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

Authors

Chen, Bingquan
External Organizations;

Cao, Jinde
External Organizations;

Gorbachev, Sergey
External Organizations;

Liu, Yang
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

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引用

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. doi:10.1109/TCNS.2022.3141023.

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

要旨

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.