## 1 Introduction and Motivation  
The handling of intersection scenarios is an important challenge in the research field of autonomous vehicles. From the aspect of control design, several crucial tasks of the autonomous vehicle control in intersection scenarios should be formulated. For example, the ordering of autonomous vehicles in intersections has an impact on the energy consumption of the vehicles, traveling time, emissions and traveling comfort (due to the acceleration/ deceleration maneuvers, for example) [1]. This leads to a multi-objective optimization task, which generally has a Pareto-optimal solution. Moreover, the solution of the optimization problem regarding autonomous vehicles in intersections can require lengthy computations. This poses the challenge of the minimization of the computational time, e.g., finding approximations of the optimal solution. From an application point of view, the accurate detection of a vehicle's position in an intersection can be difficult. There exist camera-based vehicle localization strategies [2], solutions with LiDAR and camera fusion [3] and GPS and sterevision-based visual odometry solutions [4]. The detection and prediction of human behavior are also difficult and complex problems; see [5, 6]. Nevertheless, considering position errors caused by human participants, robust control strategies are needed with which collision avoidance can be guaranteed. Due to the special challenges of the control of autonomous vehicles in intersections, in the architecture of the control system it can be handled as a special feature of a path planning algorithm in future vehicles. Its main differences from the path planning problem are as follows. First, in intersections the autonomous vehicles can have interactions. Since the other vehicles are also in motion, the handling of intersection scenarios is a complex problem, which requires sensing, decision and control functionalities. In intersections the risk of the collision is increased, e.g., compared to the motion of the autonomous vehicle along a highway. Second, various types of intersections on the road can be found--they can depend on the number of lanes, directions and signalization. A challenge of the autonomous vehicles and the intelligent transportation systems is the handling of vehicle interactions in unsignalized intersections [7]. In these types of intersections, the experiences of the human drivers has a role in the avoidance of the conflicts; e.g., the speed of the surrounding vehicles and the intentions of the further drivers must be estimated. In a general path planning algorithm, the waypoints, the rules and the information on the road and on the local traffic conditions can be considered to be given, and thus, it requires less estimation. Third, in urban areas the autonomous vehicles during their routes must travel through many intersections. Since these intersections are connected to each other, the motion of the vehicles in the intersections has an impact on the global performance of the traffic system, i.e., on the average speed or on the traffic density; see, e.g., [8]. Thus, during the design of the autonomous vehicle's motion, the time minimization is an especially important at intersections. Moreover, the inefficient motion of autonomous vehicles in intersections can lead to increased energy consumption, e.g., a high number of stop and go maneuvers. Thus, during the design of the autonomous vehicle motion in intersections, a balance between the time minimization and the energy consumption minimization must be found. Although it is also a problem in a general path planning problem, it is a greater problem for intersections. Fourth, a special problem of vehicle control in intersections is the architecture of the control system. Since in intersections a high number of vehicles can be controlled and the presence of human-driven vehicles must be handled, an optimal solution of the motion problem can be found through the coordination of the autonomous vehicles in a centralized control system [9].