## 5 Simulation Results
Some scenes of scenario 4 can be found in Figure 5.0 Moreover, the video of the entire scenario in [[https://youtu.be/VGqcoX-9](https://youtu.be/VGqcoX-9) YYY]([https://youtu.be/VGqcoX-9](https://youtu.be/VGqcoX-9) YYY) can be seen. Figure 9(a) shows that vehicle 2 and vehicle 3 already left the intersection and vehicle 4 was in the intersection performing a left turn. Since vehicles 2-4 were closer to the intersection than vehicle 1, the ego vehicle had to reduce its velocity to give way; see Figure 9(b). It was yielded by the actuation; see the acceleration command \(u\) in Figure 9(c). Moreover, after vehicle 4 left the intersection, vehicle 5 arrived at 50 km/h; see Figure 9(b). Due to the reduced velocity of vehicle 1, it was not possible to go through between vehicle 4 and vehicle 5, and thus, vehicle 1 stopped. Figure 9(c) shows when vehicle 5 left the intersection, the velocity of vehicle 1 was increased to go through the intersection before vehicle 6 and vehicle 7 arrived (Figure 9(d)). Figure 5.1 Illustration of the complex fourth scenario. Figure 5.2 Illustration on the complex intersection scenario. Figure 11 shows an insight into the operation of the control system. Figure 11a illustrates the trajectories of the vehicles and the avoidable region. The illustration shows that all of the trajectories are outside of the avoidable region, and thus, the safety constraint on the motion of the autonomous vehicle can be guaranteed. Figure 11b shows the distances between vehicle 1 and the closest \(n_{s}=3\) vehicles, where \(d_{1}\) is related to the distance between vehicle 1 and the closest vehicle and \(d_{3}\) is related to the distance between vehicle 1 and the third closest vehicle. Note that the vehicles in \(n_{s}\) vary during the simulation, e.g., directly before \(t=4\) s distance \(d_{1}\) is related to \(s_{1}\)-\(s_{4}\), \(d_{2}\) is related \(s_{1}\)-\(s_{5}\) and \(d_{3}\) is related to \(s_{1}\)-\(s_{6}\); while directly after \(t=4\) s, \(d_{1}\) is related to \(s_{1}\)-\(s_{5}\), \(d_{2}\) is related \(s_{1}\)-\(s_{6}\) and \(d_{3}\) is related to \(s_{1}\)-\(s_{7}\). If there are less than three close vehicles, virtual vehicles with constant 100 m positions are defined; see, e.g., \(d_{3}\) after 5.5 s. Figure 11b shows that all of the distances were above \(s_{safe}=8\) m during the entire simulation, independently from the selection of the closest vehicle. This was yielded by the control input \(u\), which is illustrated in Figure 11d. Figure 11d also shows the further inputs, such as \(u_{K}\) and \(u_{L}\). Since the role of \(u_{K}\) is to provide velocity tracking, its value was 3 m/s\({}^{2}\) constantly, because \(v_{1}<50\) km/h during the entire simulation, except the initial velocity. The role of \(u_{L}\) is to provide vehicle motion, with which the reward function is maximized, so energy consumption is minimized and the traveled distance of the vehicle is maximized. However, none of the control inputs \(u_{K}\) and \(u_{L}\) are acceptable, because the safety constraints are not guaranteed. Thus, \(u_{K}\) is modified through \(\Delta\), which results in the control input signal \(u\). The maximum deceleration of the vehicle before 5.5 s guaranteed the avoidance of collision with vehicles 2-5, and the maximum acceleration between 5.5 s...8 s guaranteed the avoidance of the collision with vehicles 6 and 7. After 8 s, the conflict between the vehicles ceased, and thus, vehicle 1 could move with \(u=u_{L}\) to minimize the objective in (13) to zero. As a result, the velocity of vehicle 1 was slightly increased after 8 s; see Figure 11c. Moreover, Figure 11c presents that the difference between \(v_{ref}\) and \(v_{1}\) is very small, which illustrates the effectiveness of the designed robust cruise control. Figure 5.3 Signals of the complex fourth scenario. The simulation examples have shown that the proposed control algorithm is able to guarantee the safe motion of the autonomous vehicle; i.e., the collisions in the intersection are avoided.