Traffic regulation via controlled speed limit. (English) Zbl 1377.90016
Summary: We study an optimal control problem for traffic regulation via variable speed limit. The traffic flow dynamics is described with the Lighthill-Whitham-Richards model with Newell-Daganzo flux function. We aim at minimizing the \(L^2\) quadratic error to a desired outflow, given an inflow on a single road. We first provide existence of a minimizer and compute analytically the cost functional variations due to needle-like variation in the control policy. Then, we compare three strategies: instantaneous policy; random exploration of control space; steepest descent using numerical expression of gradient. We show that the gradient technique is able to achieve a cost within 10% of the random exploration minimum with better computational performances.
MSC:
| 90B20 | Traffic problems in operations research |
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