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Controllability of higher order Boolean control networks. (English) Zbl 1311.92083
Summary: Using the semi-tensor product method, this paper investigates the controllability of a \({\mu}\)th order Boolean control network. After a brief introduction on semi-tensor product of matrices to \({\mu}\)th order Boolean control networks, the controllability issue is studied. First, a systematic procedure to reconstruct the logical dynamic of a \({\mu}\)th order Boolean control network from its network transition matrix is presented for design purpose. Then, the controllability via two types of controls is considered. Necessary and sufficient conditions are provided for each case. The application of input-state incidence matrix to the controllability of \({\mu}\)th order Boolean control networks is studied. Finally, as an application, examples are given to illustrate the effectiveness of the obtained results.

MSC:
92C42 Systems biology, networks
93B05 Controllability
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