Sampled-data general partial synchronization of Boolean control networks

Abstract In this manuscript, the general partial synchronization of a type of drive-response Boolean control networks (BCNs) is proposed for the first time and is addressed by sampled-data feedback control (SDFC). Different from all previous synchronization in the field of BCNs, the general partial generalization requires that the total number of the synchronized nodes exactly maintains at a pre-special value after finite-time step, and it removes the requirement on the anticipated synchronized nodes. To begin with, we define the general partial synchronization of derive-response BCNs based on the Hamming distance of two Boolean vectors. Subsequently, by utilizing the semi-tensor product (STP) of matrices, we obtain a series of criteria for BCNs to achieve general partial synchronization by SDFC. Then, the corresponding SDFC strategy is designed, under which the considered BCNs achieve general partial synchronization. Finally, all the results are demonstrated by an illustrative numerical example.

[1]  James Lam,et al.  Static output-feedback stabilization with optimal L1-gain for positive linear systems , 2016, Autom..

[2]  Jinde Cao,et al.  Synchronization of Arbitrarily Switched Boolean Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[3]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[4]  Tielong Shen,et al.  Optimal control of Boolean control networks with average cost: A policy iteration approach , 2019, Autom..

[5]  Zhaoxu Yu,et al.  Anti-synchronization of two coupled Boolean networks , 2016, J. Frankl. Inst..

[6]  Jinde Cao,et al.  Sampled-Data Control for the Synchronization of Boolean Control Networks , 2019, IEEE Transactions on Cybernetics.

[7]  Jinling Liang,et al.  Local Synchronization of Interconnected Boolean Networks With Stochastic Disturbances , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Yuhu Wu,et al.  Monostability and Bistability of Boolean Networks Using Semitensor Products , 2019, IEEE Transactions on Control of Network Systems.

[9]  James Lam,et al.  State feedback H ∞ control of commensurate fractional-order systems , 2014, Int. J. Syst. Sci..

[10]  Damián H. Zanette,et al.  SYNCHRONIZATION OF STOCHASTICALLY COUPLED CELLULAR AUTOMATA , 1998 .

[11]  M. Ng,et al.  Control of Boolean networks: hardness results and algorithms for tree structured networks. , 2007, Journal of theoretical biology.

[12]  Tianguang Chu,et al.  Complete Synchronization of Boolean Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Jinde Cao,et al.  Stabilization of probabilistic Boolean networks via pinning control strategy , 2020, Inf. Sci..

[14]  Qiang Wei,et al.  Delay synchronization of temporal Boolean networks , 2016 .

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

[16]  Xueying Ding,et al.  Set stability of switched delayed logical networks with application to finite-field consensus , 2020, Autom..

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

[18]  L. Glass.  Synchronization and rhythmic processes in physiology , 2001, Nature.

[19]  Haitao Li,et al.  A Control Lyapunov Function Approach to Feedback Stabilization of Logical Control Networks , 2019, SIAM J. Control. Optim..

[20]  Jinde Cao,et al.  Sampled-Data State Feedback Stabilization of Boolean Control Networks , 2016, Neural Computation.

[21]  Hongwei Chen,et al.  Partial Synchronization of Interconnected Boolean Networks , 2017, IEEE Transactions on Cybernetics.

[22]  Jianquan Lu,et al.  Synchronization of drive-response Boolean control networks with impulsive disturbances , 2020, Appl. Math. Comput..

[23]  Yongyuan Yu,et al.  On detectability of Boolean control networks , 2020 .

[24]  Bowen Li,et al.  The Outputs Robustness of Boolean Control Networks via Pinning Control , 2020, IEEE Transactions on Control of Network Systems.

[25]  T. Ideker,et al.  A new approach to decoding life: systems biology. , 2001, Annual review of genomics and human genetics.

[26]  Gang Feng,et al.  Stability and $l_1$ Gain Analysis of Boolean Networks With Markovian Jump Parameters , 2017, IEEE Transactions on Automatic Control.

[27]  C. R. Rao,et al.  SOLUTIONS TO SOME FUNCTIONAL EQUATIONS AND THEIR APPLICATIONS TO CHARACTERIZATION OF PROBABILITY DISTRIBUTIONS , 2016 .

[28]  Shun-ichi Azuma,et al.  Structural Oscillatority Analysis of Boolean Networks , 2019, IEEE Transactions on Control of Network Systems.

[29]  Yang Liu,et al.  Output feedback stabilizer design of Boolean networks based on network structure , 2019, Frontiers of Information Technology & Electronic Engineering.

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

[31]  Yuhu Wu,et al.  A congestion game framework for service chain composition in NFV with function benefit , 2020, Inf. Sci..

[32]  James Lam,et al.  Stability and Stabilization of Boolean Networks With Stochastic Delays , 2019, IEEE Transactions on Automatic Control.

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

[34]  Jianquan Lu,et al.  Asymptotical Stability of Probabilistic Boolean Networks With State Delays , 2020, IEEE Transactions on Automatic Control.

[35]  Jinde Cao,et al.  Stabilization of logical control networks: an event-triggered control approach , 2019, Science China Information Sciences.

[36]  J. Hasty,et al.  Synchronizing genetic relaxation oscillators by intercell signaling , 2002, Proceedings of the National Academy of Sciences of the United States of America.