## 1 Introduction and Motivation
Nevertheless, it can require centralized control, which can lead to additional security, legal and privacy problems. Therefore, it is requested to develop distributed control structures; e.g., in [10] the problem is formulated as distributed optimal control for a system of multiple autonomous vehicles and then solved using a nonlinear model predictive control (MPC) technique. Similarly, [PERSON] et al. [11] investigated intersection control of multiple vehicles using a distributed MPC approach, where priorities need to be assigned to vehicles. Thus, the challenge of distributed control is also different to the general path planning and tracking problems, where the coordination of the vehicles is limited, or where it is carried out on the level of the transportation system. The high number of challenges in the field of autonomous vehicle control in intersections has motivated increased research activity, i.e., several publications with different approaches. Methods of one of the most important groups are based on the MPC technique; see, e.g., [12; 13; 14; 15]. Although they can provide appropriate results, the increase in the number of vehicles can make real-time computation difficult. A possible solution to the problem of increasing computational effort is the approximation of the optimal solution with neural networks; see, e.g., [16]. However, in this case it may be difficult to provide guarantees on collision avoidance for all intersection scenarios [17]. The quadratic programming method gives the possibility of real-time implementation compared to the convex optimization using space coordinates; see [18]. Collision avoidance is guaranteed through the definition of regions in the intersection with special rules, which reduces the complexity of the problem, but the conservativeness of the solution increases. Due to the ordering problem of vehicles in an intersection, the control problem can be formed as a mixed-integer linear programming (MILP) task; see, e.g., a method on the coordination in [19]. The goal of the control is to find an arrival schedule of the vehicles, which ensures safety while it reduces the number of stops and intersection delays. [PERSON] et al. [20] presents a centralized MILP-based approach for intersection control in an urban environment of highly automated vehicles, with which the minimum vehicle delay at the intersection can be achieved. Another solution in the predictive control framework is to examine all ordering combinations of the vehicles [21], which can also be difficult for a high number of vehicles. Thus, although MPC-based methods can provide effective and handy solutions to the control problem of autonomous vehicles in intersections, a high number of vehicles can lead to numerical difficulties. A further group of solutions is based on the minimax formulations of the optimal control problem, together with the coordination of the vehicles. For example, [PERSON] et al. [22] proposed a game-theoretic approach to modeling vehicle interactions, in particular, for urban traffic environments with unsignalized intersections. In general, they are traffic models with heterogeneous control, and they are used for virtual testing, evaluation and calibration of autonomous vehicle control systems. A framework for intersection control, which is based on the queuing theory, was presented by [23]. Through this framework a capacity-optimal, slot-based intersection management system for the two-road crossing configuration was presented. A slot preassigning method for connected vehicles was also proposed in [24]. The connection of intersections can also be handled by the multi-agent viewpoint [25; 26]. This solution provides the ability to quickly reverse individual lanes in response to rapidly changing traffic conditions. A further multi-agent solution based on a heuristic optimization algorithm was presented by [27]. The objective of the research was to reduce total time delay for the entire intersection, while collisions were prevented.