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Data-driven verification of stochastic linear systems with signal temporal logic constraints
Automatica ( IF 6.4 ) Pub Date : 2021-07-01 , DOI: 10.1016/j.automatica.2021.109781
Ali Salamati , Sadegh Soudjani , Majid Zamani

Cyber–physical systems usually have complex dynamics and are required to fulfill complex tasks. In recent years, formal methods from Computer Science have been used by control theorists for both describing the required tasks and ensuring that they are fulfilled by the systems. The crucial drawback of formal methods is that a complete model of the system often needs to be available. The main goal of this paper is to study formal verification of linear time-invariant systems with respect to a fragment of temporal logic specifications when only a partial knowledge of the model is available, i.e., a parameterized model of the system is known but the exact values of the parameters are unknown. We provide a probabilistic measure for the satisfaction of the specification by trajectories of the system under the influence of uncertainty. We assume these specifications are expressed as signal temporal logic formulae and provide an approach that relies on gathering input–output data from the system and employs Bayesian inference on the collected data to associate a notion of confidence to the satisfaction of the specification. The main novelty of our approach is to combine both data-driven and model-based techniques in order to have a two-layer probabilistic reasoning over the behavior of the system. The inner layer is with respect to the uncertainties in dynamics and observed data while the outer layer is with respect to the distribution over the parameter space. The latter is updated using Bayesian inference on the collected data. The proposed approach is demonstrated in two case studies.



中文翻译:

具有信号时间逻辑约束的随机线性系统的数据驱动验证

信息物理系统通常具有复杂的动态特性,需要完成复杂的任务。近年来,控制理论家使用计算机科学的形式化方法来描述所需的任务并确保系统完成这些任务。形式方法的关键缺点是通常需要提供完整的系统模型。本文的主要目的是研究线性时不变系统在只有部分模型知识可用时,即,系统的参数化模型已知但精确的时态逻辑规范片段的形式验证参数值未知。我们通过系统在不确定性影响下的轨迹提供了满足规范的概率度量。我们假设这些规范表示为信号时间逻辑公式,并提供一种方法,该方法依赖于从系统收集输入-输出数据,并对收集的数据采用贝叶斯推理,以将置信度概念与规范的满意度相关联。我们方法的主要新颖之处在于结合了数据驱动和基于模型的技术,以便对系统的行为进行两层概率推理。内层是关于动力学和观测数据的不确定性,而外层是关于参数空间的分布。后者使用贝叶斯推理对收集的数据进行更新。所提出的方法在两个案例研究中得到了证明。

更新日期:2021-07-01
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