Robust Output Tracking of Boolean Control Networks over Finite Time

Yuan Zhao, Xiaoyu Zhao (), Shihua Fu and Jianwei Xia
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Yuan Zhao: Research Center of Semi-Tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng 252026, China
Xiaoyu Zhao: School of Mathematics, Shandong University, Jinan 250100, China
Shihua Fu: Research Center of Semi-Tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng 252026, China
Jianwei Xia: Research Center of Semi-Tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng 252026, China

Mathematics, 2022, vol. 10, issue 21, 1-15

Abstract: With an increase in tracking time, the operating cost of the controller will increase accordingly. Considering the biological applications of Boolean control networks (BCNs), it is necessary to study the control problem of BCNs over finite time. In this paper, we study the output tracking problem of a BCN with disturbance inputs in a given finite time. First, the logical form of BCNs is transformed into an algebraic form using the semi-tensor product (STP) method. Then, the robust output tracking problems of a reference output trajectory and the outputs of a reference system over finite time are transformed into the robust reachability problem of the BCNs. Based on the truth matrix technique, two necessary and sufficient conditions are provided for the trackability of the reference outputs over finite time. Moreover, two algorithms are proposed to design the controllers in the case of the traceable outputs. It should be pointed out that the truth matrix method we used here has some unique features, including its simple computation and concise expression. Finally, two illustrative examples are presented to demonstrate the results in this paper.

Keywords: Boolean control networks; robust output tracking; finite time; semi-tensor product; truth matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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