Multi-Agent Infinite Horizon Persistent Monitoring of Targets with Uncertain States in Multi-Dimensional Environments

This paper investigates the problem of persistent monitoring, where a finite set of mobile agents persistently visits a finite set of targets in a multi-dimensional environment. The agents must estimate the targets’ internal states and the goal is to minimize the mean squared estimation error over time. The internal states of the targets evolve with linear stochastic dynamics and thus the optimal estimator is a Kalman-Bucy Filter. We constrain the trajectories of the agents to be periodic and represented by a truncated Fourier series. Taking advantage of the periodic nature of this solution, we define the infinite horizon version of the problem and explore the property that the mean estimation squared error converges to a limit cycle. We present a technique to compute online the gradient of the steady state mean estimation error of the targets’ states with respect to the parameters defining the trajectories and use a gradient descent scheme to obtain locally optimal movement schedules. This scheme allows us to address the infinite horizon problem with only a small number of parameters to be optimized.