为动态障碍环境中的随机系统设计了更精确的安全验证方法
Stochastic Barrier Certificates in the Presence of Dynamic Obstacles
- 用时变障碍函数建模动态障碍，提升安全边界精度
- 在非线性系统上实现比现有方法更紧的安全概率下界
- 适合需要高可靠性验证的自动驾驶等安全关键场景
本文通过随机屏障函数视角研究存在动态障碍环境下的随机动力系统的安全性。针对离散时间、连续状态空间系统引入时不变与时变屏障证书，提供有限时域内保持在安全集内的概率下界。这些证书显式考虑由障碍物运动引起的时变不安全区域。利用贝尔曼最优性视角，时变形式直接捕捉时间结构，所得界限比现有方法更紧。通过将证书限制为多项式函数，时变屏障合成可转化为凸的平方和优化问题，实现可计算优化。在具有动态障碍的非线性系统上的实证评估表明，时变证书始终能获得紧致保障，相比最先进方法展现出更高的准确性和可扩展性。
原文摘要 · Abstract (English)
Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty, which provide certified lower bounds on the probability of remaining within a safe set over a finite horizon. These certificates explicitly account for time-varying unsafe regions induced by obstacle dynamics. By leveraging Bellman's optimality perspective, the time-varying formulation directly captures temporal structure and yields less conservative bounds than state-of-the-art approaches. By restricting certificates to polynomial functions, we show that time-varying barrier synthesis can be formulated as a convex sum-of-squares program, enabling tractable optimization. Empirical evaluations on nonlinear systems with dynamic obstacles show that time-varying certificates consistently achieve tight guarantees, demonstrating improved accuracy and scalability over state-of-the-art methods.
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