On Robust Synchronization of Drive-Response Boolean Control Networks with Disturbances

This paper investigates the robust synchronization of drive-response Boolean control networks (BCNs) with disturbances via semi-tensor product of matrices. Firstly, the definition of robust synchronization is presented for the drive-response BCNs with disturbances. Then, based on the algebraic state space representation of drive-response BCNs, the robustly reachable states/sets are presented to investigate robust synchronization of disturbed BCNs. According to the set of robustly reachable states, some necessary and sufficient criteria are obtained for robust synchronization of drive-response BCNs with disturbances under a given state feedback controller. Finally, an illustrative example is presented to demonstrate the obtained theoretical results.

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

[2]  S. Huang,et al.  Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. , 2000, Experimental cell research.

[3]  Yuxia Li,et al.  Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay , 2017, Int. J. Bifurc. Chaos.

[4]  Yuanyuan Li,et al.  Impulsive Synchronization of Stochastic Neural Networks via Controlling Partial States , 2017, Neural Processing Letters.

[5]  Jinde Cao,et al.  Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism , 2016, Neural Networks.

[6]  Lihua Xie,et al.  On robust control invariance of Boolean control networks , 2016, at - Automatisierungstechnik.

[7]  Tae H. Lee,et al.  Improved criteria for sampled-data synchronization of chaotic Lur’e systems using two new approaches , 2017 .

[8]  Jinde Cao,et al.  On Controllability of Delayed Boolean Control Networks , 2016, SIAM J. Control. Optim..

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

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

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

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

[13]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.

[14]  Junwei Lu,et al.  Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays , 2018, Appl. Math. Comput..

[15]  Jinde Cao,et al.  On Pinning Controllability of Boolean Control Networks , 2016, IEEE Transactions on Automatic Control.

[16]  Tianguang Chu,et al.  Controller design for disturbance decoupling of Boolean control networks , 2013, Autom..

[17]  Bor-Sen Chen,et al.  Robust $H_{\infty}$ Synchronization Design of Nonlinear Coupled Network via Fuzzy Interpolation Method , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Zhen Wang,et al.  Consensus for Nonlinear Stochastic Multi-agent Systems with Time Delay , 2018, Appl. Math. Comput..

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

[20]  Jinde Cao,et al.  New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks , 2017 .

[21]  Daniel W. C. Ho,et al.  Global robust stability and stabilization of Boolean network with disturbances , 2017, Autom..

[22]  Haitao Li,et al.  Controllability, Reachability, and Stabilizability of Finite Automata: A Controllability Matrix Method , 2018 .

[23]  Fuad E. Alsaadi,et al.  Stochastic stability and stabilization of n-person random evolutionary Boolean games , 2017, Appl. Math. Comput..

[24]  Daizhan Cheng,et al.  Disturbance Decoupling of Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

[25]  Jinde Cao,et al.  Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay , 2012, Int. J. Bifurc. Chaos.

[26]  B. Drossel,et al.  Number and length of attractors in a critical Kauffman model with connectivity one. , 2004, Physical review letters.

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

[28]  Hui Gao,et al.  Nonfragile Finite-Time Extended Dissipative Control for a Class of Uncertain Switched Neutral Systems , 2017, Complex..

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

[30]  Juan Yao,et al.  Input‐Output Decoupling of Boolean Control Networks , 2018 .

[31]  Shengyuan Xu,et al.  A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  D. Ho,et al.  Stabilization of complex dynamical networks with noise disturbance under performance constraint , 2011 .

[33]  Yao-Chen Hung,et al.  Stochastic coupling of two random Boolean networks , 2005 .

[34]  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).

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

[36]  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.

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

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

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

[40]  Zhen Wang,et al.  Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems , 2012, Appl. Math. Comput..

[41]  Jinde Cao,et al.  Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[42]  F. Alsaadi,et al.  Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games , 2017 .

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

[44]  Daizhan Cheng,et al.  Input-state incidence matrix of Boolean control networks and its applications , 2010, Syst. Control. Lett..

[45]  Jing Wang,et al.  synchronization for singularly perturbed complex networks with semi-Markov jump topology , 2018, Appl. Math. Comput..

[46]  Kazuyuki Aihara,et al.  Noise-induced cooperative behavior in a multicell system , 2005, Bioinform..