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2020, Volume 21, Issue 2

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Frontiers of Information Technology & Electronic Engineering >> 2020, Volume 21, Issue 2 doi: 10.1631/FITEE.1900447

Bisimulation-based stabilization of probabilisticBoolean control networkswith state feedback control

1. School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China
2. School of Mathematics, Southeast University, Nanjing 210096, China
3. Potsdam Institute for Climate Impact Research, Potsdam 14412, Germany
4. Department of Physics, Humboldt-Universität zu Berlin, Berlin 12489, Germany
5. 5Saratov State University, Saratov 410012, Russia

Available online: 2020-04-01
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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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