The paper proposes the design of a neural-network-based control strategy of autonomous vehicles in intersections. The motivation of the neural network approach is to reduce the numerically-intensive computation of the optimization problem in which the motions of autonomous vehicles are formed. In the method the neural network is trained through a preliminary optimal off-line solution. Moreover, a robustness analysis and a reconfiguration strategy for the scenarios with vehicle position disturbances are proposed. The design and the analysis are illustrated through CarSim simulation examples.