发表机构
Politecnico di Torino（都灵理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出集体管模型预测控制（CT-MPC），通过校准预测误差轨迹管并离线构建确定性收紧，实现线性系统联合状态-输入安全与递归可行性，相比传统方法减少收紧并保持安全性。
AI 中文摘要
数据校准的随机模型预测控制通常为预测时域内的许多事件（如时间、面、状态/输入分量或障碍物）分别构建风险边际，然后通过并集界将其组合。这种方法有效，但与管模型预测控制递归可行性证明中使用的关键对象（即整个误差管的平移）不匹配。本文开发了集体管模型预测控制（CT-MPC），其中校准的不确定性对象是有限时域预测误差轨迹。可复用的轨迹管离线校准，其横截面在线定义确定性庞特里亚金收紧，认证的违规事件是新的预测误差轨迹离开该管。对于具有加性不确定性和固定辅助反馈的线性系统，我们证明了预测时域上的联合状态-输入安全性、从显式平移候选的一步递归可行性、有限部署风险界以及实际价值递减不等式。有限样本证书在分裂校准下是无分布的，具有β-二项形式；其复杂度是可定义该管的已认证残差轨迹数量，而非时域约束块数量。我们还给出了多面体管的可实现平移兼容性测试，以及针对不规则管设计者的稳定压缩回退方案。数值实验将CT-MPC与Bonferroni收紧、样本包络管和联合时间共形模型预测控制基线进行了比较。集体管在保持经验安全性和递归可行性的同时减少了确定性收紧。
英文摘要
Data-calibrated stochastic MPC typically builds separate risk margins for many events along the horizon, such as times, facets, state/input components, or obstacles, and then combines them with a union bound. This approach is valid, but it does not match the key object used in the tube-MPC recursive-feasibility proof, which shifts a complete error tube. This paper develops collective tube MPC (CT-MPC), where the calibrated uncertainty object is the finite-horizon prediction-error trajectory. A reusable trajectory tube is calibrated offline, its cross-sections define deterministic Pontryagin tightenings online, and the certified violation event is that a fresh prediction-error trajectory leaves the tube. For linear systems with additive uncertainty and fixed ancillary feedback, we prove joint state-input safety over the prediction horizon, one-step recursive feasibility from an explicit shifted candidate, a finite-deployment risk bound, and a practical value-decrease inequality. The finite-sample certificate is distribution-free under split calibration and has beta-binomial form; its complexity is the certified number of residual trajectories that can define the tube, rather than the number of horizon-constraint blocks. We also give implementable shift-compatibility tests for polytopic tubes and a stable-compression fallback for irregular tube designers. Numerical experiments compare CT-MPC with Bonferroni tightening, a sample-envelope tube, and a joint-in-time conformal MPC baseline. The collective tube reduces deterministic tightening while preserving empirical safety and recursive feasibility.
