  We develop a hybrid system model to describe the behavior of multiple agents
cooperatively solving an optimal coverage problem under energy depletion and
repletion constraints. The model captures the controlled switching of agents
between coverage (when energy is depleted) and battery charging (when energy is
replenished) modes. It guarantees the feasibility of the coverage problem by
defining a guard function on each agent's battery level to prevent it from
dying on its way to a charging station. The charging station plays the role of
a centralized scheduler to solve the contention problem of agents competing for
the only charging resource in the mission space. The optimal coverage problem
is transformed into a parametric optimization problem to determine an optimal
recharging policy. This problem is solved through the use of Infinitesimal
Perturbation Analysis (IPA), with simulation results showing that a full
recharging policy is optimal.
