Stability of traffic flow networks with a polytree topology

Coogan, Samuel; Arcak, Murat

doi:10.1016/j.automatica.2015.12.015

Cited by 51 publications

(56 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 5. In the continuous-time version of Daganzo's cell transmission model studied, e.g., in [33,34,35,36,37], the network flow dynamics reaḋ…”

Section: Example 2 the Simplest Instance Of A Nonlinear Dynamical Flmentioning

confidence: 99%

On resilient control of dynamical flow networks

Como

2017

Annual Reviews in Control

View full text Add to dashboard Cite

Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -including structural properties, such as monotonicity, that enable tractability and scalability- over the specific applications, connections to well-established road traffic flow models are made.Comment: accepted for publication in Annual Reviews in Control, 201

show abstract

“…Example 5. In the continuous-time version of Daganzo's cell transmission model studied, e.g., in [33,34,35,36,37], the network flow dynamics reaḋ…”

Section: Example 2 the Simplest Instance Of A Nonlinear Dynamical Flmentioning

confidence: 99%

On resilient control of dynamical flow networks

Como

2017

Annual Reviews in Control

View full text Add to dashboard Cite

show abstract

“…Corollary 1 states that the optimal TTS for networks with controlled merging junctions decreases if external demand decreases, and this is indeed the case in this example. 9 In this particular instance, the TTS obtained for the uncontrolled system also decreases if external demand decreases, however, this is not necessarily the case for other networks or demand patterns, as demonstrated earlier in Example 1. One important observation can be made from the comparison of the performance of the optimal solution, the uncontrolled network and the NE policy: The performance of the NE policy becomes vastly suboptimal if the actual external demand deviates significantly from the worst-case external demand.…”

Section: Verification Of Monotonicitymentioning

confidence: 67%

“…The latter condition implies that as long as traffic keeps moving, all traffic eventually leaves the network [33,9]. In particular, it implies that the spectral radius of the routing matrix is strictly less than one.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Different models exist for merging junctions, most notably Daganzo's priority rule [11] and the proportionalpriority merging model [20,9]. We make the additional assumption that merging junctions are controlled [5,31]: for all cells e ∈ N , the flows φ e (t) are chosen by a control policy, subject to demand constraints 0 ≤ φ e (t) ≤ d e ρ e (t) and supply constraints e∈E β e,i · φ e (t) ≤ s i ρ i (t) , where i is the index of the unique cell immediately downstream of the merging junction.…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the latter case, we adopt the demand-proportional merge model used e.g. in [9], in which the supply of free space of a merge is allocated proportional to the demands of the upstream cells, whenever total demand exceeds supply. In particular,…”

Section: Counterexamplesmentioning

confidence: 99%

See 2 more Smart Citations

An exact convex relaxation of the freeway network control problem with controlled merging junctions

Schmitt

Lygeros

2018

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

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 flows are controlled, there exist tight convex relaxations of the corresponding optimization problem. However, model uncertainty, in particular regarding the fundamental diagram and predictions of future traffic demand, can be a problem in practice. This uncertainty poses a challenge to 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.

show abstract

State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems

Liu

Long

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

In this article, without the help of predesigned dwell time constraints, a new state-dependent switching law with guaranteed dwell time for switched nonlinear systems is studied. Some sufficient conditions for asymptotic stability of switched nonlinear systems are derived. Also, all the abovementioned conditions can be transformed to a set of sum of squares (SOS) constraints, which can be checked by using the bilinear SOS methodology. Meanwhile, an improved path following method is provided to solve a bilinear SOS problem. Finally, three simulation examples are given to demonstrate the effectiveness of the obtained results. K E Y W O R D S computation of Lyapunov functions, dwell time, state-dependent switching law, sum of squares (SOS), switched nonlinear systems 1 3314

show abstract

Stability of traffic flow networks with a polytree topology

Cited by 51 publications

References 24 publications

On resilient control of dynamical flow networks

On resilient control of dynamical flow networks

An exact convex relaxation of the freeway network control problem with controlled merging junctions

State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems

Contact Info

Product

Resources

About