J.R.D. Frejo, A. Núñez, B. De Schutter, and E.F. Camacho, "Hybrid model predictive control for freeway traffic using discrete speed limit signals," Transportation Research Part C, vol. 46, pp. 309-325, Sept. 2014.
In this paper, two hybrid Model Predictive Control (MPC) approaches for freeway traffic control are proposed considering variable speed limits (VSL) as discrete variables as in current real world implementations. These discrete characteristics of the speed limits values and some necessary constraints for the actual operation of VSL are usually underestimated in the literature, so we propose a way to include them using a macroscopic traffic model within an MPC framework. For obtaining discrete signals, the MPC controller has to solve a highly non-linear optimization problem, including mixed-integer variables. Since solving such a problem is complex and difficult to execute in real-time, we propose some methods to obtain reasonable control actions in a limited computation time. The first two methods (θ-exhaustive and θ-genetic discretization) consist of first relaxing the discrete constraints for the VSL inputs; and then, based on this continuous solution and using a genetic or an exhaustive algorithm, to find discrete solutions within a distance θ of the continuous solution that provide a good performance. The second class of methods split the problem in a continuous optimization for the ramp metering signals and in a discrete optimization for speed limits. The speed limits optimization, which is much more time-consuming than the ramp metering one, is solved by a genetic or an exhaustive algorithm in communication with a non-linear solver for the ramp metering. The proposed methods are tested by simulation, showing not only a good performance, but also keeping the computation time reduced.