Abstract
This study is concerned with probabilistic Boolean control networks (PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed to lower computational complexity. To understand more on bisimulation relations between PBCNs, we resort to a powerful matrix manipulation called semi-tensor product (STP). Because stabilization of networks is of critical importance, the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable. Additionally, the transient periods (the maximum number of steps to implement stabilization) of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation. The results are then extended to the probabilistic Boolean networks.
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Contributions
Chi HUANG formulated the research goals. Yao CHEN and Nan JIANG proposed the method and obtained the final theorems. Jurgen KURTHS and Nan JIANG built the model for verification. Nan JIANG wrote the original draft. Nan JIANG, Chi HUANG, Yao CHEN, and Jurgen KURTHS revised and edited the final version.
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Nan JIANG, Chi HUANG, Yao CHEN, and Jurgen KURTHS declare that they have no conflict of interest.
Project supported by the National Natural Science Foundation of China (Nos. 61603268 and 61773319) and the Fundamental Research Funds for the Central Universities, China (No. JBK190502)
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Jiang, N., Huang, C., Chen, Y. et al. Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control. Front Inform Technol Electron Eng 21, 268–280 (2020). https://doi.org/10.1631/FITEE.1900447
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DOI: https://doi.org/10.1631/FITEE.1900447
Key words
- Probabilistic Boolean control network
- Bisimulation
- Stabilization with probability one
- State feedback control