无需完整模型，用贝叶斯方法为隐藏状态系统生成安全证书。
Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference
- 基于贝叶斯框架，用输出数据更新状态先验，估计未知系统动态。
- 通过后验样本验证，确保证书在95%置信度下对真实系统有效。
- 适合无全量观测、需概率安全保证的复杂系统，如机器人控制。
安全认证对动态系统至关重要，但传统屏障证书通常需要明确的系统模型。当系统动态未知时，可采用数据驱动方法，但获得有效证书需严格量化不确定性。现有方法多依赖完整状态测量，限制了适用性。本文提出一种新方法，用于合成具有隐藏状态和多项式动态的未知系统的屏障证书。采用贝叶斯框架，以状态空间表示的先验通过目标边际马尔可夫链蒙特卡洛采样器，利用输出数据进行更新。所得后验样本用于构建一个平方和（SOS）程序的屏障证书。通过在额外一组后验样本上测试，获得该证书相对于真实未知系统的概率保证。数值仿真展示了该方法及其概率保证的有效性。
原文摘要 · Abstract (English)
Certifying safety in dynamical systems is crucial, but barrier certificates - widely used to verify that system trajectories remain within a safe region - typically require explicit system models. When dynamics are unknown, data-driven methods can be used instead, yet obtaining a valid certificate requires rigorous uncertainty quantification. For this purpose, existing methods usually rely on full-state measurements, limiting their applicability. This paper proposes a novel approach for synthesizing barrier certificates for unknown systems with latent states and polynomial dynamics. A Bayesian framework is employed, where a prior in state-space representation is updated using output data via a targeted marginal Metropolis-Hastings sampler. The resulting samples are used to construct a barrier certificate through a sum-of-squares program. Probabilistic guarantees for its validity with respect to the true, unknown system are obtained by testing on an additional set of posterior samples. The approach and its probabilistic guarantees are illustrated through a numerical simulation.
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。