**Reference:**

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.

**Abstract:**

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.

Online version of the paper

Corresponding technical report: pdf file (498 KB)

@article{FreNun:14-015,

author={J.R.D. Frejo and A. N{\'{u}}{\~{n}}ez and B. {D}e Schutter and E.F. Camacho},

title={Hybrid model predictive control for freeway traffic using discrete speed limit signals},

journal={Transportation Research Part C},

volume={46},

pages={309--325},

month=sep,

year={2014},

doi={10.1016/j.trc.2014.06.005}

}

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