A Note on the Local Observability of Uniform Hypergraphs

ABSTRACT Hypergraphs generalize graphs in such a way that edges may connect any number of nodes. If all edges are adjacent to the same number of nodes, the hypergraph is called uniform. Thus, a graph is a 2‐uniform hypergraph. Each uniform hypergraph can be identified with an autonomous dynamical state‐space system, whose vector field is composed of homogenous polynomials. We consider the observability of dynamical systems, which possess this special structure. In control theory, the observability of a dynamical system asks for the possibility to reconstruct the systems state from an output trajectory, where the output is a projective measurement of the systems state. In addition, one can ask for the observable subspace of the state. Nonlinear systems, although observable at almost all points in the state space, may possess not‐locally observable ones. The existence and location of such states are important for observability analysis and observer design. Recently, the observability of these hypergraph systems has been studied for the general case. We apply an extended deterministic observability test to uniform hypergraphs and also compute the not‐observable states for different linear output maps. We are able to confirm the results of the recent study, at least for graphs with a small number of nodes, due to the computational complexity of our method. In addition, the not‐locally observable states are computed for different combinations of measured nodes.