Integrating a PCA Learning Algorithm with the SUSD Strategy for a Collective Source Seeking Behavior

A challenging requirement of most of the existing swarm distributed source seeking strategies is the knowledge of the gradient of the field or communication of measurements. Yet, in this paper we integrate a PCA unsupervised learning algorithm with the Speeding-Up and Slowing-Down (SUSD) strategy to perform source seeking in a 2-dimensional space without any explicit gradient estimation and without sharing field measurements or components of body frame. The strategy scales to any arbitrary connected undirected networks. We formulate a singular perturbation problem and provide stability analysis for the case of complete networks. We demonstrate the efficiency of the proposed technique through a simulated source seeking behavior in a 2-dimensional space.