1,721,427 research outputs found
Generalized Proportional Allocation Policies for Robust Control of Dynamical Flow Networks
Full text linkWe 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
On the Stability of the Logit Dynamics in Population Games
No full textWe analyze the stability of the logit evolutionary dynamics in population games, possibly with multiple heterogeneous populations. For general population games, we prove that, on the one hand, strict Nash equilibria are asymptotically stable under the logit dynamics for low enough noise levels, on the other hand, a globally exponentially stable logit equilibrium exists for sufficiently large noise levels. This suggests the emergence of bifurcations in population games admitting multiple strict Nash equilibria, as observed in numerous examples. We then characterize a novel class of monotone separable population games for which globally asymptotically stable logit equilibria are proved to exist for every noise level. The considered class of monotone separable games finds applications, e.g., in routing games on series compositions of networks with parallel routes when there are multiple populations of users that differ in the reward function
I sistemi multi-agents e gli algoritmi di consenso
Full text linkRecently, multi-agent systems have become a central study topic in many different disciplines including biology, engineering, physics, and social science. This has led to the emergence of large and constantly growing interdisciplinary research field, known as network science. The analysis of the mathematical models describing such systems has achieved significant results, but remains mostly an open research field, where many fundamental breakthroughs are expected in the next years. Such analysis is especially motivated by the quest for the development of tools for control and design of such systems. In this paper, we deal with consensus algorithms, an important example of design of multi-agent systems that has been inspired by the dynamics of cooperative systems in natural and social sciences
Targeting interventions for displacement minimization in opinion dynamics
No full textSocial influence is largely recognized as a key factor in opinion formation processes. Recently, the role of external forces in inducing opinion displacement and polarization in social networks has attracted significant attention. This is in particular motivated by the necessity to understand and possibly prevent interference phenomena during political campaigns and elections. In this paper, we formulate and solve a targeted intervention problem for opinion displacement minimization on a social network. Specifically, we consider a min-max problem whereby a social planner (the defender) aims at selecting the optimal network intervention within her given budget constraint in order to minimize the opinion displacement in the system that an adversary (the attacker) is instead trying to maximize. Our results show that the optimal intervention of the defender has two regimes. For large enough budget, the optimal intervention of the social planner acts on all nodes proportionally to a new notion of network centrality. For lower budget values, such optimal intervention has a more delicate structure and is rather concentrated on a few target individuals
On the well-posedness of deterministic queuing networks with feedback control
Full text linkWe study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop outflow controls, our result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers
Stability and optimality of multi-scale transportation networks with distributed dynamic tolls
Full text linkWe study transportation networks controlled by dynamical feedback tolls. We consider a multiscale transportation network model whereby the dynamics of the traffic flows are intertwined with those of the drivers' route choices. The latter are influenced by the congestion status on the whole network as well as dynamic tolls set by the system operator. Our main result shows that a broad class of decentralized congestion-dependent tolls globally stabilise the transportation network around a Wardrop equilibrium. Moreover, using dynamic marginal cost tolls, stability of the transportation network can be guaranteed around the social optimum traffic assignment. This is particularly remarkable as the considered decentralized feedback toll policies do not require any global information about the network structure or the exogenous traffic load on the network or state and can be computed in a fully local way. We also evaluate the performance of these feedback toll policies both in the asymptotic and during the transient regime, through numerical simulations
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