Optimal Periodic Multi-Agent Persistent Monitoring of a Finite Set of Targets with Uncertain States

Abstract

We investigate the problem of persistently monitoring a finite set of targets with internal states that evolve with linear stochastic dynamics using a finite set of mobile agents. We approach the problem from the infinite-horizon perspective, looking for periodic movement schedules for the agents. Under linear dynamics and some standard assumptions on the noise distribution, the optimal estimator is a Kalman-Bucy filter. It is shown that when the agents are constrained to move only over a line and that they can see at most one target at a time, the optimal movement policy is such that the agent is always either moving with maximum speed or dwelling at a fixed position. Periodic trajectories of this form admit finite parameterization, and we show how to compute a stochastic gradient estimate of the performance with respect to the parameters that define the trajectory using Infinitesimal Perturbation Analysis. A gradient-descent scheme is used to compute locally optimal parameters. This approach allows us to deal with a very long persistent monitoring horizon using a small number of parameters.