Set reachability and observability of probabilistic Boolean networks
| Autor: | Rongpei Zhou, Weihua Gui, Yuqian Guo |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Reachability problem Computer science 020208 electrical & electronic engineering Probabilistic logic 02 engineering and technology Set (abstract data type) 020901 industrial engineering & automation Control and Systems Engineering Reachability 0202 electrical engineering electronic engineering information engineering Graph (abstract data type) Observability Electrical and Electronic Engineering Invariant (mathematics) Dynamical system (definition) Algorithm |
| Zdroj: | Automatica. 106:230-241 |
| ISSN: | 0005-1098 |
| DOI: | 10.1016/j.automatica.2019.05.021 |
| Popis: | In this paper, the set reachability and observability of probabilistic Boolean networks (PBNs) are investigated. Using a parallel extension technique, we proved that the observability problem of a PBN can be recast as a set reachability problem of an interconnected PBN. For set reachability analysis, we designed a random logic dynamical system (RLDS) from the PBN under consideration by reconstructing the state transfer graph (STG). We proved that, for a PBN, a target subset is reachable from an initial subset if and only if all solutions to the corresponding RLDS starting from the initial subset converge to the zero state. Based on the STG reconstruction technique and using the largest invariant subset algorithm, the necessary and sufficient conditions for finite-time set reachability with probability one and asymptotical set reachability in distribution were obtained. All the results are expressed in terms of the transition probability matrix between non-zero states of the RLDS. Further, the results related to set reachability were applied to the observability problem of PBNs. The necessary and sufficient conditions for finite-time observability with probability one and asymptotical observability in distribution were obtained. Finally, examples were presented to illustrate the effectiveness of the proposed method. |
| Databáze: | OpenAIRE |
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