用有限采样构建安全可达集，实现高概率闭环安全控制。
Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics
- 从GP后验中有限采样动态函数，传播认知不确定性。
- 在两个数值实验中实现精确的可达集上界和安全闭环性能。
- 适合需要高概率安全保证的机器人控制场景。
高斯过程（GP）回归在学习未知动力学方面表现出色，可支持高效且安全感知的控制策略，适用于多种场景。然而，现有的基于GP的模型预测控制（GP-MPC）方法要么依赖近似而缺乏理论保证，要么过于保守，限制了实际应用。为弥合这一差距，我们提出一种基于采样的框架，能高效传播模型的认知不确定性，同时避免过度保守。我们建立了新的样本复杂度结果，利用从GP后验中有限采样得到的动力学函数构建可达集。基于此，设计了一种采样型GP-MPC方案，具备递归可行性，并以高概率保证闭环安全与稳定性。最后，通过两个数值例子验证了该方法的有效性，展示了精确的可达集过估计和安全的闭环表现。
原文摘要 · Abstract (English)
Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To close this gap, we present a sampling-based framework that efficiently propagates the model's epistemic uncertainty while avoiding conservatism. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop performance.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。