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Controllability of Markovian jump Boolean control networks. (English) Zbl 1429.93040

Summary: In this paper, controllability of Markovian jump Boolean control networks (MJBCNs) is studied via semi-tensor product of matrices. First, based on the algebraic expression of the considered Boolean control networks, a necessary and sufficient condition for controllability is presented by iteration equations, which however may lead to high-dimensional matrices. To avoid having such matrices, a new matrix is defined and applied to derive another equivalent condition to verify controllability of MJBCNs. Moreover, a maximum principle of MJBCNs is established to further study the minimal controllable time. Finally, two examples are presented to illustrate the obtained results.

MSC:

93B05 Controllability
93E03 Stochastic systems in control theory (general)
93C29 Boolean control/observation systems
93B70 Networked control
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