Observability Variation in Emergent Dynamics: A Study using Krylov Subspace-based Model Order Reduction

Large-scale self-organizing systems often exhibit emergent behaviors which manifest as reduced-order dynamics on a low-dimensional manifold with a dimension much smaller than that of the original state-space. The ability to influence such self-organizing systems in a meaningful manner relies on observing the resulting emergent behaviors. While prior research has examined observability-related concepts from the viewpoint of network structure and connectivity in multiagent system, there exist limited insights into macroscopic-scale observability, i.e. the ability to observe reduced-order states of self-organizing systems. In this work, the ability to perceive or observe emergent behaviors in complex systems has been studied, and the relationship between an observability metric and model orders has been presented. Krylov subspace-based methods have been used to perform model order reduction for nonlinear systems such as coupled Rössler systems and interconnected electrical circuits that exhibit low-manifold emergent behaviors. The resulting numerical simulations indicate that reduced-order models, which are representative of emergent phenomena, usually possess higher observability metrics.