Bouvier Jean-Baptiste, Xu Kathleen, Ornik Melkior
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign. Urbana, IL 61801, USA.
Department of Aerospace Engineering and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign. Urbana, IL 61801, USA.
Proc SIAM Conf Control Appl. 2021;2021:32-39. doi: 10.1137/1.9781611976847.5.
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.
本文介绍了控制系统定量弹性的概念。继先前的工作之后，我们研究了在部分执行器失去控制权限的情况下的线性无漂移系统。这种故障会导致执行器产生可能不理想的输入，控制器对这些输入有实时读数但无法控制。根据定义，如果一个系统在部分控制权限丧失后仍能到达目标，则该系统具有弹性。然而，发生故障后，与初始能力相比，弹性系统到达目标的速度可能会显著变慢。我们通过定量弹性的新概念来量化这种性能损失。我们将这样一个度量定义为初始系统和故障系统到达任何目标所需的最短时间的最大比率。直接根据定义对定量弹性进行简单计算是一项复杂的任务，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一种计算定量弹性的有效方法。依靠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一个单一的线性优化问题。我们在一个舆论动态场景中展示了我们的方法。
