Asymptotic Analysis for Greedy Initialization of Threshold-Based Distributed Optimization of Persistent Monitoring on Graphs

TL;DR

This paper introduces an asymptotic analysis-based greedy method to improve the initialization of threshold parameters in distributed multi-agent persistent monitoring, significantly enhancing performance over existing local optima.

Contribution

It develops a novel off-line greedy technique using asymptotic analysis to generate effective initial thresholds for distributed control in persistent monitoring tasks.

Findings

Initial thresholds are nearly optimal or quickly become optimal.

The proposed method outperforms existing local optima.

Numerical results validate the efficiency and effectiveness of the approach.

Abstract

This paper considers the optimal multi-agent persistent monitoring problem defined for a team of agents on a set of nodes (targets) interconnected according to a fixed network topology. The aim is to control this team so as to minimize a measure of overall node state uncertainty evaluated over a finite time interval. A class of distributed threshold-based parametric controllers has been proposed in prior work to control agent dwell times at nodes and next-node destinations by enforcing thresholds on the respective node states. Under such a Threshold Control Policy (TCP), an on-line gradient technique was used to determine optimal threshold values. However, due to the non-convexity of the problem, this approach often leads to a poor local optima highly dependent on the initial thresholds used. To overcome this initialization challenge, we develop a computationally efficient off-line greedy technique based on the asymptotic analysis of the network system. This analysis is then used to generate a high-performing set of initial thresholds. Extensive numerical results show that such initial thresholds 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.