Limits of Observability in Large-Scale Linear Networked Clocks

Abstract

Large-scale networks of undamped coupled oscillators represent both modern engineered systems and systems from the biological world. The neural network of the brain is a particular example of motivating interest. The degree to which tracking, predicting and controlling dynamics in such networks will be successful is conditional on observability. Observability is considered using large-scale networked clocks, a linearisation of networked oscillators, through the structure of the observability matrix using Vandermonde matrices. Observability is found to be particularly poor for these undamped networked clocks. This raises interesting challenges to elucidate sufficient information from these ne..