MPC-based optimal coordination of variable speed limits to suppress shock waves in freeway traffic

At freeway bottlenecks shock waves may appear. These shock waves result in longer travel times and in sudden, large variations in the speeds of the vehicles, which could lead to unsafe and dangerous situations. Dynamic speed limits can be used to eliminate or at least to reduce the effects of shock waves. However, in order to prevent the occurrence of new shock waves and/or negative impacts on the traffic flows in other locations, coordination of the variable speed limits is necessary. In this paper we further extend our results in connection with a model predictive control (MPC) approach to optimally coordinate variable speed limits for freeway traffic. First of all, we include a safety constraint that prevents drivers from encountering speed limit drops larger than, e.g., 10 km/h. Furthermore, to get a better correspondence between the computed and the applied control signals, we now consider discrete-valued speed limits.