Title: A singular perturbation approach to average consensus
algorithms

Abstract: In networked systems, the consensus objective consist in
reaching an agreement by all agents regarding a certain quantity of
interest.  A consensus algorithm is an interaction rule that specifies
the information exchange between each agent and its neighbors in order
to arrive to the desired agreement. One of the common consensus
problems is the average consensus where the agreement valye is the
average of a reference value at each agent. This talk describes a new
framework for devising average consensus algorithms using singularly
perturbed dynamical systems. The proposed algorithms work for networks
whose communication topologies are balanced and weakly-connected
directed graphs. The main characteristics of the resulted algorithms
are the following: 1) In the case of the dynamic average consensus,
the proposed algorithms do not need any knowledge about the dynamics
creating the inputs; to guarantee convergence, the only requirement on
the set of reference inputs involves continuous bounded derivatives,
up to (at most) the third derivative; 2) The exact rate of the
convergence of the algorithms can be assigned a priori, and is
independent of the graph topology; 3) The messages communicated among
the agents do not include the agreement state (i.e., the state
evolving towards the agreement), therefore, if a message is
intercepted, adversaries can not trivially learn about the agreement
state of the corresponding agent.