Traffic Regulation Via Controlled Speed Limit

Maria Laura Delle Monache (1, 2) , Benedetto Piccoli (2, 3) , Francesco Rossi (4)

1 NECS - Networked Controlled Systems
2 Department of Mathematical Sciences [Camden]
3 CCIB - Center for Computational and Integrative Biology [Camden]
4 LSIS - Laboratoire des Sciences de l'Information et des Systèmes

We study an optimal control problem for traffic regulation via variable speed limit. The traffic flow dynamics is described with the Lighthill-Whitham-Richards (LWR) 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 random exploration minimum with better computational performances.

Mots clés: Optimal control problem; Traffic problems; Variable speed limit

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Automatique / Robotique

Maria Laura Delle Monache, Benedetto Piccoli, Francesco Rossi. Traffic Regulation Via Controlled Speed Limit. SIAM Journal on Control and Optimization, 2017, 55 (5), pp.2936-2958. ⟨10.1137/16M1066038⟩. ⟨hal-01577927⟩