Controllability Metrics, Limitations and Algorithms for Complex Networks

This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem (i) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, (ii) we derive bounds based on the system dynamics (network topology and weights) to characterize the tradeoff between the control energy and the number of control nodes, and (iii) we propose an open-loop control strategy with performance guarantees. In our strategy we select control nodes by relying on network partitioning, and we design the control input by leveraging optimal and distributed control techniques. Our findings show several control limitations and properties. For instance, for Schur stable and symmetric networks: (i) if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes, (ii) if the number of control nodes is a fixed fraction of the network nodes, then certain networks can be controlled with constant energy independently of the network dimension, and (iii) clustered networks may be easier to control because, for sufficiently many control nodes, the control energy depends only on the controllability properties of the clusters and on their coupling strength. We validate our results with examples from power networks, social networks, and epidemics spreading

Optimal strategies in the average consensus problem

We prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely many steps. A more general family of strategies, constructed by block Kronecker products, is investigated and compared to Cayley strategies.Comment: 9 pages; extended preprint with proofs of a CDC 2007 (Conference on decision and Control) pape

Gossip consensus algorithms via quantized communication

This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise ''gossip'' communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.Comment: Accepted for publicatio

Distributed reactive power feedback control for voltage regulation and loss minimization

We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage regulation. In the proposed strategy, microgenerators are smart agents that can measure their phasorial voltage, share these data with the other agents on a cyber layer, and adjust the amount of reactive power injected into the grid, according to a feedback control law that descends from duality-based methods applied to the optimal reactive power flow problem. Convergence to the configuration of minimum losses and feasible voltages is proved analytically for both a synchronous and an asynchronous version of the algorithm, where agents update their state independently one from the other. Simulations are provided in order to illustrate the performance and the robustness of the algorithm, and the innovative feedback nature of such strategy is discussed

A distributed control strategy for reactive power compensation in smart microgrids

We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems. We then consider the specific problem of commanding the microgenerators connected to the microgrid, in order to achieve the optimal injection of reactive power. For this task, we design a randomized, gossip-like optimization algorithm. We show how a distributed approach is possible, where microgenerators need to have only a partial knowledge of the problem parameters and of the state, and can perform only local measurements. For the proposed algorithm, we provide conditions for convergence together with an analytic characterization of the convergence speed. The analysis shows that, in radial networks, the best performance can be achieved when we command cooperation among units that are neighbors in the electric topology. Numerical simulations are included to validate the proposed model and to confirm the analytic results about the performance of the proposed algorithm

EXPERIENCES OF AUTOMATED CARTOGRAPHIC GENERALIZATION IN ITALY: TECHNIQUES AND RESULTS OF THE CARGEN PROJECT

La generalizzazione automatica è un campo di ricerca attivo da ormai oltre trenta anni. Recentemente il costante progresso delle tecniche e il miglioramento dei risultati ha portato all'introduzione di procedure di derivazione automatica all'interno dei processi produttivi di alcuni enti cartografici europei. Questo articolo illustra lo stato della ricerca nel campo della generalizzazione cartografica automatica in Italia e mostra come anche nel nostro paese si stiano conseguendo risultati significativi; in particolare verranno descritti i progressi del progetto CARGEN, che studia la derivazione alla scala 1:25000 e 1:50000 del DBT nazionale.The achievements in the field of automated cartographic generalization have recently lead to the actual deployment of automatic processes in the production workflow of some European NMAs. This article describes the state of the research on automated cartographic generalization in Italy, focusing in particular on the results of the CARGEN project, studying the generalization of the National DBT to the 1:25000 and 1:50000 scales

Scale Free Controllability of Large-Scale Networks: an Output Controllability Approach

International audienceIn this paper we consider the problem of controllability and energy consumption for large scale networks. Instead of controlling separately all the nodes of the network we control an output which is defined as some measurement (for instance the average) of the nodes which are not directly controlled. We thus exploit the concept of Output Controllability and the Output Controllability Gramian to analyze the properties of the system. In this context, we show that it is possible to obtain a reduced-order model which makes the Gramian compution and control design much easier. Simulations show that the reduced model is consistent with the original one and for low ratios of controlled nodes, more robust and performing with respect to the original