Further results on dynamic-algebraic Boolean control networks

Abstract

Restricted coordinate transformation, controllability, observability and topological structures of dynamic-algebraic Boolean control networks are investigated under an assumption. Specifically, given the input-state at some point, assume that the subsequent state is certain or does not exist. First, the system can be expressed in a new form after numbering the elements in admissible set. Then, restricted coordinate transformation is raised, which allows the dimension of new coordinate frame to be different from that of the original one. The system after restricted coordinate transformation is derived in the proposed form. Afterwards, three types of incidence matrices are constructed and the results of controllability, observability and topological structures are obtained. Finally, two practical examples are shown to demonstrate the theory in this paper.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61773371).

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Correspondence to Jun-E. Feng.

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Wang, S., Feng, JE., Yu, Y. et al. Further results on dynamic-algebraic Boolean control networks. Sci. China Inf. Sci. 62, 12208 (2019). https://doi.org/10.1007/s11432-018-9447-4

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Keywords

  • controllability
  • dynamic-algebraic Boolean control network
  • fixed point and cycle
  • observability
  • restricted coordinate transformation