Resilience as a Dynamical Property of Risk Trajectories in CPSoS
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914461422452736 |
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| author | Vogel, Elisabeth Langendörfer, Peter |
| author_facet | Vogel, Elisabeth Langendörfer, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08112 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resilience as a Dynamical Property of Risk Trajectories in CPSoS Vogel, Elisabeth Langendörfer, Peter Systems and Control 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. |
| title | Resilience as a Dynamical Property of Risk Trajectories in CPSoS |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.08112 |