  We propose an optimal control framework for persistent monitoring problems
where the objective is to control the movement of mobile nodes to minimize an
uncertainty metric in a given mission space. For multi agent in a
one-dimensional mission space, we show that the optimal solution is obtained in
terms of a sequence of switching locations and waiting time on these switching
points, thus reducing it to a parametric optimization problem. Using
Infinitesimal Perturbation Analysis (IPA) we obtain a complete solution through
a gradient-based algorithm. We also discuss a receding horizon controller which
is capable of obtaining a near-optimal solution on-the-fly.
