Partitioning and Observability in Linear Systems via Submodular Optimization

TL;DR

This paper proposes a scalable method for partitioning large linear systems to maximize subsystem observability, using submodular optimization, with theoretical bounds and case studies validating the approach.

Contribution

It introduces a novel submodular optimization framework for partitioning linear systems to enhance observability, addressing computational challenges and providing theoretical performance bounds.

Findings

Partitioning problem formulated as submodular maximization.

Theoretical bounds established for observability metrics post-partition.

Case studies confirm the effectiveness of the proposed method.

Abstract

Network partitioning has gained recent attention as a pathway to enable decentralized operation and control in large-scale systems. This paper addresses the interplay between partitioning, observability, and sensor placement (SP) in dynamic networks. The problem, being computationally intractable at scale, is a largely unexplored, open problem in the literature. To that end, the paper's objective is designing scalable partitioning of linear systems while maximizing observability metrics of the subsystems. We show that the partitioning problem can be posed as a submodular maximization problem -- and the SP problem can subsequently be solved over the partitioned network. Consequently, theoretical bounds are derived to compare observability metrics of the original network with those of the resulting partitions, highlighting the impact of partitioning on system observability. Case studies on networks of varying sizes corroborate the derived theoretical bounds.