  We address the issue of identifying conditions under which the centralized
solution to the optimal multi-agent persistent monitoring problem can be
recovered in a decentralized event-driven manner. In this problem, multiple
agents interact with a finite number of targets and the objective is to control
their movement in order to minimize an uncertainty metric associated with the
targets. In a one-dimensional setting, it has been shown that the optimal
solution can be reduced to a simpler parametric optimization problem and that
the behavior of agents under optimal control is described by a hybrid system.
This hybrid system can be analyzed using Infinitesimal Perturbation Analysis
(IPA) to obtain a complete on-line solution through an event-driven centralized
gradient-based algorithm. We show that the IPA gradient can be recovered in a
distributed manner in which each agent optimizes its trajectory based on local
information, except for one event requiring communication from a non-neighbor
agent. Simulation examples are included to illustrate the effectiveness of this
"almost decentralized" algorithm and its fully decentralized counterpart where
the aforementioned non-local event is ignored.
