Generalized Proportional Allocation Policies for Robust Control of Dynamical Flow Networks
(2022) In IEEE Transactions on Automatic Control 67(1). p.32-47- Abstract
We study a robust control problem for dynamical flow networks. In the considered framework, traffic flows along the links of a transportation network —modeled as a capacited multigraph— and queues up at the nodes, whereby control policies determine which incoming queues are to be allocated service simultaneously, within some predetermined scheduling constraints. We first prove fundamental performance limitations on the system performance by showing that for a dynamical flow network to be stabilizable by some control policy it is necessary that the exogenous inflows belong to a certain stability region, that is determined by the network topology, the link capacities, and the scheduling constraints. Then, we... (More)
We study a robust control problem for dynamical flow networks. In the considered framework, traffic flows along the links of a transportation network —modeled as a capacited multigraph— and queues up at the nodes, whereby control policies determine which incoming queues are to be allocated service simultaneously, within some predetermined scheduling constraints. We first prove fundamental performance limitations on the system performance by showing that for a dynamical flow network to be stabilizable by some control policy it is necessary that the exogenous inflows belong to a certain stability region, that is determined by the network topology, the link capacities, and the scheduling constraints. Then, we introduce a family of distributed controls, referred to as Generalized Proportional Allocation (GPA) policies, and prove that they stabilize a dynamical transportation network whenever the exogenous inflows belong to such stability region. The proposed GPA control policies are decentralized and fully scalable as they rely on local feedback information only. Differently from previously studied maximally stabilizing control strategies, the GPA control policies do not require any global information about the network topology, the exogenous inflows, or the routing, which makes them robust to unpredicted network load variations and changes in the link capacities or the routing decisions. Moreover, the proposed GPA control policies also take into account the overhead time while switching between services. Our theoretical results find one application in the control of urban traffic networks with signalized intersections, where vehicles have to queue up at junctions and the traffic signal controls determine the green light allocation to the different incoming lanes.
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- author
- Nilsson, Gustav LU and Como, Giacomo LU
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Decentralized control, distributed control, Dynamical flow networks, Network topology, non-linear control, Resource management, robust control, Robust control, Routing, Switches, traffic signal control, Transportation, transportation networks
- in
- IEEE Transactions on Automatic Control
- volume
- 67
- issue
- 1
- pages
- 16 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85098751823
- ISSN
- 0018-9286
- DOI
- 10.1109/TAC.2020.3046026
- project
- Modeling and Control of Large Scale Transportation Networks
- language
- English
- LU publication?
- no
- id
- 7b09608f-9874-404a-8508-0da188ad3369
- date added to LUP
- 2021-02-08 22:53:00
- date last changed
- 2022-04-27 00:27:38
@article{7b09608f-9874-404a-8508-0da188ad3369,
abstract = {{<p>We study a robust control problem for dynamical flow networks. In the considered framework, traffic flows along the links of a transportation network &#x2014;modeled as a capacited multigraph&#x2014; and queues up at the nodes, whereby control policies determine which incoming queues are to be allocated service simultaneously, within some predetermined scheduling constraints. We first prove fundamental performance limitations on the system performance by showing that for a dynamical flow network to be stabilizable by some control policy it is necessary that the exogenous inflows belong to a certain stability region, that is determined by the network topology, the link capacities, and the scheduling constraints. Then, we introduce a family of distributed controls, referred to as Generalized Proportional Allocation (GPA) policies, and prove that they stabilize a dynamical transportation network whenever the exogenous inflows belong to such stability region. The proposed GPA control policies are decentralized and fully scalable as they rely on local feedback information only. Differently from previously studied maximally stabilizing control strategies, the GPA control policies do not require any global information about the network topology, the exogenous inflows, or the routing, which makes them robust to unpredicted network load variations and changes in the link capacities or the routing decisions. Moreover, the proposed GPA control policies also take into account the overhead time while switching between services. Our theoretical results find one application in the control of urban traffic networks with signalized intersections, where vehicles have to queue up at junctions and the traffic signal controls determine the green light allocation to the different incoming lanes.</p>}},
author = {{Nilsson, Gustav and Como, Giacomo}},
issn = {{0018-9286}},
keywords = {{Decentralized control; distributed control; Dynamical flow networks; Network topology; non-linear control; Resource management; robust control; Robust control; Routing; Switches; traffic signal control; Transportation; transportation networks}},
language = {{eng}},
number = {{1}},
pages = {{32--47}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Automatic Control}},
title = {{Generalized Proportional Allocation Policies for Robust Control of Dynamical Flow Networks}},
url = {{http://dx.doi.org/10.1109/TAC.2020.3046026}},
doi = {{10.1109/TAC.2020.3046026}},
volume = {{67}},
year = {{2022}},
}