Improved generalization by training on adversarial examples

This question is based on the following intuition: To my understanding adversarial attacks work, because the model is stuck in a local minima and the adversarial attack finds this with gradient descent. Could this be used to train a Neural Network that is able to generalize better? This way the model would be trained on exactely the examples it completely misunderstands. Intuitively it feels like the teacher trying to find where the student misunderstood the topic and than correcting it instead of giving the model random examples. What do you think about this idea? Do you know if it has already been attempted?