Pinning Control of Hypergraphs

Abstract

A standard assumption in control of network dynamical systems is that its nodes interact through pairwise interactions, which can be described by means of a directed graph. However, in several contexts, multibody, directed interactions may occur, thereby requiring the use of directed hypergraphs rather then digraphs. For the first time, we propose a strategy, inspired by the classic pinning control on graphs, that is tailored for controlling network systems coupled through a directed hypergraph. By drawing an analogy with signed graphs, we provide sufficient conditions for controlling the network onto the desired trajectory provided by the pinner, and a dedicated algorithm to design the control hyperedges.

Synchronization on higher-order networks

“…Node importance based on pinning control has also been developed [58]. Recent works on pinning control of higher-order networks [26,59,60] have mainly focused on the extension of traditional pinning control laws.…”

“…De Lellis et al [60] provided a different perspective of pinning control, by decomposing a directed hypergraph into a signed graph. The authors also proposed two algorithms, respectively computing if the system can be asymptotically controlled onto the target trajectory, and how to add pinners in a sequence.…”

Dynamics of diseases spreading on networks in the forms of reaction-diffusion systems

“…Due to the intricate topological complexity of higherorder networks, there is limited literature on their control, and the corresponding methodologies are not yet fully developed. Nevertheless, insights can be gleaned from classical theories of network attribute control on nodes and edges, such as pinning control [43], bang-bang control [44] Fig. 2: A 2-dimentional simplicial complex model comprising five 0-simplices (nodes), six 1-simplices (links), one 2-simplex.…”