Partitioning and Observability in Linear Systems via Submodular Optimization
For control engineers dealing with large-scale systems, this work provides a scalable partitioning method with theoretical guarantees on observability, addressing an open problem.
The paper addresses the problem of partitioning large-scale linear dynamic networks to enable decentralized control while maximizing observability, and shows it can be formulated as submodular optimization. Theoretical bounds compare observability metrics between original and partitioned networks, validated on networks of varying sizes.
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.