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We investigate the problem of persistently monitoring a finite set of targetswith internal states that evolve with linear stochastic dynamics using a finiteset of mobile agents. We approach the problem from the infinite-horizonperspective, looking for periodic movement schedules for the agents. Underlinear dynamics and some standard assumptions on the noise distribution, theoptimal estimator is a Kalman-Bucy filter and the mean estimation error is afunction of its covariance matrix, which evolves as a differential Riccatiequation. It is shown that when the agents are constrained to move only over aline and they can see at most one target at a time, the movement policy thatminimizes the mean estimation error over time is such that the agent is alwayseither moving with maximum speed or dwelling at a fixed position. This type oftrajectory can be fully defined by a finite set of parameters. For periodictrajectories, under some observability conditions, the estimation errorconverges to a steady state condition and the stochastic gradient estimate ofthe cost with respect to the trajectory parameters of each agent and the globalperiod can be explicitly computed using Infinitesimal Perturbation Analysis. Agradient-descent approach is used to compute locally optimal parameters. Thisapproach allows us to deal with a very long persistent monitoring horizon usinga small number of parameters.

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