发表机构
University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于PINNs的S2R求解器，通过自适应配点采样分布改进HJ可达性分析，在减少相对L2误差的同时达到或优于SoTA方法的安全指标，且无需多阶段训练或MPC监督。
AI 中文摘要
哈密顿-雅可比（HJ）可达性为动态系统的安全控制提供了数学上严谨的框架，但其实际应用受到高维情况下求解哈密顿-雅可比-艾萨克斯变分不等式偏微分方程（PDE）的计算复杂性瓶颈限制。物理信息神经网络（PINNs）近期已成为经典基于网格求解器的有前景替代方案，但其性能对配点采样的选择高度敏感。为学习准确的安全值函数，现有基于PINNs的HJ可达性求解器必须依赖复杂的训练流程和辅助监督。本研究提出STEER2REACH（S2R），一种基于PINNs的HJ可达性求解器，仅需对标准PINNs训练进行极少修改。S2R的核心贡献是一种轻量、低开销的自适应配点采样分布，该分布通过结合当前值函数诱导的最优控制与干扰信号，并注入随机探索噪声来引导前向轨迹构建。我们证明，尽管S2R结构简单，但在一系列可达性基准测试中，其在安全指标上达到了与现有技术（SoTA）MPC引导的HJ可达性求解器相当甚至更优的性能，同时降低了相对L2误差，且无需多阶段训练或基于MPC的监督。
英文摘要
Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to classical mesh-based solvers, yet their performance is highly sensitive to the choice of collocation sampling. In order to learn accurate safety value functions, existing PINNs-based HJ reachability solvers must rely on complex training pipelines and auxiliary supervision. In this work, we propose STEER2REACH (S2R), a PINNs-based HJ reachability solver that requires minimal modification on top of standard PINNs training. S2R's key contribution is a lightweight, low-overhead adaptive collocation sampling distribution constructed by steering forward trajectories using a combination of the optimal control and disturbance signals induced by the current value function, with injected stochastic exploration noise. We demonstrate that despite its simplicity, S2R achieves competitive--and in some cases improved--performance on safety metrics while reducing relative L2 error across a range of reachability benchmarks compared with SoTA MPC-guided HJ reachability solvers, all without requiring multi-stage training or MPC-based supervision.
CommentsIEEE CDC 2026
