On resilient control of dynamical flow networks

Abstract

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

Stability Theory of Stochastic Models in Opinion Dynamics

“…This proves the second part (part (b)).Remark 1. We note that analogous results to Theorem 1 for 1contractivity for monotone nonlinear compartmental continuous-time systems were proven in Como etal [15],[16]. (e.g., see[15, Lemma 1]), and that similar ideas underlie the differential Finsler-Lyapunov framework of Forni and Sepulchre[17],[18] as well as work on monotone and hierarchical systems[19],[20],[21].…”

Optimal regulation of flow networks with transient constraints

“…(iii) The proposed distributed controllers are applied, besides flow networks, to compartmental systems, studied in e.g. Blanchini et al [2016] and Como [2017], and we show that additional control on some inputs and flows is sufficient to achieve regulation. Although setpoint regulation for (linear) compartmental systems has been studied before in Lee and Ahn [2015] and Ahn et al [2017], our approach is different.…”

On Distributed Optimal Control of Traffic Flows in Transportation Networks

“…For future development, it would be desirable to formally prove under which conditions the algorithm converges by, e.g., giving an upper limit of the penalty ρ and to further examine is how many iterations are necessary to yield a solution with sufficient accuracy. Finally, it would be interesting to study stability and robustness of the resulting optimal controls with respect to dynamic routing [16], [17].…”

“…(ii) for every feasible solution {x k , f k , µ k } kmax k=0 of the convex optimization (16), let z k and u k be as in (17). Then, x k satisfies the controlled traffic dynamics (5)- (7), so that {x k , u k , z k } kmax k=0 is a feasible solution of the DTA problem (9).…”