In this paper, we consider the problem of driving a group of agents communicating through an undirected and weighted network towards a consensus point. We assume that agents obey to double-integrator dynamics and study decentralized control schemes for consensus of the position variables. In particular we revisit control policies proposed in (Xie and Wang, 2007) and (Ren and Atkins, 2005) in the unified framework of Partial difference Equations over graphs and highlight the link between the closed-loop system dynamics and the damped wave equation describing the motion of a free elastic beam.
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