Probabilistic Conformance for Cyber-Physical Systems

Abstract

Conformance is a key concept in the analysis of cyber-physical systems (CPS). It indicates that two models simultaneously satisfy the same specifications of interest practically so that the result of analyzing one model automatically transfers to the other. In this paper, we propose a new concept of probabilistic conformance for CPS, extending previous study to the probabilistic domain. It is defined by the approximately equal satisfaction probabilities for a given parameterized signal temporal logic specification. Then we propose the first statistical verification method for probabilistic conformance of temporal logic specifications for grey-box CPS. To this end, we introduce a novel extended Kolmogorov-Smirnov test that can check approximately equal of two probability distributions for any desired confidence level (< 1). We apply our technique to verify the probabilistic conformance of: (1) the startup time of the widely-used full and simplified models of the Toyota Powertrain system, (2) the settling time of lane-keeping controllers based on model predictive control and neural network (NN)-based lanekeeping controllers of different sizes for an autonomous car, and (3) the maximal deviation of DC voltage between the full and simplified models of a power grid system.