4 research outputs found
Real-valued average consensus over noisy quantized channels
This paper concerns the average consensus problem
with the constraint of quantized communication between
nodes. A broad class of algorithms is analyzed, in which the
transmission strategy, which decides what value to communicate
to the neighbours, can include various kinds of rounding, probabilistic
quantization, and bounded noise. The arbitrariness
of the transmission strategy is compensated by a feedback
mechanism which can be interpreted as a self-inhibitory action.
The result is that the average of the nodes state is not conserved
across iterations, and the nodes do not converge to a consensus;
however, we show that both errors can be made as small
as desired. Bounds on these quantities involve the spectral
properties of the graph and can be proved by employing
elementary techniques of LTI systems analysis
Design and Analysis of Distributed Averaging with Quantized Communication
Consider a network whose nodes have some initial values, and it is desired to
design an algorithm that builds on neighbor to neighbor interactions with the
ultimate goal of convergence to the average of all initial node values or to
some value close to that average. Such an algorithm is called generically
"distributed averaging," and our goal in this paper is to study the performance
of a subclass of deterministic distributed averaging algorithms where the
information exchange between neighboring nodes (agents) is subject to uniform
quantization. With such quantization, convergence to the precise average cannot
be achieved in general, but the convergence would be to some value close to it,
called quantized consensus. Using Lyapunov stability analysis, we characterize
the convergence properties of the resulting nonlinear quantized system. We show
that in finite time and depending on initial conditions, the algorithm will
either cause all agents to reach a quantized consensus where the consensus
value is the largest quantized value not greater than the average of their
initial values, or will lead all variables to cycle in a small neighborhood
around the average. In the latter case, we identify tight bounds for the size
of the neighborhood and we further show that the error can be made arbitrarily
small by adjusting the algorithm's parameters in a distributed manner
Coordination of passive systems under quantized measurements
In this paper we investigate a passivity approach to collective coordination
and synchronization problems in the presence of quantized measurements and show
that coordination tasks can be achieved in a practical sense for a large class
of passive systems.Comment: 40 pages, 1 figure, submitted to journal, second round of revie