Resilience as a Dynamical Property of Risk Trajectories in CPSoS

TL;DR

This paper models resilience in cyber-physical systems of systems as a dynamic property of risk trajectories, linking it to stability and energy dissipation concepts.

Contribution

It introduces a formal, system-theoretic framework for assessing resilience based on risk dynamics, emphasizing maximum deviation and damping effects.

Findings

Resilience is determined by maximum risk deviation and damping properties.

Cumulative risk exposure depends on the ratio of peak deviation to damping.

A simplified energy-dependent system illustrates differences in recovery and impact.

Abstract

Resilience in cyber-physical systems of systems (CPSoS) is often assessed using static indices or point-in-time metrics that do not adequately account for the temporal evolution of risk following a disruption. This paper formalizes resilience as a functional of the risk trajectory by modelling risk as a dynamic state variable. It is analytically shown that key resilience properties are structurally determined by maximum deviation (peak) and effective damping, and that cumulative risk exposure depends on their ratio. A simplified energy-dependent system illustrates the resulting differences in peak magnitude, recovery dynamics, and cumulative impact. The proposed approach links resilience assessment to stability properties of dynamic systems and provides a system-theoretically consistent foundation for the analysis of time-dependent resilience in CPSoS.