Asynchronous Networks and Event Driven Dynamics

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks

Average Consensus in the Presence of Delays and Dynamically Changing Directed Graph Topologies

Classical approaches for asymptotic convergence to the global average in a distributed fashion typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practical settings due to varying delays that might affect transmissions at different times, as well as possible changes in the underlying interconnection topology (e.g., due to component mobility). In this work, we propose protocols to overcome these limitations. We first consider a fixed interconnection topology (captured by a - possibly directed - graph) and propose a discrete-time protocol that can reach asymptotic average consensus in a distributed fashion, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its outgoing links (i.e., the number of components to which it sends information). We subsequently extend the protocol to also handle changes in the underlying interconnection topology and describe a variety of rather loose conditions under which the modified protocol allows the components to reach asymptotic average consensus. The proposed algorithms are illustrated via examples.Comment: 37 page

A survey of distributed data aggregation algorithms

Distributed data aggregation is an important task, allowing the decentralized determination of meaningful global properties, which can then be used to direct the execution of other applications. The resulting values are derived by the distributed computation of functions like COUNT, SUM, and AVERAGE. Some application examples deal with the determination of the network size, total storage capacity, average load, majorities and many others. In the last decade, many different approaches have been proposed, with different trade-offs in terms of accuracy, reliability, message and time complexity. Due to the considerable amount and variety of aggregation algorithms, it can be difficult and time consuming to determine which techniques will be more appropriate to use in specific settings, justifying the existence of a survey to aid in this task. This work reviews the state of the art on distributed data aggregation algorithms, providing three main contributions. First, it formally defines the concept of aggregation, characterizing the different types of aggregation functions. Second, it succinctly describes the main aggregation techniques, organizing them in a taxonomy. Finally, it provides some guidelines toward the selection and use of the most relevant techniques, summarizing their principal characteristics.info:eu-repo/semantics/publishedVersio

A Decomposition Approach to Multi-Agent Systems with Bernoulli Packet Loss

In this paper, we extend the decomposable systems framework to multi-agent systems with Bernoulli distributed packet loss with uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance - which are expressed in the form of linear matrix inequalities - scale linearly with increased network size and thus allow to analyse even very large-scale multi-agent systems. A numerical example demonstrates the potential of the approach by application to a first-order consensus problem.Comment: 11 pages, 4 figure

Two-Stage Consensus-Based Distributed MPC for Interconnected Microgrids

In this paper, we propose a model predictive control based two-stage energy management system that aims at increasing the renewable infeed in interconnected microgrids (MGs). In particular, the proposed approach ensures that each MG in the network benefits from power exchange. In the first stage, the optimal islanded operational cost of each MG is obtained. In the second stage, the power exchange is determined such that the operational cost of each MG is below the optimal islanded cost from the first stage. In this stage, a distributed augmented Lagrangian method is used to solve the optimisation problem and determine the power flow of the network without requiring a central entity. This algorithm has faster convergence and same information exchange at each iteration as the dual decomposition algorithm. The properties of the algorithm are illustrated in a numerical case study