Realization of Boolean control networks

Authors:
Daizhan Cheng;Zhiqiang Li;Hongsheng Qi
Affiliations:
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

Based on the linear expression of the dynamics of Boolean networks, the coordinate transformation of Boolean variables is defined. It follows that the state space coordinate transformation for the dynamics of Boolean networks is revealed. Using it, the invariant subspace for a Boolean control network is defined. Then the structure of a Boolean control network is analyzed, and the controllable and observable normal forms and the Kalman decomposition form are presented. Finally the realization problem, including minimum realization, of Boolean control networks is investigated.