We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

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An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

Power Aware Routing in Mobile Ad Hoc Networks

Decentralized estimation of Laplacian eigenvalues in multi-agent systems

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.

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

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.

Distributed Averaging in Sensor Networks Based on Broadcast Gossip Algorithms

In this paper we present a novel decentralized algorithm to estimate the eigenvalues of the Laplacian of the network topology of a multi-agent system. The basic idea is to provide a local interaction rule among agents so that their state oscillates only at frequencies corresponding to eigenvalues of the network topology. In this way, the problem of decentralized eigenvalue estimation is mapped into a problem of signal processing, solvable by applying the Fast Fourier Transform (FFT).

Decentralized Laplacian eigenvalues estimation for networked multi-agent systems

In this paper, we propose a novel continuous-time protocol that solves the consensus problem on the median value, i.e., it provides distributed agreement in networked multi-agent systems where the quantity of interest is the median value of the agents' initial values. In contrast to the average value, the median value is a statistical measure inherently robust to the presence of outliers, which is a significant robustness issue in large-scale sensor and multi-agent networks. The proposed protocol requires only binary information regarding the relative state differences among the neighboring agents and achieves consensus on the median value in finite time by exploiting a suitable ad-hoc discontinuous local interaction rule. In addition, we characterize certain resiliency properties of the proposed protocol against the presence of uncooperative agents which do not implement the underlying local interaction rule whereas they interact with their neighbors thus influencing the network. In particular, we prove that despite the persistent influence of (at most) a certain number of uncooperative agents, the cooperative agents achieve finite time consensus on a value lying inside the convex hull of the cooperative agents' initial conditions, provided that the special class of so-called “ $k$ -safe” network topology is considered. Capabilities of the proposed consensus protocol and its effectiveness are supported by numerical studies.

Mauro Franceschelli

Papers

Decentralized estimation of Laplacian eigenvalues in multi-agent systems

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

Distributed Averaging in Sensor Networks Based on Broadcast Gossip Algorithms

Decentralized Laplacian eigenvalues estimation for networked multi-agent systems

Finite-Time Consensus on the Median Value With Robustness Properties