Before revision: In this paper, we develop the notion of controllability for uniform hypergraphs via tensor algebra and the theory of polynomial control . We propose a tensor-based multilinear system representation to characterize the multidimensional state dynamics of uniform hypergraphs , and derive a Kalman-rank-like condition to identify the minimum number of driver vertices in order to achieve full control of the whole hypergraph.
After revision: In this paper, we develop the notion of controllability for uniform hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear system representation to characterize the multidimensional state dynamics of uniform hypergraphs , and derive a Kalman-rank-like condition to identify the minimum number of driver vertices in order to achieve full control of the whole hypergraph.