Maintaining stability in feedback systems, from aircraft and autonomous robots to biological and physiological systems, relies on monitoring their behavior and continuously adjusting their inputs. Incremental damage can make such control fragile. This tends to go unnoticed until a small perturbation induces instability (i.e. loss of control). Traditional methods in the field of engineering rely on accurate system models to compute a safe set of operating instructions, which become invalid when the, possibly damaged, system diverges from its model. Here we demonstrate that the approach of such a feedback system towards instability can nonetheless be monitored through dynamical indicators of resilience. This holistic system safety monitor does not rely on a system model and is based on the generic phenomenon of critical slowing down, shown to occur in the climate, biology and other complex nonlinear systems approaching criticality. Our findings for engineered devices opens up a wide range of applications involving real-time early warning systems as well as an empirical guidance of resilient system design exploration, or "tinkering". While we demonstrate the validity using drones, the generic nature of the underlying principles suggest that these indicators could apply across a wider class of controlled systems including reactors, aircraft, and self-driving cars.

翻译：从飞机、自主机器人到生物与生理系统，反馈系统的稳定性维持依赖于对其行为的监测与输入的持续调整。渐进性损伤可使此类控制变得脆弱，而这一过程往往在微小扰动引发失稳（即失控）前难以察觉。工程领域的传统方法依赖精确的系统模型来计算安全操作指令集，但当系统（可能已受损）偏离其模型时，这些指令将失效。本文证明，通过动态恢复力指标仍可监测此类反馈系统趋近失稳的过程。该整体系统安全监测器不依赖系统模型，其理论基础是临界减速这一普遍现象——该现象已被证实存在于气候、生物学及其他趋近临界态的非线性复杂系统中。我们在工程设备中的发现为实时预警系统开辟了广阔应用前景，同时为恢复力系统设计的探索（即"试错优化"）提供了实证指导。虽然我们使用无人机验证了该方法的有效性，但其底层原理的普适性表明，这些指标可适用于更广泛的受控系统类别，包括反应堆、飞机及自动驾驶汽车。