Multiagent Persistent Monitoring of Targets with Uncertain States

We approach the problem of persistent monitoring of a finite set of fixed targets located in a one-dimensional environment with internal, linear, stochastic dynamics. Monitoring is performed by a set of agents with limited sensing range and range-dependent sensing quality. The optimal estimator of the target dynamics from the agent measurements is the Kalman-Bucy Filter. We formulate an optimal control problem to minimize the estimation error across all the targets as a function of the trajectories of the agents. Using Hamiltonian analysis, the structure of the optimal controller is defined and, given this structure, we reformulate the problem as a hybrid systems optimization problem. Using Infinitesimal Perturbation Analysis (IPA), stochastic gradient estimates of the hybrid system are computed and gradient descent is used in order to achieve a locally optimal solution.