后仍能到达目标，则系统具有弹性。然而，在发生故障后，弹性系统达到目标的速度可能会比其初始能力慢得多。我们通过量化弹性的新概念来量化这种性能损失。我们将这样的度量定义为达到初始和故障系统的任何目标所需的最小时间的最大比率。Naïve直接从定义中计算定量弹性是一项复杂的任务，因为它需要解决四个嵌套的、可能是非线性的优化问题。这项工作的主要技术贡献是提供了一种有效的计算定量弹性的方法。基于控制理论和两个新的几何结果，我们将定量弹性的计算简化为单个线性优化问题。我们在一个意见动态场景中演示了我们的方法。
This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study linear driftless systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a partial loss of control authority. However, after a malfunction, a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define such a metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naïve computation of quantitative resilience directly from the definition is a complex task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on two novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We demonstrate our method on an opinion dynamics scenario.