350 research outputs found
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
Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks
We study nonconvex distributed optimization in multiagent networks where the
communications between nodes is modeled as a time-varying sequence of arbitrary
digraphs. We introduce a novel broadcast-based distributed algorithmic
framework for the (constrained) minimization of the sum of a smooth (possibly
nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a
convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually
employed to enforce some structure in the solution, typically sparsity. The
proposed method hinges on Successive Convex Approximation (SCA) techniques
coupled with i) a tracking mechanism instrumental to locally estimate the
gradients of agents' cost functions; and ii) a novel broadcast protocol to
disseminate information and distribute the computation among the agents.
Asymptotic convergence to stationary solutions is established. A key feature of
the proposed algorithm is that it neither requires the double-stochasticity of
the consensus matrices (but only column stochasticity) nor the knowledge of the
graph sequence to implement. To the best of our knowledge, the proposed
framework is the first broadcast-based distributed algorithm for convex and
nonconvex constrained optimization over arbitrary, time-varying digraphs.
Numerical results show that our algorithm outperforms current schemes on both
convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual
Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA,
US
Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication
This paper proposes a novel class of distributed continuous-time coordination
algorithms to solve network optimization problems whose cost function is a sum
of local cost functions associated to the individual agents. We establish the
exponential convergence of the proposed algorithm under (i) strongly connected
and weight-balanced digraph topologies when the local costs are strongly convex
with globally Lipschitz gradients, and (ii) connected graph topologies when the
local costs are strongly convex with locally Lipschitz gradients. When the
local cost functions are convex and the global cost function is strictly
convex, we establish asymptotic convergence under connected graph topologies.
We also characterize the algorithm's correctness under time-varying interaction
topologies and study its privacy preservation properties. Motivated by
practical considerations, we analyze the algorithm implementation with
discrete-time communication. We provide an upper bound on the stepsize that
guarantees exponential convergence over connected graphs for implementations
with periodic communication. Building on this result, we design a
provably-correct centralized event-triggered communication scheme that is free
of Zeno behavior. Finally, we develop a distributed, asynchronous
event-triggered communication scheme that is also free of Zeno with asymptotic
convergence guarantees. Several simulations illustrate our results.Comment: 12 page
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