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We consider the optimal multi-agent persistent monitoring problem defined bya team of cooperating agents visiting a set of nodes (targets) on a graph withthe objective of minimizing a measure of overall node state uncertainty. Thesolution to this problem involves agent trajectories defined both by thesequence of nodes to be visited by each agent and the amount of time spent ateach node. Since such optimal trajectories are generally intractable, wepropose a class of distributed threshold-based parametric controllers throughwhich agent transitions from one node to the next are controlled by thresholdparameters on the node uncertainty states. The resulting behavior of theagent-target system can be described by a hybrid dynamic system. This enablesthe use of Infinitesimal Perturbation Analysis (IPA) to determine on line(locally) optimal threshold parameters through gradient descent methods andthus obtain optimal controllers within this family of threshold-based policies.We further show that in a single-agent case the IPA gradient is monotonic,which implies a simple structure whereby an agent visiting a node should reducethe uncertainty state to zero before moving to the next node. Simulationexamples are included to illustrate our results and compare them to optimalsolutions derived through dynamic programming when this is possible.

Optimal Threshold-Based Control Policies for Persistent Monitoring on Graphs