Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Coordination of passive systems under quantized measurements

In this paper we investigate a passivity approach to collective coordination and synchronization problems in the presence of quantized measurements and show that coordination tasks can be achieved in a practical sense for a large class of passive systems.Comment: 40 pages, 1 figure, submitted to journal, second round of revie

Consensus with Linear Objective Maps

A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics

Consensus Algorithms for Estimation and Discrete Averaging in Networked Control Systems

In this thesis several topics on consensus and gossip algorithms for multi-agent systems are addressed. An agent is a dynamical system that can be fully described by a state-space representation of its dynamics. A multi-agent system is a network of agents whose pattern of interactions or couplings is described by a graph. Consensus problems in multi-agent systems consist in the study of local interaction rules between the agents such that as global emergent behavior the network converges to the so called "consensus" or "agreement" state where the value of each agent's state is the same and it is possibly a function of the initial network state, for instance the average. A consensus algorithm is thus a set of local interaction rules that solve the consensus problem under some assumptions on the network topology. A gossip algorithm is a set of local state update rules between the agents that, disregarding their objective, are supposed to be implemented in a totally asynchronous way between pairs of neighboring agents, thus resembling the act of "gossiping" in a crowd of people. In this thesis several algorithms based on gossip that solve the consensus and other related problems are presented. In the �first part, several solutions to the consensus problem based on gossip under different sets of assumptions are proposed. In the fi�rst case, it is assumed that the state of the agents is discretized and represents a collection of tasks of different size. In the second case, under the same discretization assumptions of the �rst case, it is assumed that the network is represented by a Hamiltonian graph and it is shown how under this assumption the convergence speed can be improved. In the third case, a solution for the consensus problem for networks represented by arbitrary strongly connected directed graphs is proposed, assuming that the state of the agents is a real number. In the fourth case, a coordinate-free consensus algorithm based on gossip is designed and applied to a network of vehicles able to sense the relative distance between each other but with no access to absolute position information or to a common coordinate system. The proposed algorithm is then used to build in a decentralized way a common reference frame for the network of vehicles. In the second part, a novel local interaction rule based on the consensus equation is proposed together with an algorithm to estimate in a decentralized way the spectrum of the Laplacian matrix that encodes the network topology. As emergent behavior, each agent's state oscillates only at frequencies corresponding to the eigenvalues of the Laplacian matrix thus mapping the spectrum estimation problem into a signal processing problem solvable using the Fourier Transform. It is further shown that the constant component of the emergent behavior in the frequency domain solves the consensus on the average problem. The spectrum estimation algorithm is then applied to leader-follower networks of mobile vehicles to infer in a decentralized way properties such as controllability, osservability and other topological features of the network such as its topology. Finally, a fault detection and recovery technique for sensor networks based on the so called motion-probes is presented to address the inherent lack of robustness against outlier agents in networks implementing consensus algorithms to solve the distributed averaging problem

How to Quantize Forces(?): An Academic Essay How the Strings Could Enter Classical Mechanics

Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or Hamiltonian description is an odd dimensional line element contact bundle. Time evolution is governed by certain canonical two-form $\Omega$ (an analog of dp/\dq-dH/\dt), which is constructed purely from forces and the metric tensor entering the kinetic energy of the system. Attempt to "dissipative quantization" in terms of the two-form $\Omega$ is proposed. The Feynman's path integral over histories of the system is rearranged to a "world-sheet" functional integral. The "umbilical string" surfaces entering the theory connect the classical trajectory of the system and the given Feynman history. In the special case of potential-generated forces, "world-sheet" approach precisely reduces to the standard quantum mechanics. However, a transition probability amplitude expressed in terms of "string functional integral" is applicable (at least academically) when a general dissipative environment is discussed.Comment: 13 pages, 3 pictures, comments are welcom