### Abstract

The stabilization of probabilistic Boolean networks with pinning control is investigated. Only a part of nodes are chosen to be controlled for the aim of high efficiency. Stabilization with probability one and stabilization in probability are respectively discussed. Since the probability of stabilization is not required to be strict one, stabilization in probability is a more practical extension of the former, which is also proven in this work. Stabilization with probability one needs the target state to be transferred to itself with 100% certainty, while stabilization in probability cannot even guarantee the existence of such a possibility. Thus, stabilization in probability is a different and challenging problem. Some necessary and sufficient conditions are proposed for both types of stabilization via the semi-tensor product of matrices. Based on them, approaches to controller design are also developed. Finally, illustrative examples are provided to demonstrate the effectiveness of the derived results.

Original language | English |
---|---|

Pages (from-to) | 205-217 |

Number of pages | 13 |

Journal | Information Sciences |

Volume | 510 |

DOIs | |

Publication status | Published - 2020 Feb 1 |

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### Keywords

- Pinning control
- Probabilistic Boolean network
- Stabilization in probability
- Stabilization with probability one

### ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Theoretical Computer Science
- Computer Science Applications
- Information Systems and Management
- Artificial Intelligence

### Cite this

*Information Sciences*,

*510*, 205-217. https://doi.org/10.1016/j.ins.2019.09.029

**Stabilization of probabilistic Boolean networks via pinning control strategy.** / Huang, Chi; Lu, Jianquan; Ho, Daniel W.C.; Zhai, Guisheng; Cao, Jinde.

Research output: Contribution to journal › Article

*Information Sciences*, vol. 510, pp. 205-217. https://doi.org/10.1016/j.ins.2019.09.029

}

TY - JOUR

T1 - Stabilization of probabilistic Boolean networks via pinning control strategy

AU - Huang, Chi

AU - Lu, Jianquan

AU - Ho, Daniel W.C.

AU - Zhai, Guisheng

AU - Cao, Jinde

PY - 2020/2/1

Y1 - 2020/2/1

N2 - The stabilization of probabilistic Boolean networks with pinning control is investigated. Only a part of nodes are chosen to be controlled for the aim of high efficiency. Stabilization with probability one and stabilization in probability are respectively discussed. Since the probability of stabilization is not required to be strict one, stabilization in probability is a more practical extension of the former, which is also proven in this work. Stabilization with probability one needs the target state to be transferred to itself with 100% certainty, while stabilization in probability cannot even guarantee the existence of such a possibility. Thus, stabilization in probability is a different and challenging problem. Some necessary and sufficient conditions are proposed for both types of stabilization via the semi-tensor product of matrices. Based on them, approaches to controller design are also developed. Finally, illustrative examples are provided to demonstrate the effectiveness of the derived results.

AB - The stabilization of probabilistic Boolean networks with pinning control is investigated. Only a part of nodes are chosen to be controlled for the aim of high efficiency. Stabilization with probability one and stabilization in probability are respectively discussed. Since the probability of stabilization is not required to be strict one, stabilization in probability is a more practical extension of the former, which is also proven in this work. Stabilization with probability one needs the target state to be transferred to itself with 100% certainty, while stabilization in probability cannot even guarantee the existence of such a possibility. Thus, stabilization in probability is a different and challenging problem. Some necessary and sufficient conditions are proposed for both types of stabilization via the semi-tensor product of matrices. Based on them, approaches to controller design are also developed. Finally, illustrative examples are provided to demonstrate the effectiveness of the derived results.

KW - Pinning control

KW - Probabilistic Boolean network

KW - Stabilization in probability

KW - Stabilization with probability one

UR - http://www.scopus.com/inward/record.url?scp=85072524176&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072524176&partnerID=8YFLogxK

U2 - 10.1016/j.ins.2019.09.029

DO - 10.1016/j.ins.2019.09.029

M3 - Article

AN - SCOPUS:85072524176

VL - 510

SP - 205

EP - 217

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

ER -