发表机构
North Carolina State University（北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对重尾扰动下安全关键系统，提出基于极值理论的随机模型预测控制方法，通过渐近精确的管误差尾部和极值指数校正约束，降低罕见事件违反安全约束的频率。
AI 中文摘要
安全关键控制系统必须应对其极端偏差发生频率远高于经典轻尾模型预测的扰动。现有的随机模型预测控制（SMPC）公式通过假设分布、矩约束或有限场景样本来收紧约束，每种方法在未知的重尾扰动下都会性能退化。本文针对仅假设为规则变化的重尾扰动下的线性系统，开发了一种SMPC公式，用管误差尾部的显式极值理论（EVT）特征（渐近精确）替代这些方法。我们进一步证明，闭环动力学在预测范围内引起罕见偏离的时间聚集，并通过可从数据估计的闭式极值指数来表征这种聚集。由此得到的θ校正约束限制了在预测范围内罕见事件情节的概率，而不仅仅是每步边际超限概率。在Student-t扰动下，非线性独轮车绕行障碍物的仿真验证了这两种方法，并展示了安全约束违反频率的降低。
英文摘要
Safety-critical control systems must contend with disturbances whose extreme deviations occur far more frequently than classical light-tailed models predict. Existing stochastic MPC (SMPC) formulations tighten constraints using an assumed distribution, a moment bound, or a finite scenario sample, each of which degrades under an unknown heavy-tailed disturbance. This paper develops an SMPC formulation for linear systems under heavy-tailed disturbances that is only assumed to be regular varying, replacing these approaches with an explicit extreme value theory (EVT) characterization of the tube error tail that is asymptotically exact. We further show that closed-loop dynamics induce temporal clustering of rare excursions across the prediction horizon, and characterize this clustering through a closed-form extremal index estimable from data. The resulting $θ$-corrected constraint bounds the probability of a rare-event episode over the horizon, rather than only the marginal per-step exceedance probability. Simulation on a nonlinear unicycle navigating past an obstacle under Student-$t$ disturbances validates both approaches and demonstrates reduced frequencies of safety constraint violations.
Comments10 pages, 4 figures, submitted to Systems and Control Letter
