Stabilization of k-valued logical control networks by open-loop control via the reverse-transfer method

Abstract A reverse-transfer method is proposed to study the stabilization problem of k -valued logical control networks (LCNs). Main results consist of two parts. (1) Two necessary and sufficient stabilization conditions are derived for k -valued LCNs. The stabilization results are much superior to the existing relevant results in the literature. (2) Based on the above conditions, some algorithms for solving the open-loop stabilization problem of k -valued LCNs are developed. These algorithms cut useless control paths off as many as possible, which, compared with existing results, reduce the related computational cost markedly.

[1]  Ettore Fornasini,et al.  Output feedback stabilization of Boolean control networks , 2015, Autom..

[2]  Tamer Kahveci,et al.  Scalable Steady State Analysis of Boolean Biological Regulatory Networks , 2009, PloS one.

[3]  Jitao Sun,et al.  Stability and stabilization of multivalued logical networks , 2011 .

[4]  Yuzhen Wang,et al.  Output feedback stabilization control design for Boolean control networks , 2013, Autom..

[5]  E. Fornasini,et al.  Output feedback stabilization ofBoolean control networks ? , 2015 .

[6]  Daizhan Cheng,et al.  Algebraic Approach to Dynamics of Multivalued Networks , 2010, Int. J. Bifurc. Chaos.

[7]  Pan Wang,et al.  Set stability and set stabilization of Boolean control networks based on invariant subsets , 2015, Autom..

[8]  D. Cheng,et al.  Stability and stabilization of Boolean networks , 2011 .

[9]  Huaguang Zhang,et al.  Synchronization Analysis and Design of Coupled Boolean Networks Based on Periodic Switching Sequences , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Tianguang Chu,et al.  State Feedback Stabilization for Boolean Control Networks , 2013, IEEE Transactions on Automatic Control.

[11]  Daizhan Cheng,et al.  Modeling, Analysis and Control of Networked Evolutionary Games , 2015, IEEE Transactions on Automatic Control.

[12]  WangPan,et al.  Set stability and set stabilization of Boolean control networks based on invariant subsets , 2015 .

[13]  A. Adamatzky.  On dynamically non-trivial three-valued logics: oscillatory and bifurcatory species , 2003 .

[14]  Aurélien Naldi,et al.  Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle , 2006, ISMB.

[15]  Ettore Fornasini,et al.  On the periodic trajectories of Boolean control networks , 2013, Autom..

[16]  Daizhan Cheng,et al.  Optimal Control of Logical Control Networks , 2011, IEEE Transactions on Automatic Control.