2,936 research outputs found
The Most Exigent Eigenvalue: Guaranteeing Consensus under an Unknown Communication Topology and Time Delays
This document aims to answer the question of what is the minimum delay value
that guarantees convergence to consensus for a group of second order agents
operating under different protocols, provided that the communication topology
is connected but unknown. That is, for all the possible communication
topologies, which value of the delay guarantees stability? To answer this
question we revisit the concept of most exigent eigenvalue, applying it to two
different consensus protocols for agents driven by second order dynamics. We
show how the delay margin depends on the structure of the consensus protocol
and the communication topology, and arrive to a boundary that guarantees
consensus for any connected communication topology. The switching topologies
case is also studied. It is shown that for one protocol the stability of the
individual topologies is sufficient to guarantee consensus in the switching
case, whereas for the other one it is not
Fixed-time Distributed Optimization under Time-Varying Communication Topology
This paper presents a method to solve distributed optimization problem within
a fixed time over a time-varying communication topology. Each agent in the
network can access its private objective function, while exchange of local
information is permitted between the neighbors. This study investigates first
nonlinear protocol for achieving distributed optimization for time-varying
communication topology within a fixed time independent of the initial
conditions. For the case when the global objective function is strictly convex,
a second-order Hessian based approach is developed for achieving fixed-time
convergence. In the special case of strongly convex global objective function,
it is shown that the requirement to transmit Hessians can be relaxed and an
equivalent first-order method is developed for achieving fixed-time convergence
to global optimum. Results are further extended to the case where the
underlying team objective function, possibly non-convex, satisfies only the
Polyak-\L ojasiewicz (PL) inequality, which is a relaxation of strong
convexity.Comment: 25 page
Parameterized Verification of Safety Properties in Ad Hoc Network Protocols
We summarize the main results proved in recent work on the parameterized
verification of safety properties for ad hoc network protocols. We consider a
model in which the communication topology of a network is represented as a
graph. Nodes represent states of individual processes. Adjacent nodes represent
single-hop neighbors. Processes are finite state automata that communicate via
selective broadcast messages. Reception of a broadcast is restricted to
single-hop neighbors. For this model we consider a decision problem that can be
expressed as the verification of the existence of an initial topology in which
the execution of the protocol can lead to a configuration with at least one
node in a certain state. The decision problem is parametric both on the size
and on the form of the communication topology of the initial configurations. We
draw a complete picture of the decidability and complexity boundaries of this
problem according to various assumptions on the possible topologies.Comment: In Proceedings PACO 2011, arXiv:1108.145
Reconfiguration and Message Losses in Parameterized Broadcast Networks
Broadcast networks allow one to model networks of identical nodes communicating through message broadcasts. Their parameterized verification aims at proving a property holds for any number of nodes, under any communication topology, and on all possible executions. We focus on the coverability problem which dually asks whether there exists an execution that visits a configuration exhibiting some given state of the broadcast protocol. Coverability is known to be undecidable for static networks, i.e. when the number of nodes and communication topology is fixed along executions. In contrast, it is decidable in PTIME when the communication topology may change arbitrarily along executions, that is for reconfigurable networks. Surprisingly, no lower nor upper bounds on the minimal number of nodes, or the minimal length of covering execution in reconfigurable networks, appear in the literature.
In this paper we show tight bounds for cutoff and length, which happen to be linear and quadratic, respectively, in the number of states of the protocol. We also introduce an intermediary model with static communication topology and non-deterministic message losses upon sending. We show that the same tight bounds apply to lossy networks, although, reconfigurable executions may be linearly more succinct than lossy executions. Finally, we show NP-completeness for the natural optimisation problem associated with the cutoff
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