Leaky Forcing in Graphs for Resilient Controllability in Networks

Abstract

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.