  In this paper we study an infinite-horizon persistent monitoring problem in a
two-dimensional mission space containing a finite number of statically placed
targets, at each of which we assume a constant rate of uncertainty
accumulation. Equipped with a sensor of finite range, the agent is capable of
reducing the uncertainty of nearby targets. We derive a steady-state minimum
time periodic trajectory over which each of the target uncertainties is driven
down to zero during each visit. A hierarchical decomposition leads to purely
local optimal control problems, coupled via boundary conditions. We optimize
both the local trajectory segments as well as the boundary conditions in an
on-line bilevel optimization scheme.
