Reachability analysis of cooperative adaptive cruise controller

In this paper, a set based approach to safety analysis of Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) is presented. Reachability analysis techniques are used to compare the minimum safe intervehicle distances which can be achieved with ACC and CACC controllers. Not surprisingly, the results indicate that a shorter inter-vehicle distance can be achieved with a CACC controller. The presented method can also be used to design the required inter-vehicle distance for a given controller. Furthermore, we show how backward reachability analysis and invariant set theory can be used to find the Maximal Asymptotic Safe Set. This is defined as a set of position error, relative speeds and acceleration, which a given controller is guaranteed to control to the desired speed and inter-vehicle distance, while fulfilling vehicle physical constraints and avoiding rear-end collisions with the preceding vehicle. The calculation of the Maximal Asymptotic Safe Set is demonstrated for ACC and CACC controller designed based on mixed H_2/∞ state feedback. Finally, the calculation of the Maximal Asymptotic Safe Set is extended to the case of vehicle model uncertainties.