Controllability of Boolean control networks with impulsive effects and forbidden states

This paper investigates the controllability of Boolean control networks (BCNs) with impulsive effects while avoiding certain forbidden states. Using semi‐tensor product of matrices, the BCNs with impulsive effects can be converted into impulsive discrete‐time systems. Then, some necessary and sufficient conditions for the controllability are obtained. It is interesting to find that impulsive effects play an important role in the controllability of BCNs. Finally, an example is given to show the efficiency of the obtained results. Copyright © 2013 John Wiley & Sons, Ltd.

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

[2]  Albert,et al.  Dynamics of complex systems: scaling laws for the period of boolean networks , 2000, Physical review letters.

[3]  Sui Huang,et al.  Regulation of Cellular States in Mammalian Cells from a Genomewide View , 2002, Gene Regulations and Metabolism.

[4]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[5]  B. Samuelsson,et al.  Superpolynomial growth in the number of attractors in Kauffman networks. , 2003, Physical review letters.

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

[7]  M. Aldana.  Boolean dynamics of networks with scale-free topology , 2003 .

[8]  H. Othmer,et al.  The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. , 2003, Journal of theoretical biology.

[9]  John Maloney,et al.  Scalar equations for synchronous Boolean networks with biological applications , 2004, IEEE Transactions on Neural Networks.

[10]  Aniruddha Datta,et al.  External control in Markovian genetic regulatory networks: the imperfect information case , 2004, Bioinform..

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

[12]  Aniruddha Datta,et al.  Optimal infinite horizon control for probabilistic Boolean networks , 2006, 2006 American Control Conference.

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

[14]  Jinde Cao,et al.  Robust impulsive synchronization of coupled delayed neural networks with uncertainties , 2007 .

[15]  Daizhan Cheng,et al.  Input-State Approach to Boolean Networks , 2009, IEEE Transactions on Neural Networks.

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

[17]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[18]  Daizhan Cheng,et al.  Realization of Boolean control networks , 2010, Autom..

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

[20]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

[21]  Jitao Sun,et al.  Observability analysis of Boolean control networks with impulsive effects , 2011 .

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

[23]  Yang Liu,et al.  Controllability for a Class of Linear Time-Varying Impulsive Systems With Time Delay in Control Input , 2011, IEEE Transactions on Automatic Control.

[24]  D. Cheng,et al.  Stability and stabilization of Boolean networks , 2011 .

[25]  M. Margaliot,et al.  A Pontryagin Maximum Principle for Multi – Input Boolean Control Networks ⋆ , 2011 .

[26]  Yu Zhang,et al.  Robust exponential stability of discrete‐time uncertain impulsive neural networks with time‐varying delay , 2012 .

[27]  Fangfei Li,et al.  Stability and stabilization of Boolean networks with impulsive effects , 2012, Syst. Control. Lett..

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

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