Hybrid modeling for the evaluation of risk perception by air-traffic controllers

We present a mathematical framework for the estimation of the level of risk perceived by Air-Traffic Controllers (ATCo) in a given traffic situation. We first derive a hybrid model to represent trajectory prediction performed by ATCo. The hybrid framework makes it possible to have a description of the aircraft evolution, including flight plans seen as a succession of legs with constant parameters, very close to the description used by ATCo. Using this model, we consider a worst case approach to compute a cost related to the worst possible predicted situation and the time before this situation can occur. In order to compute the risk function, we reformulate the optimization problem using impulse differential inclusions and a viability approach. We illustrate our approach on a simple traffic situation for which human-in-the-loop experimentations provide validation data, and we provide numerical result for more complex traffic situations.