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

Abstract

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 input-output 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.