Safety Verification of Stochastic Systems: A Repetitive Scenario Approach
Safety Verification of Stochastic Systems: A Repetitive Scenario Approach
复制标题
随机系统的安全验证：重复场景方法
DOI：
10.1109/lcsys.2022.3186932
复制
发表时间：
2023
影响因子：
3
通讯作者：
Zamani, Majid
中科院分区：
文献类型：
--
作者：
Salamati, Ali;Zamani, Majid
在这封信中，我们开发了数据驱动的方法，用于具有未知动态的随机系统的安全性验证。首先，我们使用了屏障证书的概念，以铸造作为一个强大的凸规划（RCP）的安全验证。求解这个优化程序是困难的，因为模型的随机系统，这是未知的，出现在一个约束。因此，我们构造了一个场景凸规划（SCP）通过收集一些样本的轨迹系统。然后，我们开发了一个基于重复的场景框架，为构建的SCP提供样本外的性能保证。特别是，我们迭代地解决一个SCP为给定数量的样本，然后检查其可行性，使用一定数量的新样本后，取代最佳决策变量从解决SCP。我们继续迭代，直到达到所需的违规错误。最后，在可行性问题之上检查安全条件。如果满足安全条件，那么我们可以通过利用成功迭代的最优解来提供原始随机系统的安全满足概率的下限。我们说明了所提出的结果的有效性，通过一个两罐系统的案例研究，其中的安全目标是确保在两个坦克的水位在一些安全区。
In this letter, we develop adata-drivenapproach for the safety verification of stochastic systems with unknown dynamics. First, we use a notion of barrier certificates in order to cast the safety verification as a robust convex program (RCP). Solving this optimization program is difficult because the model of the stochastic system, which is unknown, appears in one of the constraints. Therefore, we construct a scenario convex program (SCP) by collecting a number of samples from trajectories of the system. Then, we develop a repetition-based scenario framework to provide an out-of-sample performance guarantee for the constructed SCP. In particular, we iteratively solve an SCP for a given number of samples, and then check its feasibility using a certain number of new samples after substituting the optimal decision variables from solving the SCP. We continue the iterations until a desired violation error is achieved. Eventually, a safety condition is checked on top of the feasibility problem. If the safety condition is fulfilled, then we can provide a lower bound on the probability of safety satisfaction for the original stochastic system by leveraging the optimal solution of the successful iteration. We illustrate the effectiveness of the proposed results through a two-tank system case study, where the safety objective is to ensure that the water levels in both tanks are within some safe zones.