Network Topology Identification using Supervised Pattern Recognition Neural Networks

This paper studies the network topology identification of multi-agent systems with single-integrator dynamics using supervised pattern recognition networks. We split the problem into two classes: (i) small-scale systems, and (ii) large-scale systems. In the small-scale case, we generate all connected (undirected) graphs. A finite family of vectors represent all possible initial conditions by gridding the interval 0 and 1 for each agent. The system responses for all graphs with all initial conditions are the training data for the supervised pattern recognition neural network. This network is successful in identification of the most connected node in up to nearly 99% of cases involving small-scale systems. We present the accuracy of the trained network for network topology identification with respect to grid space. Then, an algorithm predicated on the pattern recognition network, which is trained for a small-scale system, identifies the most connected node in largescale systems. Monte Carlo simulations estimate the accuracy of the algorithm. We also present the results for these simulations, which demonstrate that the algorithm succeeds in finding the most connected node in more than 60% of the test cases.