Eigen-Analysis of Multi-Agent Systems and Large Scale Systems Using Data Driven and Machine Learning Algorithms

Eigenvalue analysis is central in stability analysis and control design of linear
dynamic systems. While eigen-analysis is a standard tool, determining eigenvalues of
multi-agent systems and/or interconnected dynamical systems remains challenging
due to the sheer size of such systems, changes of their topology, and limited information about subsystems’ dynamics. In this chapter, a set of scalable, data-driven estimation and machine learning algorithms are presented to determine eigenvalue(s) and in turn stability of such large-scale complex systems. We begin with distributed algorithms that estimate all the eigenvalues of multi-agent cooperative systems, where their subsystems are modeled as a single integrator and interconnected by local communication networks. The algorithms are then extended to the data-driven version that estimate the dominant eigenvalues of large-scale interconnected systems with unknown dynamical model. Subsequently, we study input-output stability of subsystems and extend eigen-analysis to investigation of passivity shortage using the inputoutput data. This analysis is then further extended to machine learning algorithms by which stability properties of unknown subsystems can be learned. These results are illustrated by examples.