Asymptotic Analysis for Greedy Initialization of Threshold-Based Distributed Optimization of Persistent Monitoring on Graphs
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We consider the optimal multi-agent persistent monitoring problem defined for a team of agents on a set of nodes (targets) interconnected according to a fixed graph topology. The objective is to minimize a measure of mean overall node state uncertainty evaluated over a finite time interval. In prior work, a class of distributed threshold-based parametric controllers has been proposed where agent dwell times at nodes and transitions from one node to the next are controlled by enforcing thresholds on the respective node uncertainties. Under such a threshold policy, on-line gradient-based techniques (such as the Infinitesimal Perturbation Analysis (IPA)) are then used to determine optimal threshold values. However, due to the non-convexity of the problem, this approach leads to often poor local optima highly dependent on the initial thresholds used. To overcome this initialization challenge, in this paper, the asymptotic steady-state behavior of the agent-target system is extensively analyzed. Based on the obtained theoretical results, a computationally efficient off-line greedy technique is developed to systematically generate initial thresholds. Extensive numerical results show that the initial thresholds provided by this greedy technique are almost immediately (locally) optimal or quickly lead to optimal values. In all cases, they perform significantly better than the locally optimal solutions known to date.
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