Controllability and observability of Boolean control networks

By DaiZhan Cheng, Hongsheng Qi. at - Automatisierungstechnik, 2009

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Modeling, Analysis and Control of Networked Evolutionary Games (2015, background): “) A B is the semi-tensor product (STP) of two matrices A and B. (Please refer to the Appendix for STP.”
Control Principles of Complex Networks (2015, background): “Necessary and sufficient conditions to assure controllability of Boolean networks can then be proved (Cheng and Qi, 2009).”
A Linear Representation of Dynamics of Boolean Networks (2010, background): “For instance, if , is a logical coordinate transformation, iff is nonsingular [9].”
Controllability of Boolean control networks via the Perron-Frobenius theory (2012, background): “Applying the algorithm described in Cheng and Qi (2009) yields the transition matrix L = [ e18 e 3 8 e 5 8 e 7 8 e 1 8 e 3 8 e 5 8 e 7 8 e 1 8 e 4 8 e 6 8 e 8 8 e 1 8 e 4 8 e 6 8 e 8 8 ] , (4) To demonstrate the equivalence of (2) and (3), consider for example the case x1(k) = x2(k) = x3(k) =…”
Controllability of Boolean control networks with impulsive effects and forbidden states (2014, background): “Controllability analysis in biological systems model using BCNs may reveal how the structure and organization of the systems guarantee the property of controllability (see [16, 17]).”