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SCIENCE CHINA Information Sciences, Volume 61, Issue 9: 092201(2018) https://doi.org/10.1007/s11432-017-9135-4

Observability of Boolean control networks

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  • ReceivedMar 16, 2017
  • AcceptedMay 16, 2017
  • PublishedOct 26, 2017

Abstract

We show some new results on the observability of Boolean control networks (BCNs). First, to study the observability, we combine two BCNs with the same transition matrix into a new BCN. Then, we propose the concept of a reachable set that results in a given set of initial states, and we derive four additional necessary and sufficient conditions for the observability of BCNs. In addition, we present an algoriTheoRemark and construct an observability graph to determine the observability of BCNs. Finally, we illustrate the obtained results using three numerical examples.


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  • Figure 1

    Row index of the column vector $\tilde{R}_k({B})$. Each point is the row index of $\tilde{R}_k({B})$. It holds that $\tilde{R}_0({B})~\subset~\tilde{R}_1({B})=\tilde{R}_2({B})={\tilde{C}}$.

  • Figure 2

    (Color online) The observability graph of the considered BCN. $0$ is a virtual node, green circles denote the initial distinguishable states, and blue circles denote otherwise. For simplicity, number $i$ in each circle denotes the node $\delta_{16}^i$, and the weight $j$ beside each edge denotes the weight $\delta_2^j$ of the edge.

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