Control design for output tracking of delayed Boolean control networks

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Abstract

This paper investigates the output tracking control of delayed Boolean control networks (DBCNs) by using the algebraic state space representation method. Firstly, the output tracking control problem of DBCNs is formulated, and the dynamics of DBCNs is converted into an equivalent algebraic form. Secondly, based on the algebraic form and controllability of DBCNs, a necessary and sufficient condition is presented for the output tracking control of DBCNs without state constraints. Thirdly, a necessary and sufficient condition is presented for the output tracking control of DBCNs with state constraints by constructing a constrained reachability matrix. The study of an illustrative example shows the effectiveness of the obtained new results.

Keywords

Boolean control network
Output tracking
Time delay
State constraints
Semi-tensor product of matrices

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The research was supported by the National Natural Science Foundation of China under grants 61374065, 61503225 and 61673247, the Research Fund for the Taishan Scholar Project of Shandong Province, the Natural Science Foundation of Shandong Province under grant ZR2015FQ003, the Natural Science Fund for Distinguished Young Scholars of Shandong Province under grant JQ201613, and the Research Fund for Excellent Youth Scholars of Shandong Province under grant ZR2016JL024.