Controller synthesis for hybrid systems that satisfy temporal specifications expressing various system properties is a challenging problem that has drawn the attention of many researchers. However, making the assumption that such temporal properties are deterministic is far from the reality. For example, many of the properties the controller has to satisfy are learned through machine learning techniques based on sensor input data. In this paper, we propose a new logic, Probabilistic Signal Temporal Logic (PrSTL), as an expressive language to define the stochastic properties, and enforce probabilistic guarantees on them. We further show how to synthesize safe controllers using this logic for cyber-physical systems under the assumption that the stochastic properties are based on a set of Gaussian random variables. One of the key distinguishing features of PrSTL is that the encoded logic is adaptive and changes as the system encounters additional data and updates its beliefs about the latent random variables that define the safety properties. We demonstrate our approach by synthesizing safe controllers under the PrSTL specifications for multiple case studies including control of quadrotors and autonomous vehicles in dynamic environments.

本文提出了一种新的逻辑PrSTL作为表达随机性质和强制其概率保证的表现语言，并展示了如何使用这种逻辑对具有随机性质的智能物理系统进行控制器合成，其关键特点是适应性逻辑并随着系统遇到附加数据而变化，并通过合成多种情况下无人机和自主车辆的控制器来演示我们的方法。

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