Quantitative Resilience of Linear Driftless Systems

Abstract

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 such 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.

Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods

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An STL-based Formulation of Resilience in Cyber-Physical Systems

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Dynamic Certification for Autonomous Systems

“…Toward this goal, research must be conducted at the intersection of robotics, control, learning, safety, security, resilience, testing, and formal methods. For example, roboticists must include realistic dynamical models for surrounding information that can be given by learning [28], learning must be interpretable based on test vectors [27], control must account for clashing safety requirements based on dynamics [24], and safety [22], security [33], and resilience [7] must be given formal interpretations that are based on realism but allow partial modeling, precisely to account for the uncertainty arising from coupled learning systems. Two recent improvements that will assist with developing dynamic certification are compositional verification, which relates different model types [5], and more operational data, e.g., high-definition maps for streets in major cities [1].…”