Sampled-Data Control for the Synchronization of Boolean Control Networks

In this paper, we investigate the sampled-data state feedback control (SDSFC) for the synchronization of Boolean control networks (BCNs) under the configuration of drive-response coupling. Necessary and sufficient conditions for the complete synchronization of BCNs are obtained by the algebraic representations of logical dynamics. Based on the analysis of the sampling periods, we establish an algorithm to guarantee the synchronization of drive-response coupled BCNs by SDSFC. An example is given to illustrate the significance of the obtained results.

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

[2]  L. Hood,et al.  A Genomic Regulatory Network for Development , 2002, Science.

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

[4]  Dragan Nesic,et al.  A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models , 2004, IEEE Transactions on Automatic Control.

[5]  J.P. Hespanha,et al.  On the robust stability and stabilization of sampled-data systems: A hybrid system approach , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  E. Fridman,et al.  Robust Sampled-Data Control: An Input Delay Approach , 2007 .

[7]  Jianqiang Yi,et al.  BP neural network prediction-based variable-period sampling approach for networked control systems , 2007, Appl. Math. Comput..

[8]  Madalena Chaves,et al.  Methods for qualitative analysis of genetic networks , 2009, 2009 European Control Conference (ECC).

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

[10]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[11]  B. Stigler,et al.  Boolean Models Can Explain Bistability in the lac Operon , 2008, J. Comput. Biol..

[12]  Youyi Wang,et al.  Stabilization for Sampled-Data Neural-Network-Based Control Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[14]  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.

[15]  M. Margaliot Controllability and observability of Boolean control networks , 2012 .

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

[17]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

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

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

[20]  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.

[21]  Feng Qian,et al.  Synchronization in complex networks and its application - A survey of recent advances and challenges , 2014, Annu. Rev. Control..

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

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

[24]  Yongqing Yang,et al.  On sampled-data control for stabilization of genetic regulatory networks with leakage delays , 2015, Neurocomputing.

[25]  Young Hoon Joo,et al.  A Note on Sampled-Data Stabilization of LTI Systems With Aperiodic Sampling , 2015, IEEE Transactions on Automatic Control.

[26]  Fangfei Li,et al.  Pinning Control Design for the Synchronization of Two Coupled Boolean Networks , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[28]  Jinde Cao,et al.  Exponential H∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities , 2016, Science China Technological Sciences.

[29]  Yang Liu,et al.  Feedback Controller Design for the Synchronization of Boolean Control Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[30]  P. Shi,et al.  Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays. , 2016, IEEE/ACM transactions on computational biology and bioinformatics.

[31]  Jinde Cao,et al.  Sampled-Data $$H_{\infty }$$H∞ Synchronization of Chaotic Lur’e Systems with Time Delay , 2015, Circuits Syst. Signal Process..

[32]  T. Shen,et al.  A stochastic logical system approach to model and optimal control of cyclic variation of residual gas fraction in combustion engines , 2016 .

[33]  Lihua Xie,et al.  Output Regulation of Boolean Control Networks , 2017, IEEE Transactions on Automatic Control.

[34]  Jinde Cao,et al.  Function perturbations on singular Boolean networks , 2017, Autom..

[35]  Tielong Shen,et al.  Policy Iteration Approach to Control Residual Gas Fraction in IC Engines Under the Framework of Stochastic Logical Dynamics , 2017, IEEE Transactions on Control Systems Technology.

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

[37]  Yang Liu,et al.  Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems , 2017 .

[38]  Tingwen Huang,et al.  Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks , 2017, IEEE Transactions on Cybernetics.

[39]  Jinde Cao,et al.  Observability of Boolean control networks , 2018, Science China Information Sciences.

[40]  Yang Liu,et al.  Nonsingularity of Grain-like cascade FSRs via semi-tensor product , 2017, Science China Information Sciences.

[41]  Jinde Cao,et al.  Pinning Control for the Disturbance Decoupling Problem of Boolean Networks , 2017, IEEE Transactions on Automatic Control.

[42]  Yang Cao,et al.  Observer-Based Consensus Tracking of Nonlinear Agents in Hybrid Varying Directed Topology , 2017, IEEE Transactions on Cybernetics.

[43]  Fangfei Li,et al.  Stability of Boolean Networks With Delays Using Pinning Control , 2018, IEEE Transactions on Control of Network Systems.

[44]  Peng Shi,et al.  Global $H_\infty $ Pinning Synchronization of Complex Networks With Sampled-Data Communications , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[45]  Yang Liu,et al.  Strategy optimization for static games based on STP method , 2018, Appl. Math. Comput..

[46]  Yang Liu,et al.  The equivalence issue of two kinds of controllers in Boolean control networks , 2018, Appl. Math. Comput..

[47]  Peng Shi,et al.  Sampled-Data Synchronization of Complex Networks With Partial Couplings and T–S Fuzzy Nodes , 2018, IEEE Transactions on Fuzzy Systems.

[48]  Jinde Cao,et al.  Normalization and Solvability of Dynamic-Algebraic Boolean Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.