Mauro Franceschelli

Decentralized estimation of Laplacian eigenvalues in multi-agent systems

In this paper, we present a decentralized algorithm to estimate the eigenvalues of the Laplacian matrix that encodes the network topology of a multi-agent system. We consider network topologies modeled by undirected graphs. The basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the Laplacian matrix. In this way, the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates.

Distributed Averaging in Sensor Networks Based on Broadcast Gossip Algorithms

In this paper, we propose a new decentralized algorithm to solve the consensus on the average problem on sensor networks through a gossip algorithm based on broadcasts. We directly extend previous results by not requiring that the digraph representing the network topology be balanced. Our algorithm is an improvement with respect to known gossip algorithms based on broadcasts in that the average of the initial state is preserved after each broadcast. The nodes are assumed to know their out-degree anytime they transmit information.

A Gossip-Based Algorithm for Discrete Consensus Over Heterogeneous Networks

Quantized consensus assumes that the state of each node may only take nonnegative integer values. Reaching consensus under quantization is equivalent to determining a balanced assignment of identical tasks to nodes. In this note, we generalize this problem in two ways and denote the resulting framework discrete consensus. First, we consider tasks that are not identical: each one is characterized by its own weight. Secondly, we assume that nodes are not identical as well. As an example, in the case of task assignment, that we consider as a reference problem in this framework, nodes may have different speeds and should be assigned a total weight proportional to their speed. We provide a gossip-based distributed algorithm that aims to minimize the maximum execution time over nodes, whose convergence to a bounded set is guaranteed. We show that the convergence time of the proposed algorithm relies ultimately on the average meeting time between two agents performing a random walk on a graph.

Finite-Time Consensus With Disturbance Rejection by Discontinuous Local Interactions in Directed Graphs

In this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous-time first-order integrator dynamics affected by bounded disturbances. The topology of the network is described by a directed graph. The proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time. An upper bound to the convergence time is explicitly derived in the technical note. Simulation results, referring to a network of coupled Kuramoto-like oscillators, are illustrated to corroborate the theoretical analysis.

On agreement problems with gossip algorithms in absence of common reference frames

In this paper a novel approach to the problem of decentralized agreement toward a common point in space in a multi-agent system is proposed. Our method allows the agents to agree on the relative location of the network centroid respect to themselves, on a common reference frame and therefore on a common heading. Using this information a global positioning system for the agents using only local measurements can be achieved. In the proposed scenario, an agent is able to sense the distance between itself and its neighbors and the direction in which it sees its neighbors with respect to its local reference frame. Furthermore only point-to-point asynchronous communications between neighboring agents are allowed thus achieving robustness against random communication failures. The proposed algorithms can be thought as general tools to locally retrieve global information usually not available to the agents.

Load balancing over heterogeneous networks with gossip-based algorithms

In this paper we consider the problem of load balancing over heterogeneous networks, i.e. networks whose nodes have different speeds. We assume that tasks are indivisible and with different weights. Our goal is that of minimizing the maximum execution time over nodes. We provide a gossip-based distributed algorithm whose convergence to a bounded set is guaranteed. We show that the convergence time of the proposed algorithm relies ultimately on the average meeting time between two agents performing a random walk on a graph.

Brief paper: Quantized consensus in Hamiltonian graphs

The main contribution of this paper is an algorithm to solve an extended version of the quantized consensus problem over networks represented by Hamiltonian graphs, i.e., graphs containing a Hamiltonian cycle, which we assume to be known in advance. Given a network of agents, we assume that a certain number of tokens should be assigned to the agents, so that the total number of tokens weighted by their sizes is the same for all the agents. The algorithm is proved to converge almost surely to a finite set containing the optimal solution. A worst case study of the expected convergence time is carried out, thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature. Moreover, the algorithm has a decentralized stop criterion once the convergence set is reached.

Load balancing on networks with gossip-based distributed ]algorithms

We study the distributed and decentralized load balancing problem on arbitrary connected graphs, representing an homogeneous network. The network contains several tasks, represented by possibly different integer numbers, to be processed at nodes. We propose a randomized algorithm based on gossip that achieves consensus on the load distribution within fixed bounds of the optimal one; we also show by simulations that in most cases the achieved consensus is optimal. We finally present a computationally convenient heuristic and show that it ensures the same bounds: simulation results, however, show that the heuristic performs worse.

Observability and controllability verification in multi-agent systems through decentralized Laplacian spectrum estimation

In this paper we show how the decentralized estimation of the spectrum of a network can be used to infer its controllability and observability properties. The proposed approach is applied to networked multi-agent systems whose local interaction rule is based on Laplacian feedback. We provide a decentralized necessary and sufficient condition for observability and controllability based on the estimated eigenvalues. Furthermore we show an example of application of the proposed method and show that the estimated spectrum can also be envisioned as a tool for decentralized formation identification.

Finite-time consensus for a network of perturbed double integrators by second-order sliding mode technique

This paper considers the problem of achieving consensus in a network of agents whose dynamics consist of perturbed double integrators. The considered class of perturbations is a bounded additive uncertainty, different for each agent, and such that the maximal magnitude is the only information available a-priori. Agents are supposed to interact through an undirected, static and connected, communication topology. The main contribution of the present work is a discontinuous local interaction rule which is able to provide finite time consensus while completely rejecting the effect of the perturbations. The local interaction rule, whose performance is investigated by Lyapunov approach, is accompanied by a set of simple tuning rules for setting the algorithms parameters. Simulation results demonstrate the effectiveness of the suggested scheme.