257,567 research outputs found
Scheduling for finite time consensus
We study the problem of link scheduling for
discrete-time agents to achieve average consensus in finite
time under communication constraints. We provide necessary
and sufficient conditions under which finite time consensus is
possible. Furthermore, we prove bounds on the consensus time
and exhibit provably optimal communication policies. We also
discuss the dual problem of designing communication schedules
given a fixed consensus-time requirement
Sensor Networks with Random Links: Topology Design for Distributed Consensus
In a sensor network, in practice, the communication among sensors is subject
to:(1) errors or failures at random times; (3) costs; and(2) constraints since
sensors and networks operate under scarce resources, such as power, data rate,
or communication. The signal-to-noise ratio (SNR) is usually a main factor in
determining the probability of error (or of communication failure) in a link.
These probabilities are then a proxy for the SNR under which the links operate.
The paper studies the problem of designing the topology, i.e., assigning the
probabilities of reliable communication among sensors (or of link failures) to
maximize the rate of convergence of average consensus, when the link
communication costs are taken into account, and there is an overall
communication budget constraint. To consider this problem, we address a number
of preliminary issues: (1) model the network as a random topology; (2)
establish necessary and sufficient conditions for mean square sense (mss) and
almost sure (a.s.) convergence of average consensus when network links fail;
and, in particular, (3) show that a necessary and sufficient condition for both
mss and a.s. convergence is for the algebraic connectivity of the mean graph
describing the network topology to be strictly positive. With these results, we
formulate topology design, subject to random link failures and to a
communication cost constraint, as a constrained convex optimization problem to
which we apply semidefinite programming techniques. We show by an extensive
numerical study that the optimal design improves significantly the convergence
speed of the consensus algorithm and can achieve the asymptotic performance of
a non-random network at a fraction of the communication cost.Comment: Submitted to IEEE Transaction
Distributed Weight Selection in Consensus Protocols by Schatten Norm Minimization
In average consensus protocols, nodes in a network perform an iterative
weighted average of their estimates and those of their neighbors. The protocol
converges to the average of initial estimates of all nodes found in the
network. The speed of convergence of average consensus protocols depends on the
weights selected on links (to neighbors). We address in this paper how to
select the weights in a given network in order to have a fast speed of
convergence for these protocols. We approximate the problem of optimal weight
selection by the minimization of the Schatten p-norm of a matrix with some
constraints related to the connectivity of the underlying network. We then
provide a totally distributed gradient method to solve the Schatten norm
optimization problem. By tuning the parameter p in our proposed minimization,
we can simply trade-off the quality of the solution (i.e. the speed of
convergence) for communication/computation requirements (in terms of number of
messages exchanged and volume of data processed). Simulation results show that
our approach provides very good performance already for values of p that only
needs limited information exchange. The weight optimization iterative procedure
can also run in parallel with the consensus protocol and form a joint
consensus-optimization procedure.Comment: N° RR-8078 (2012
A Consensus Approach to Distributed Convex Optimization in Multi-Agent Systems
In this thesis we address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where a network of agents, each endowed with local private convex cost and subject to communication constraints, wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proven, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We consider both a scalar and a multidimensional scenario of the Synchronous Newton-Raphson Consensus, proposing some alternative strategies which trade-off communication and computational requirements with convergence speed. We provide analytical proofs of convergence and we show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers, the Distributed Subgradient Method and Distributed Control Method.
Moreover, we consider the convergence rates of the Synchronous Newton-Raphson Consensus and the Gradient Descent Consensus under the simplificative assumption of quadratic local cost functions. We derive sufficient conditions which guarantee the convergence of the algorithms. From these conditions we then obtain closed form expressions that can be used to tune the parameters for maximizing the rate of convergence. Despite these formulas have been derived under quadratic local cost functions assumptions, they can be used as rules-of-thumb for tuning the parameters of the algorithms.
Finally, we propose an asynchronous version of the Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. Again, we analytically prove that under some assumptions it shows either local or global convergence properties. Through numerical simulations we corroborate these results and we compare the performance of the Asynchronous Newton-Raphson Consensus with other distributed optimization methods
Distributed Random Convex Programming via Constraints Consensus
This paper discusses distributed approaches for the solution of random convex
programs (RCP). RCPs are convex optimization problems with a (usually large)
number N of randomly extracted constraints; they arise in several applicative
areas, especially in the context of decision under uncertainty, see [2],[3]. We
here consider a setup in which instances of the random constraints (the
scenario) are not held by a single centralized processing unit, but are
distributed among different nodes of a network. Each node "sees" only a small
subset of the constraints, and may communicate with neighbors. The objective is
to make all nodes converge to the same solution as the centralized RCP problem.
To this end, we develop two distributed algorithms that are variants of the
constraints consensus algorithm [4],[5]: the active constraints consensus (ACC)
algorithm, and the vertex constraints consensus (VCC) algorithm. We show that
the ACC algorithm computes the overall optimal solution in finite time, and
with almost surely bounded communication at each iteration. The VCC algorithm
is instead tailored for the special case in which the constraint functions are
convex also w.r.t. the uncertain parameters, and it computes the solution in a
number of iterations bounded by the diameter of the communication graph. We
further devise a variant of the VCC algorithm, namely quantized vertex
constraints consensus (qVCC), to cope with the case in which communication
bandwidth among processors is bounded. We discuss several applications of the
proposed distributed techniques, including estimation, classification, and
random model predictive control, and we present a numerical analysis of the
performance of the proposed methods. As a complementary numerical result, we
show that the parallel computation of the scenario solution using ACC algorithm
significantly outperforms its centralized equivalent
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