678 research outputs found

    On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

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    This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results

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

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    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

    Consensus with Linear Objective Maps

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    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

    Broadcast Gossip Algorithms for Consensus on Strongly Connected Digraphs

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    We study a general framework for broadcast gossip algorithms which use companion variables to solve the average consensus problem. Each node maintains an initial state and a companion variable. Iterative updates are performed asynchronously whereby one random node broadcasts its current state and companion variable and all other nodes receiving the broadcast update their state and companion variable. We provide conditions under which this scheme is guaranteed to converge to a consensus solution, where all nodes have the same limiting values, on any strongly connected directed graph. Under stronger conditions, which are reasonable when the underlying communication graph is undirected, we guarantee that the consensus value is equal to the average, both in expectation and in the mean-squared sense. Our analysis uses tools from non-negative matrix theory and perturbation theory. The perturbation results rely on a parameter being sufficiently small. We characterize the allowable upper bound as well as the optimal setting for the perturbation parameter as a function of the network topology, and this allows us to characterize the worst-case rate of convergence. Simulations illustrate that, in comparison to existing broadcast gossip algorithms, the approaches proposed in this paper have the advantage that they simultaneously can be guaranteed to converge to the average consensus and they converge in a small number of broadcasts.Comment: 30 pages, submitte
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