Quantitative resilience of linear driftless systems

Jean Baptiste Bouvier, Kathleen Xu, Melkior Ornik

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationSIAM Conference on Control and Its Applications, CT 2021
PublisherSiam Society
Number of pages8
ISBN (Electronic)9781611976847
StatePublished - 2021
Event2021 SIAM Conference on Control and Its Applications, CT 2021 - Virtual, Online
Duration: Jul 19 2021Jul 21 2021

Publication series

NameSIAM Conference on Control and Its Applications, CT 2021


Conference2021 SIAM Conference on Control and Its Applications, CT 2021
CityVirtual, Online

ASJC Scopus subject areas

  • Control and Systems Engineering


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