  The objective is to design distributed coordination strategies for a network
of agents in a cyber-physical environment. In particular, we concentrate on the
rendez-vous of agents having double-integrator dynamics with the addition of a
damping term in the velocity dynamics. We start with distributed controllers
that solve the problem in continuous-time, and we then explain how to implement
these using event-based sampling. The idea is to define a triggering rule per
edge using a clock variable which only depends on the local variables. The
triggering laws are designed to compensate for the perturbative term introduced
by the sampling, a technique that reminds of Lyapunov-based control redesign.
We first present an event-triggered solution which requires continuous
measurement of the relative position and we then explain how to convert it to a
self-triggered policy. The latter only requires the measurements of the
relative position and velocity at the last transmission instants, which is
useful to reduce both the communication and the computation costs. The
strategies guarantee the existence of a uniform minimum amount of times between
any two edge events. The analysis is carried out using an invariance principle
for hybrid systems.
