Uncertainty Quantification for Closed-Loop Dynamical Systems: An application-based comparison

When developing safety-critical control applications such as autonomous driving, it is crucial to assess the impact of model uncertainties on the system’s closed-loop behaviour. Various methods, referred to as uncertainty quantification, are available in the literature with different levels of accuracy and computational costs. This paper investigates and compares the application of different uncertainty quantification techniques based on the Unscented Transformation and the Polynomial Chaos Expansion to a highway lane change manoeuvre in a closed-loop setting. The resulting means and standard deviations of the trajectory error of the closed-loop system are compared with the corresponding Monte-Carlo estimates, which serve as ground truth. It turns out that the Unscented Transformation provides accurate results at moderate computational costs and is best suitable for realtime deployment.