Pinning Asymptotic Stabilization of Probabilistic Boolean Networks: A Digraph 
Approach

Chen, Bingquan; Cao, Jinde; Gorbachev, Sergey; Liu, Yang; Kurths, Jürgen

doi:10.1109/TCNS.2022.3141023

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Pinning Asymptotic Stabilization of Probabilistic Boolean Networks: A Digraph Approach

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Chen, Bingquan
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Cao, Jinde
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Gorbachev, Sergey
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Liu, Yang
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Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

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Chen, B., Cao, J., Gorbachev, S., Liu, Y., Kurths, J. (2022): Pinning Asymptotic Stabilization of Probabilistic Boolean Networks: A Digraph Approach. - IEEE Transactions on Control of Network Systems, 9, 3, 1251-1260.
https://doi.org/10.1109/TCNS.2022.3141023

Cite as: https://publications.pik-potsdam.de/pubman/item/item_27942

Abstract

This article investigates the pinning asymptotic stabilization of probabilistic Boolean networks (PBNs) by a digraph approach. In order to stabilize the PBN asymptotically, a mode-independent pinning control (MIPC) is designed to make the target state a fixed point, and transform the state transition digraph into one that has a spanning branching rooted at the target vertex. It is shown that if there is a mode-dependent pinning control that can asymptotically stabilize the PBN, then there must exist an MIPC that can do the same with fewer pinned nodes and control inputs. A necessary and sufficient condition is given to verify the feasibility of a set of pinned nodes based on an auxiliary digraph. Three algorithms are proposed to find a feasible set of pinned nodes with the minimum cardinality. The main results are extended to the case where the target is a limit cycle. Compared with the existing results, the total computational complexity of these algorithms is strongly reduced. The obtained results are applied to a numerical example and a cell apoptosis network.