On convexity of the robust freeway network control problem in the presence of prediction and model uncertainty

Marius Schmitt and John Lygeros

Transportation Research Part B: Methodological, 2020, vol. 134, issue C, 167-190

Abstract: In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging junctions are controlled, there exist tight convex relaxations of the corresponding optimization problem. In practice, many parameters of this optimization problem are not known with certainty, in particular the fundamental diagram and predictions of future traffic demand. This uncertainty poses a challenge for control approaches that pursue a model- and optimization-based strategy. In this work, we propose a robust counterpart to the FNC problem, where we introduce uncertainty sets for both the fundamental diagram and future, external traffic demands and seek to optimize the system operation, minimizing the worst-case cost. For a network with controlled merging junctions, and assuming that certain technical conditions on the uncertainty sets are satisfied, we show that the robust counterpart of the FNC problem can be reduced to a convex, finite-dimensional and deterministic optimization problem, whose numerical solution is tractable.

Keywords: Traffic control; Cell transmission model; Optimal control; Robust control; Monotone system (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0191261519303054
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:134:y:2020:i:c:p:167-190

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.trb.2020.02.005

Access Statistics for this article

Transportation Research Part B: Methodological is currently edited by Fred Mannering

More articles in Transportation Research Part B: Methodological from Elsevier
Bibliographic data for series maintained by Catherine Liu ().