Controllability Analysis and Control Design for Switched Boolean Networks with State and Input Constraints

This paper investigates the controllability analysis and the control design for switched Boolean networks (SBNs) with state and input constraints by using the semi-tensor product method and presents a number of new results on their controllability, optimal control, and stabilization. First, the constrained incidence matrix is proposed for SBNs, based on which several necessary and sufficient conditions are obtained for the controllability. Second, using the results on the controllability, two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed/designed shortest termination time. Third, the constrained SBN is converted to an equivalent unconstrained one, based on which some necessary and sufficient conditions are presented for the stabilization of the constrained SBN with open-loop and closed-loop controls, respectively. Finally, a practical example of the apoptosis network is studied by using the new results obtained in this paper. The s...

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