A Lyapunov Redesign of Coordination Algorithms for Cyber-Physical Systems

We present an approach for the coordination of
a network of agents in a cyber-physical environment. The
agents’s dynamics are nonlinear, of arbitrary dimensions and
possibly heterogeneous. The objective is to design resource-aware
distributed control strategies to ensure a coordination task. In
particular, we aim at ensuring the convergence of the differences
between the agents’ output variables to a prescribed compact
set, hence covering rendez-vous and formation control as specific
scenarios. We develop event-based sampling strategies for that
purpose. Three scenarios are studied. We first focus on eventtriggered
control, in which case the agents continuously measure
the relative distances with their neighbours and only update their
control input at some time instants. This set-up is relevant to limit
changes in control signals and therefore to reduce the resources
usage of the actuators. A triggering rule is defined for each
edge using an auxiliary variable, whose dynamics only depends
on the local variables. We then explain how to derive timetriggered
and self-triggered distributed controllers. These control
strategies collect measurements and update the control inputs
only at some discrete time instants, which save communication
and computation resources. The existence of a uniform minimum
amount of times between any two edge events is guaranteed in all
cases, thus ruling out Zeno phenomenon. The analysis is carried
out within the framework of hybrid systems and an invariance
principle is used to conclude about coordination.