  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.
