In this paper, we focus on the problem of shrinking-horizon Model Predictive Control (MPC) in uncertain dynamic environments. We consider controlling a deterministic autonomous system that interacts with uncontrollable stochastic agents during its mission. Employing tools from conformal prediction, existing works derive high-confidence prediction regions for the unknown agent trajectories, and integrate these regions in the design of suitable safety constraints for MPC. Despite guaranteeing probabilistic safety of the closed-loop trajectories, these constraints do not ensure feasibility of the respective MPC schemes for the entire duration of the mission. We propose a shrinking-horizon MPC that guarantees recursive feasibility via a gradual relaxation of the safety constraints as new prediction regions become available online. This relaxation enforces the safety constraints to hold over the least restrictive prediction region from the set of all available prediction regions. In a comparative case study with the state of the art, we empirically show that our approach results in tighter prediction regions and verify recursive feasibility of our MPC scheme.

翻译：本文聚焦于不确定动态环境中的缩域模型预测控制问题。我们考虑控制一个确定性自主系统，该系统在执行任务期间与不可控的随机智能体进行交互。现有研究利用共形预测工具，推导出未知智能体轨迹的高置信度预测区域，并将这些区域整合到模型预测控制的适当安全约束设计中。尽管这些约束能保证闭环轨迹的概率安全性，但无法确保相应模型预测控制方案在整个任务期间的可行性。为此，我们提出一种缩域模型预测控制方法，通过在线获取新预测区域时逐步放宽安全约束来保证递归可行性。该放松策略将安全约束强制应用于所有可用预测区域集合中限制性最弱的预测区域。通过与现有技术的对比案例研究，我们通过实证表明该方法能获得更紧凑的预测区域，并验证了所提模型预测控制方案的递归可行性。