An Improved Criterion for Controllability of Boolean Control Networks

This paper tackles the controllability problem of Boolean control networks (BCNs). By resorting to the semi-tensor product technique and the Warshall algorithm, several improved novel reachability and controllability criteria are obtained for the BCNs. Through constructing a sequence of rigorous Boolean matrices, controllability matrix of the considered BCNs is derived iteratively. It is worth pointing out that the proposed method has lower computational complexity, and thus facilitates the reachability and controllability analysis for BCNs. In addition, the issue concerning controllability of BCNs with undesirable interior states is investigated by checking a set of designated Boolean matrices. Finally, to test the effectiveness of the obtained theoretical results, a genetic network model known as the $\lambda$ switch is used as an example for numerical simulation.

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