Generalized cluster synchronization of Boolean control networks with delays in both the states and the inputs

Abstract In this paper, we study the generalized cluster synchronization problem for the Boolean control networks (BCNs) with delays in both the states and the inputs. First, by using the method of semi-tensor product of matrices, the original network is transformed into an equivalent extended system. Next, based on the updated iterative equation of the system, two types of generalized cluster synchronization are investigated: 1) generalized internal cluster synchronization within the BCN, and 2) generalized cluster synchronization between the BCN and the target reference network. Some necessary and sufficient conditions are proposed guaranteeing the realization of the generalized cluster synchronization. What is more, the gain matrices of the state-feedback controllers are explicitly designed. Numerical simulations are also given to illustrate effectiveness of the theoretical results obtained.

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

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

[3]  Yang Liu,et al.  Synchronisation analysis of Boolean networks based on equivalence , 2015 .

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

[5]  James Lam,et al.  An Improved Criterion for Controllability of Boolean Control Networks , 2017, IEEE Transactions on Automatic Control.

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

[7]  Jianlong Qiu,et al.  Synchronization for the Realization-Dependent Probabilistic Boolean Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Yuqian Guo,et al.  Controllability of Boolean Control Networks With Multiple Time Delays , 2018, IEEE Transactions on Control of Network Systems.

[9]  Daniel W. C. Ho,et al.  Switching-signal-triggered pinning control for output tracking of switched Boolean networks , 2017 .

[10]  Yue Hu,et al.  Cluster synchronization for a class of complex dynamical network system with randomly occurring coupling delays via an improved event-triggered pinning control approach , 2020, J. Frankl. Inst..

[11]  Daizhan Cheng,et al.  Controllability and observability of Boolean control networks , 2009, Autom..

[12]  Biao Wang,et al.  Detectability of Boolean Control Networks , 2020, Discrete-Time and Discrete-Space Dynamical Systems.

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

[14]  Lihua Xie,et al.  Output tracking control of Boolean control networks via state feedback: Constant reference signal case , 2015, Autom..

[15]  Jun‐e Feng,et al.  Synchronization of Interconnected Multi‐valued Logical Networks , 2014 .

[16]  Lijun Zhang,et al.  Observability of Boolean Control Networks: A Unified Approach Based on Finite Automata , 2014, IEEE Transactions on Automatic Control.

[17]  Daizhan Cheng,et al.  On finite potential games , 2014, Autom..

[18]  Yang Liu,et al.  Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks , 2018, IEEE Transactions on Cybernetics.

[19]  Michael Margaliot,et al.  Observability of Boolean networks: A graph-theoretic approach , 2013, Autom..

[20]  Shuang Liang,et al.  Structural controllability of Boolean control networks with an unknown function structure , 2020, Science China Information Sciences.

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

[22]  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.

[23]  Hao Zhang,et al.  Cluster synchronization of Boolean network , 2018, Commun. Nonlinear Sci. Numer. Simul..

[24]  Michael Margaliot,et al.  Controllability of Boolean control networks via the Perron-Frobenius theory , 2012, Autom..

[25]  Lijun Zhang,et al.  Controllability and Observability of Boolean Control Networks With Time-Variant Delays in States , 2013, IEEE Transactions on Neural Networks and Learning Systems.

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

[27]  Fangfei Li,et al.  Controllability of higher order Boolean control networks , 2012, Appl. Math. Comput..

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

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

[30]  Chen Hao,et al.  A new approach for global controllability of higher order Boolean control network , 2012, Proceedings of the 31st Chinese Control Conference.

[31]  Yuqian Guo,et al.  Observability of Boolean Control Networks Using Parallel Extension and Set Reachability , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Zhen Wang,et al.  Observability of switched Boolean control networks using algebraic forms , 2021, Discrete & Continuous Dynamical Systems - S.

[33]  Jinde Cao,et al.  Robust Output Tracking of Delayed Boolean Networks Under Pinning Control , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[35]  Yang Liu,et al.  Robust Control Invariance of Probabilistic Boolean Control Networks via Event-Triggered Control , 2018, IEEE Access.

[36]  Zidong Wang,et al.  State Estimation for Stochastic Time-Varying Boolean Networks , 2020, IEEE Transactions on Automatic Control.

[37]  Yang Liu,et al.  Robust sampled-data control invariance for Boolean control networks , 2017, 2017 36th Chinese Control Conference (CCC).

[38]  DaeEun Kim.  A spiking neuron model for synchronous flashing of fireflies. , 2004, Bio Systems.

[39]  Jinling Liang,et al.  Output regulation of Boolean control networks with stochastic disturbances , 2017 .

[40]  Fangfei Li,et al.  Cluster consensus of Boolean multi-agent systems , 2013, 2013 9th Asian Control Conference (ASCC).

[41]  Jinde Cao,et al.  Delayed Feedback Control for Stabilization of Boolean Control Networks With State Delay , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[42]  Francesco Sorrentino,et al.  Cluster synchronization and isolated desynchronization in complex networks with symmetries , 2013, Nature Communications.

[43]  Yang Liu,et al.  Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks , 2018, Appl. Math. Comput..

[44]  Peng Liu,et al.  Asymptotic and Finite-Time Cluster Synchronization of Coupled Fractional-Order Neural Networks With Time Delay , 2020, IEEE Transactions on Neural Networks and Learning Systems.

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