Feedback Controller Design for the Synchronization of Boolean Control Networks

This brief investigates the partial and complete synchronization of two Boolean control networks (BCNs). Necessary and sufficient conditions for partial and complete synchronization are established by the algebraic representations of logical dynamics. An algorithm is obtained to construct the feedback controller that guarantees the synchronization of master and slave BCNs. Two biological examples are provided to illustrate the effectiveness of the obtained results.

[1]  Vreeswijk,et al.  Partial synchronization in populations of pulse-coupled oscillators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Nikolai F. Rulkov,et al.  Images of synchronized chaos: Experiments with circuits. , 1996, Chaos.

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

[4]  Yang Liu,et al.  Controllability of probabilistic Boolean control networks based on transition probability matrices , 2015, Autom..

[5]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Michael Margaliot,et al.  A Maximum Principle for Single-Input Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

[8]  Fangfei Li Synchronization of coupled large-scale Boolean networks. , 2014, Chaos.

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

[10]  Yiguang Hong,et al.  Solvability and control design for synchronization of Boolean networks , 2013, Journal of Systems Science and Complexity.

[11]  Jianquan Lu,et al.  Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks , 2014 .

[12]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[13]  Yuzhen Wang,et al.  Simultaneous stabilization for a set of Boolean control networks , 2013, Syst. Control. Lett..

[14]  D. Cheng,et al.  Analysis and control of Boolean networks: A semi-tensor product approach , 2010, 2009 7th Asian Control Conference.

[15]  Shouwei Zhao,et al.  A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization. , 2011, Chaos.

[16]  Tianguang Chu,et al.  Synchronization Design of Boolean Networks Via the Semi-Tensor Product Method , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Panos Louvieris,et al.  Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Jinde Cao,et al.  Synchronization in output-coupled temporal Boolean networks , 2014, Scientific Reports.

[19]  Jinde Cao,et al.  Synchronization in an Array of Output-Coupled Boolean Networks With Time Delay , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Peng Shi,et al.  Exponential Synchronization of Neural Networks With Discrete and Distributed Delays Under Time-Varying Sampling , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[21]  John Maloney,et al.  Finding Cycles in Synchronous Boolean Networks with Applications to Biochemical Systems , 2003, Int. J. Bifurc. Chaos.

[22]  Chu Tianguang,et al.  General synchronization of multi-valued logical networks , 2012, Proceedings of the 31st Chinese Control Conference.

[23]  Kunihiko Kaneko,et al.  Relevance of dynamic clustering to biological networks , 1993, chao-dyn/9311008.