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This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing those edges/links has at least the same network controllability as the original network while assuming the same set of input/leader vertices. We consider the strong structural controllability (SSC) in our work, which is useful but computationally challenging. Thus, we utilize two lower bounds on the network’s SSC based on the zero forcing notion and graph distances. We provide algorithms to compute controllability backbones while preserving these lower bounds. We thoroughly analyze the proposed algorithms and compute the number of edges in the controllability backbones. Finally, we compare and numerically evaluate our methods on random graphs.
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This content will become publicly available on March 1, 2026
Leaky Forcing in Graphs for Resilient Controllability in Networks
In this article, the author studies resilient strong structural controllability (SSC) in networks with misbehaving agents and edges. The author considers various misbehavior models and identifies the set of input agents offering resilience against such disruptions. The author's approach leverages a graph-based characterization of SSC, utilizing the concept of zero forcing in graphs. Specifically, the author examines three misbehavior models that disrupt the zero forcing process and compromise network SSC. The author then characterizes a leader set that guarantees SSC despite misbehaving nodes and edges, utilizing the concept of leaky forcing—a variation of zero forcing in graphs. The author's main finding reveals that resilience against one misbehavior model inherently provides resilience against others, thus simplifying the design process. Furthermore, the author explores combining multiple networks by augmenting edges between their nodes to achieve SSC in the combined network using a reduced leader set compared to the leader sets of individual networks. The author analyzes the tradeoff between added edges and leader set size in the resulting combined graph. Finally, the author discusses computational aspects and provides numerical evaluations to demonstrate the effectiveness of the author's approach.
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- Award ID(s):
- 2325416
- PAR ID:
- 10626552
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Control of Network Systems
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2372-2533
- Page Range / eLocation ID:
- 190 to 201
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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